qlazy package¶

Subpackages¶

Submodules¶

qlazy.Backend module¶

Backend device of quantum computing

class qlazy.Backend.Backend(product=None, device=None)[source]¶

Bases: object

Backend device of quantum computing

product¶

product name of the backend (‘qlazy’ or ‘qulacs’ or ‘ibmq’)

Type: str

device¶

device name of the product

Type: str

config_braket¶

config for amazon braket backend {‘backet_name’: str, ‘poll_timeout_seconds’: int}

Type: dict

Notes

If you use amazon braket backend (braket_local, braket_aws, braket_ionq, braket_rigetti, braket_oqc), you must have config.ini file in your ‘~/.qlazy/’ directory, and discribe like following example …

Example

>>> bk = Backend(product='qlazy', device='stabilizer_simulator')
>>> bk = Backend(product='qulacs', device='gpu_simulator')
>>> bk = Backend(product='ibmq', device='least_busy')
>>> bk = Backend(product='braket_rigetti', device='aspen_11') # read ~/.qlazy/config.ini
...
$ cat ~/.qlazy/config.ini
[backend_braket]
backet_name = amazon-braket-xxxx # set your s3 backet name
...
$ cat ~/.qlazy/config.ini
[backend_braket]
backet_name = amazon-braket-xxxx # set your s3 backet name
poll_timeout_seconds = 86400  # set 1-day (default: 5-days)

classmethod devices(product)[source]¶: get devices list for the product

expect(qcirc=None, observable=None, shots=None, precise=False, init=None)[source]¶

run the quantum circuit.

Parameters

qcirc (instance of QCirc) – quantum circuit.
observable (instance of Observable) – obserbable considerd.
shots (int, default - None) – number of measurements for estimating the expectation value.
precise (bool, default - False) – precise calculation (only qlazy and qulacs) or estimation by measurements.
init (instance of QState, MPState) – initial quantum state

Returns

expval – expectation value

Return type

complex

Examples

>>> # simple example
>>> from qlazy import QCirc, Backend
>>> from qlazy.Observable import X,Y,Z
>>> bk = Backend(product='qlazy', device='qstate_simulator')
>>> ob = Z(0)*X(1)
>>> qc = QCirc().h(0).cx(0,1)
>>> exp = bk.expect(qcirc=qc, shots=10000, observable=ob)
>>> print(exp.real)
>>> 0.0074

classmethod ibmq_devices()[source]¶: get ibmq’s devices list

classmethod products()[source]¶: get products list

classmethod qlazy_devices()[source]¶: get qlazy’s devices list

classmethod qulacs_devices()[source]¶: get qulacs’s devices list

run(qcirc=None, shots=1, cid=None, out_state=False, init=None, **kwargs)[source]¶

run the quantum circuit.

Parameters

qcirc (instance of QCirc) – quantum circuit.
shots (int, default 1) – number of measurements.
cid (list, default None) – classical register id list to count frequency.
out_state (bool, default False) – output classical and quantum information after execting circuit. (only for qlazy’s qstate and stabilizer simulator)
init (instance of QState, Stabilizer, MPState) – initial quantum state

Returns

result – measurement result.

Return type

incetance of Result

Examples

>>> # simple example
>>> from qlazy import QCirc, Backend
>>> bk = Backend(product='qlazy', device='qstate_simulator')
>>> qc = QCirc().h(0).cx(0,1).measure(qid=[0,1], cid=[0,1])
>>> result = bk.run(qcirc=qc, shots=100)
>>> print(result.frequency)
Counter({'00': 51, '11': 49})
>>> ...
>>> # control quantum gate by measured results
>>> from qlazy import QCirc, Backend
>>> bk = Backend(product='qlazy', device='qstate_simulator')
>>> qc = QCirc.h(0)
>>> qc.cx(0,1).measure(qid=[0],cid=[0])
>>> qc.x(0, ctrl=0).x(1, ctrl=0).measure(qid=[0,1], cid=[0,1])
>>> result = bk.run(qcirc=qc, shots=100)
>>> print(result.frequency)
Counter({'00': 100})

qlazy.CMem module¶

Classical Memory

class qlazy.CMem.CMem(cmem_num, **kwargs)[source]¶

Bases: Structure

Classical Memory

cmem_num¶

number of the classical register (classical memory size).

Type: int

bit_array¶

bit array of classical memory.

Type: list (int)

bit_array¶: Structure/Union member

property bits¶: bit list of classical memory.

clone()[source]¶

get the copy of the classical memory.

Parameters: None –
Returns: cmem – copy of the original classical memory.
Return type: instance of CMem

cmem_num¶: Structure/Union member

get_bits()[source]¶

get bit list of the classical memory.

Parameters: None –
Returns: bits – bits array of the classical memory
Return type: numpy.ndarray (int)

set_bits(bits)[source]¶

set bit list to the classical memory.

Parameters: bits (list) – bits array of the classical memory
Return type: None

qlazy.DensOp module¶

Density Operator

class qlazy.DensOp.DensOp(qubit_num=0, qstate=None, prob=None, matrix=None, **kwargs)[source]¶

Bases: Structure, QObject

Density Operator

row¶

dimension of density operator (= 2**qubit_num).

Type: int

col¶

dimension of density operator (= 2**qubit_num).

Type: int

element¶

matrix elements of density operator.

Type: list of list of complex

add(densop=None)[source]¶

add the density operator.

Parameters: densop (instance of DensOp) – density operator to add.
Returns: self
Return type: instance of DensOp

Notes

This method change the original density operator.

classmethod add_method(method)[source]¶

add method (custum gate).

Parameters: method (func) – method (custum gate) to add.

Examples

>>> def bell(self, q0, q1):
>>>     self.h(q0).cx(q0,q1)
>>> ...
>>> DensOp.add_method(bell)
>>> qs = DensOp(qubit_num=2)
>>> qs.bell(0,1)
>>> ...

classmethod add_methods(*methods)[source]¶

add methods (custum gates).

Parameters: methods (func, func, ...) – arguments of methods (custum gates) to add.

Examples

>>> def bell(self, q0, q1):
>>>     self.h(q0).cx(q0,q1)
>>>     return self
>>> ...
>>> def flip(self, q0, q1):
>>>     self.x(q0).x(q1)
>>>     return self
>>> ...
>>> DensOp.add_methods(bell, flip, ...)
>>> de = DensOp(qubit=2)
>>> de.bell(0,1)
>>> de.flip(0,1)
>>> ...

amp_dump(q, prob=0.0)[source]¶

execute the quantum channel of amplitude dumping.

Parameters

q (int) – qubit id to execute.
prob (float) – probability of the quantum channel.

Returns

self

Return type

instance of DensOp

apply(matrix=None, qid=None, dire='both')[source]¶

apply the matrix to density operator. (= [matrix] * [self] * [dagger of matrix])

Parameters: matrix (list of list) – matrix to apply.
Return type: None

Notes

If ‘qid’ isn’t set, dimension of the matrix must be equal to dimension of the density operator. If ‘qid’ is set, dimension of the matrix must be equal to the 2 power of ‘qid’ length.

bit_flip(q, prob=0.0)[source]¶

execute the quantum channel of bit flip.

Parameters

q (int) – qubit id to execute.
prob (float) – probabillity of the quantum channel.

Returns

self

Return type

instance of DensOp

bit_phase_flip(q, prob=0.0)[source]¶

execute the quantum channel of bit and phase flip.

Parameters

q (int) – qubit id to execute.
prob (float) – probability of the quantum channel.

Returns

self

Return type

instance of DensOp

buf_id¶: Structure/Union member

buffer_0¶: Structure/Union member

buffer_1¶: Structure/Union member

clone()[source]¶

get the copy of density operator.

Parameters: None –
Returns: densop – copy of the original density operator.
Return type: instance of DensOp

col¶: Structure/Union member

composite(num=0)[source]¶

get the composite density operator of same density operators.

Parameters: num (int) – number of density operators..
Returns: de – composite density operator.
Return type: instance of DensOp

cond_entropy(qid_0=None, qid_1=None)[source]¶

get the conditional entropy.

Parameters

qid_0 (list of int) – qubit id’s list (sub-system) to calculate the entropy.
qid_1 (list of int) – qubit id’s list (sub-system) to calculate the entropy.

Returns

ent – conditianal entropy (S(qid_0|qid_1)).

Return type

float

classmethod create_register(num)[source]¶

create registers (qubit id’s list) and initialize zero.

Parameters: num (int) – qubit number you want to use.
Returns: qid – qubit id’s list.
Return type: list of int

Examples

>>> qid = DensOp.create_register(3)
>>> print(qid)
[0,0,0]

classmethod del_all(*densops)[source]¶

free memory of the all density operators.

Parameters: densops (instance of DensOp,instance of DensOp,...) – set of DensOp instances
Return type: None

depolarize(q, prob=0.0)[source]¶

execute the quantum channel of depolarize.

Parameters

q (int) – qubit id to execute.
prob (float) – probability of the quantum channel.

Returns

self

Return type

instance of DensOp

distance(densop=None, qid=None)[source]¶

get the trace distance with the density operator.

Parameters

densop (instance of DensOp) – density operator to get the trace distance.
qid (list of int, default - all of the qubit id's list) – qubit id’s list.

Returns

dis – trace distance.

Return type

float

property element¶: matrix elements of density operator.

elm¶: Structure/Union member

entropy(qid=None)[source]¶

get the von neumann entropy (or entanglement entropy).

Parameters: qid (list of int, default - list all of the qubit id) – qubit id’s list (sub-system) to calculate the entropy.
Returns: ent – von neumann entropy.
Return type: float

expect(matrix=None)[source]¶

get the expectation value of matrix under this density operator.

Parameters: matrix (list of list of complex) – matrix expression of hermitian operator.
Returns: value – expectation value.
Return type: float

Notes

‘matrix’ must be hermitian, and its dimension is equal to the dimension of density operator.

fidelity(densop=None, qid=None)[source]¶

get the fidelity with density operator.

Parameters

densop (instance of DensOp) – density operators to get fidelity.
qid (list of int, default - all of the qubit id's list) – qubit id’s list.

Returns

fid – fidelity of two density operators.

Return type

float

gbank¶: Structure/Union member

get_elm(qid=None)[source]¶

get the matrix elements of density operator.

Parameters: qid (list of int, default - list of all of the qubit id) – qubit id’s list.
Returns: elm – elements of the density matrix.
Return type: list of complex

Notes

If ‘qid’ is set, matrix elements of specified density operator are got after partial trace for remaining qubits. If no qubits are specified, you get all matrix elements of the density operator.

classmethod init_register(*args)[source]¶

initialize registers (qubit id’s list).

Parameters: args (list, list,...) – arguments of qubit registers.
Returns: idx – total qubit number.
Return type: int

Examples

>>> qid_0 = DensOp.create_register(3)
>>> qid_1 = DensOp.create_register(2)
>>> print(qid_0, qid_1)
[0,0,0] [0,0]
>>> qnum = DensOp.init_register(qid_0, qid_1)
>>> print(qnum, qid_0, qid_1)
5 [0,1,2] [3,4]

instrument(kraus=None, qid=None, measured_value=None)[source]¶

instrument to the density operator

Parameters

kraus (list of list of comprex) – Kraus operators.
qid (list) – qubit id’s list to measure.
measured_value (int) – index of measurement (in the case of selective measurement).

Returns

self

Return type

instance of DensOp

Notes

If ‘measured_value’ is set, selective measurement of the index corresponding to ‘measured_value’ is done (but not normalize). If ‘measured_value’ is not set, non-selective measurement is done (only operator sum for the Kraus operators are executed). This method does change the original density operator.

join(de_list)[source]¶

get tensor product state (density operator) of the density operators’ list.

Parameters: de_list (list (DensOp)) – list of density operators.
Returns: de_out – tensor product state (density operator).
Return type: instance of DensOp

static mat_norm(mat)[source]¶: norm of the matrix

static mat_spectrum(mat)[source]¶: spectrum of the hermitian matrix

static mat_sqrt(mat)[source]¶: square root of the matrix

classmethod mix(densop=None, prob=None)[source]¶

linear sum of the density operators.

Parameters

densop (list of instances of DensOp) – densitiy operators.
prob (list of float) – probabilities (coefficients of the linear sum).

mul(factor=1.0)[source]¶

multiply the density operator by factor.

Parameters: factor (float, default 1.0) – number to multiply.
Returns: self
Return type: instance of DensOp

Notes

This method change the original density operator.

mutual_info(qid_0=None, qid_1=None)[source]¶

get the mutual information.

Parameters

qid_0 (list of int) – qubit id’s list (sub-system) to calculate the mutual information.
qid_1 (list of int) – qubit id’s list (sub-system) to calculate the mutual information.

Returns

ent – mutual information (S(qid_0:qid_1)).

Return type

float

operate_gate(kind=None, qid=None, phase=0.0, **kwargs)[source]¶

operate gate

Parameters

kind (int) – kind of the gate
qid (list) – quantum id list
phase (float) – phase for rotation gate

Returns

self – quantum state

Return type

instance of DensOp

operate_qcirc(qcirc, qctrl=None)[source]¶

operate quantum circuit

Parameters

qcirc (instance of QCirc) – quantum circuit
qctrl (int) – control qubit id

Returns

self – quantum state after executing the quantum circuit

Return type

instance of DensOp

Notes

The quantum circut must be unintary.

partial(qid=None)[source]¶

get the density operator for partial system.

Parameters: qid (list of int) – qubit id’s list to show.
Returns: densop – density operator for partial system (= partial trace for remaining system).
Return type: instance of DensOp

patrace(qid=None)[source]¶

get the partial trace of density operator.

Parameters: qid (list of int) – qubit id’s list to show.
Returns: densop – density operator after partial trace.
Return type: instance of DensOp

phase_dump(q, prob=0.0)[source]¶

execute the quantum channel of phase dumping.

Parameters

q (int) – qubit id to execute.
prob (float) – probability of the quantum channel.

Returns

self

Return type

instance of DensOp

phase_flip(q, prob=0.0)[source]¶

execute the quantum channel of phase flip.

Parameters

q (int) – qubit id to execute.
prob (float) – probability of the quantum channel.

Returns

self

Return type

instance of DensOp

probability(kraus=None, povm=None, qid=None)[source]¶

get the probabilities for measuring operators. (Kraus or POVM operators).

Parameters

kraus (list of list of comprex) – Kraus operators.
povm (list of list of comprex) – POVM operators.
qid (list) – qubit id’s list to measure.

Returns

prob – probabilities for measuring operators.

Return type

list of float

Notes

Either ‘kraus’ or ‘povm’ must be set. If ‘qid’ is not set, all of the qubits are measured, the dimention of Kraus or POVM operator must be equal to the dimension of density operator. If ‘qid’ is set, the part of qubits are measured, the dimension of Kraus or POVM operator must be equal to the 2 power of ‘qid’ length. This method does not change the original density operator.

relative_entropy(densop=None)[source]¶

get the relative entropy.

Parameters: densop (instance of DensOp) – density operator to get the relative entropy.
Returns: ent – relative entropy.
Return type: float

row¶: Structure/Union member

show(qid=None, nonzero=False)[source]¶

show the elements of density operator.

Parameters

qid (list of int, default - list of all of the qubit id) – qubit id’s list to show.
nonzero (bool, default False) – if True, only non-zero elements are printed.

Return type

None

Notes

If ‘qid’ is set, it shows the matrix elements of density operator for partial quantum system specified by ‘qid’. If ‘qid’ isn’t set, it shows the matrix elements of whole quantum system.

Examples

>>> de = DensOp(qubit_num=1)
>>> ...
>>> de.show()
elm[0][0] = +0.5000+0.0000*i : 0.2500 |++++
elm[0][1] = +0.0000+0.0000*i : 0.0000 |
elm[1][0] = +0.0000+0.0000*i : 0.0000 |
elm[1][1] = +0.5000+0.0000*i : 0.2500 |++++
...
>>> de.show(nonzero=True)
elm[0][0] = +0.5000+0.0000*i : 0.2500 |++++
elm[1][1] = +0.5000+0.0000*i : 0.2500 |++++

spectrum()[source]¶

get the spectrum.

Parameters

None –

Returns

qstate (list of QState) – list of the quantum state basis.
prob (list of float) – list of coefficients for each quantum states basis.

sqtrace()[source]¶

get the square trace of density operator.

Parameters: None –
Returns: sqtrace – square trace of the density operator.
Return type: float

tenspro(densop)[source]¶

get the tensor product with density operator.

Parameters: densop (instance of DensOp) – density operator to get the tensor product..
Returns: densop_out – tensor produt of ‘self’ and ‘densop’.
Return type: instance of DensOp

trace()[source]¶

get the trace of density operator.

Parameters: None –
Returns: trace – trace of the density operator.
Return type: float

von_neumann_entropy()[source]¶

get the von neumann entropy (or entanglement entropy).

Parameters: None –
Returns: ent – von neumann entropy.
Return type: float

qlazy.MData module¶

Mesured data

class qlazy.MData.MData(qubit_num=None, shots=1, angle=0.0, phase=0.0, qid=None, **kwargs)[source]¶

Bases: Structure

Measured data

qubit_num¶

number of qubits

Type: int

shot_num¶

number of measureings

Type: int

angle¶

angle

Type: float

phase¶

phase

Type: float

qubit_id¶

list of qubit ids

Type: list of int

freq¶

list of frequencies

Type: list of float

last_val¶

last measurement value

Type: int

angle¶: Structure/Union member

freq¶: Structure/Union member

property frequency¶: frequencies of measured value (Counter)

property frq¶: frequencies of measured value (list)

property last¶: last measured value (binary string)

last_val¶: Structure/Union member

property lst¶: last measured value (integer)

phase¶: Structure/Union member

qubit_id¶: Structure/Union member

qubit_num¶: Structure/Union member

shot_num¶: Structure/Union member

show()[source]¶: show the measured data

property state_num¶: number of states

qlazy.MPState module¶

Matrix Product State

class qlazy.MPState.MDataMPState(frequency=None, last=None, qid=None, qubit_num=0)[source]¶

Bases: object

Measured Data for MPState

frequency¶

frequencies of measured value.

Type: Counter

last¶

last measured value.

Type: str

qid¶

qubit id’s list.

Type: list of int

qubit_num¶

qubit number of the quantum state (= log(state_num)).

Type: int

class qlazy.MPState.MPState(qubit_num=0, bits_str=None, tensors=None, max_truncation_err=1e-06, **kwargs)[source]¶

Bases: FiniteMPS, QObject

Matrix Product State

qubit_num¶

number of qubits (number of nodes)

Type: int

bond_dimensions¶

list of bond dimensions

Type: list (int)

max_truncation_err¶

maximum of truncation error

Type: float

tensors¶

list of 3-rank tensors for the matrix product

Type: list (np.ndarray)

property amp¶: elements of quantum state vector.

clone()[source]¶

get the copy of the matrix product state.

Parameters: None –
Returns: mps – copy of the original matrix product state.
Return type: instance of MPState

classmethod del_all(*mpstates)[source]¶

free memory of the all matrix product states.

Parameters: mpstates (instance of MPState,instance of MPState,...) – set of MPState instances
Return type: None

expect(observable=None)[source]¶

get the expectation value for observable under the matrix product state.

Parameters: observable (instance of Observable) – obserbable of the system.
Returns: expect – expect value.
Return type: complex

See also

Obserbable

fidelity(mps, qid=None)[source]¶

get fidelity with the matrix product state.

Parameters

mps (instance of MPState) – one of the two matrix product states.
qid (list of int) – qubit id’s list.

Returns

fid – fidelity of the two matrix product states. absolute value of the inner product of two matrix product states.

Return type

float

Notes

If ‘qid’ is set, you can get the fidelity for partial quantum state. If the specified quantum system are entangled with the remaining system, output value is probabilistic, while original quantum states do not change.

get_amp(qid=None)[source]¶

get the elements of quantum state vector.

Parameters: qid (list of int, default - list of all of the qubit id) – qubit id’s list.
Returns: ret – elements of the quantum state vector.
Return type: numpy.ndarray (complex)

Notes

If ‘qid’ is set, specified qubit state are got after remaining qubits are measured. So if the specified qubits are entangled with the remaining qubits, output quantum state is probabilistic. If no qubits are specified, you get all elements of the quantum state.

inpro(mps, qid=None)[source]¶

get the inner product with matrix product state.

Parameters

mps (instance of MPState) – one of the two matrix product state.
qid (list of int, default - list of all of the qubit id) – qubit id’s list.

Returns

inp – inner produt (<self|mps>).

Return type

complex

Notes

If ‘qid’ is set, you can get the inner product for partial quantum state. If the specified quantum system are entangled with the remaining system, output value is probabilistic, while original quantum states do not change.

m(qid=None, shots=1)[source]¶

measurement in Z-direction

Parameters

qid (list of int) – qubit id list to measure.
shots (int, default 1) – number of measurements.

Returns

md – measurement data.

Return type

instance of MDataMPState

See also

MDataMPState

property max_truncation_err¶

measure(qid=None)[source]¶

one shot measurement in Z-direction.

Parameters: qid (list of int) – qubit id list to measure.
Returns: mval – measurement value.
Return type: str

Examples

>>> mps = MPState(qubit_num=2).h(0).cx(0,1)
>>> mps.show()
>>> print(mps.measure(qid=[0,1]))
>>> mps.show()
c[00] = +0.7071+0.0000*i : 0.5000 |++++++
c[01] = +0.0000+0.0000*i : 0.0000 |
c[10] = +0.0000+0.0000*i : 0.0000 |
c[11] = +0.7071+0.0000*i : 0.5000 |++++++
00
c[00] = +1.0000+0.0000*i : 1.0000 |+++++++++++
c[01] = +0.0000+0.0000*i : 0.0000 |
c[10] = +0.0000+0.0000*i : 0.0000 |
c[11] = +0.0000+0.0000*i : 0.0000 |

operate_1qubit_gate(gate_str, q, para=0.0)[source]¶

operate 1-qubit gate.

Parameters

gate_str (str) – gate stiring (ex. ‘x’,’y’,’z’,’h’,’s’, ..)
q0 (int) – qubit id.
para (float) – angle for rotation gate (unit of angle is PI radian).

Returns

self

Return type

instance of MPState

operate_2qubit_gate(gate_str, q0, q1, para=0.0)[source]¶

operate 2-qubit gate.

Parameters

gate_str (str) – gate stiring (ex. ‘cx’,’cy’,’cz’,’ch’,’crz’, ..)
q0 (int) – qubit id.
q1 (int) – qubit id.
para (float) – angle for rotation gate (unit of angle is PI radian).

Returns

self

Return type

instance of MPState

operate_gate(kind=None, qid=None, phase=0.0, **kwargs)[source]¶

operate gate

Parameters

kind (int) – kind of the gate
qid (list) – quantum id list
phase (float) – phase for rotation gate

Returns

self – quantum state

Return type

instance of MPState

operate_qcirc(qcirc, qctrl=None)[source]¶

operate quantum circuit

Parameters

qcirc (instance of QCirc) – quantum circuit
qctrl (int) – control qubit id

Returns

self – quantum state after executing the quantum circuit

Return type

instance of MPState

Notes

The quantum circut must be unintary.

property qubit_num¶

reset_qubits(qid=None)[source]¶

reset to |00..0> state.

Parameters: qid (list, default - qubit id's list for all of the qubits) – qubit id’s list to reset.
Returns: self – matrix product state.
Return type: instance of MPState

Notes

If ‘qid’ is set, specified qubits are reset after measurement. So if the specified qubits are entangled with the remaining qubits, output quantum state is probabilistic. If no qubits are set, all qubits are zero reset.

show(qid=None, nonzero=False, preal=0)[source]¶

show the quantum state (elements of the state vector and probabilities).

Parameters

qid (list of int, default - list of all of the qubit id) – qubit id’s list to show.
nonzero (bool, default False) – if True, only non-zero amplitudes are printed.
preal (int, default 0) – state id to make positive real amplitude. (if -1 is set, do not go out the global phase factor)

Return type

None

Notes

If ‘qid’ is set, it shows the elements of quantum state vector for partial quantum system specified by ‘qid’. If the specified quantum system are entangled with the remaining system, output is probabilistic. If no qubits are specified, it shows the whole quantum state. This method does not change the original quantum state.

Examples

>>> mps = MPState(qubit_num=2).h(0).cx(0,1)
>>> mps.show()
c[00] = +0.7071+0.0000*i : 0.5000 |++++++
c[01] = +0.0000+0.0000*i : 0.0000 |
c[10] = +0.0000+0.0000*i : 0.0000 |
c[11] = +0.7071+0.0000*i : 0.5000 |++++++
...
>>> mps.show(qid=[0])
c[0] = +1.0000+0.0000*i : 1.0000 |+++++++++++
c[1] = +0.0000+0.0000*i : 0.0000 |
...
>>> mps.show(nonzero=True)
c[00] = +0.7071+0.0000*i : 0.5000 |++++++
c[11] = +0.7071+0.0000*i : 0.5000 |++++++

qlazy.Observable module¶

Obserbavle for quantum many-body spin system.

class qlazy.Observable.Observable(string=None)[source]¶

Bases: object

Observable for quantum many-body spin system.

base¶

observable

Type: instance of ObservableBase

string¶

string of observable description ex) “-2.0+Z_0*Z_1+X_0+X_1” for 2-qubit system

Type: str

weighted_pp_list¶

weighted pauli product list

Type: list of dict ({‘weight’:weight, ‘pp’:pauli_product})

qubit_num¶

total qubit number

Type: int

add_wpp(weight=1.0, pp=None)[source]¶

add the weighted pauli product to the list (self.weighted_pp_list).

Parameters

weight (float) – weight value correspond to the pauli product
pp (instance of PauliProduct) – pauli product

Returns

self – observable after adding weighted pauli product

Return type

instance of Ovservable

property base¶

clone()[source]¶

clone observable.

Parameters: None –
Returns: ob – observable
Return type: instance of Observable

get_idx_weight(pp)[source]¶

get index and weight value correspond to the pauli product.

Parameters

pp (instance of PauliProduct) – pauli product

Returns

idx (int) – index number of the list (self.weighted_pp_list) correspond to the pauli product
weight (float) – weight value correspond to the pauli product

get_observable_base()[source]¶

get ObservableBase instance.

Parameters: None –
Returns: ob_base – observable
Return type: instance of ObservableBase

get_qubit_num()[source]¶

get the total qubit number considerd

Parameters: None –
Returns: qubit_num – total qubit number considerd by the observable.
Return type: inst

get_string()[source]¶

get string of observable.

Parameters: None –
Returns: s – string of observable
Return type: str

get_weighted_pp_list(string)[source]¶

get weighted pauli product list.

Parameters: string (str) – string of observable
Returns: weighted_pp_list – weighted pauli product list
Return type: list of dict (weight:pauli_product)

is_hermitian()[source]¶

hermitian or not

Parameters: None –
Returns: ans – is the observable hermitian or not
Return type: bool

property qubit_num¶

recalc_weight()[source]¶

recalculate the weights of weighted_pp_list: (weight <= weight * pp.factor, pp.factor <= 1.0)

Parameters: None –
Returns: ans – is the observable hermitian or not
Return type: bool

property string¶

qlazy.Observable.X(q)[source]¶

Parameters: q (int) – qubit id
Returns: ob – obserbable X(q)
Return type: instance of Observable

qlazy.Observable.Y(q)[source]¶

Parameters: q (int) – qubit id
Returns: ob – obserbable Y(q)
Return type: instance of Observable

qlazy.Observable.Z(q)[source]¶

Parameters: q (int) – qubit id
Returns: ob – obserbable X(q)
Return type: instance of Observable

qlazy.ObservableBase module¶

Obserbavle for quantum many-body spin system.

class qlazy.ObservableBase.ObservableBase(string=None, **kwargs)[source]¶

Bases: Structure

Observable for quantum many-body spin system.

array_num¶: Structure/Union member

spin_num¶: Structure/Union member

spro_array¶: Structure/Union member

qlazy.PauliProduct module¶

Pauli Product

class qlazy.PauliProduct.PauliProduct(pauli_str, qid=None, factor=1 + 0j)[source]¶

Bases: object

Pauli Product

qid¶

list of qubit id.

Type: list of int

pauli_list¶

list of pauli operators.

Type: list of str

factor¶

factor of pauli product.

Type: complex

get_binary_rep(qubit_num=None)[source]¶

get binary representation of pauli product.

Parameters: qubit_num (int, default - max(self.qid)+1) – qubit number of binary representation.
Returns: binary_rep – output binary representation of the pauli product.
Return type: list of int

Examples

>>> pp = PauliProduct(pauli_str="XYZ", qid=[0,1,2])
>>> print(pp.get_binary_rep())
[1,1,0,0,1,1]

get_qubit_num()[source]¶

get the total qubit number considerd

Parameters: None –
Returns: qubit_num – total qubit number considerd by the pauli product.
Return type: inst

is_commute(pp)[source]¶

is pauli product commute to other pauli product or not.

Parameters: pp (instance of PauliProduct) – pauli product
Returns: ans – commute (True) or anti-commute (False)
Return type: bool

tenspro(pp)[source]¶

get tensor product with other pauli product.

Parameters: pp (instance of PauliProduct) – pauli product
Returns: pp_out – output pauli product
Return type: instance of PauliProduct

qlazy.QCirc module¶

Quantum Circuit

class qlazy.QCirc.QCirc(**kwargs)[source]¶

Bases: Structure, QObject

Quantum Circuit

qubit_num¶

qubit number of the quantum state (= log(state_num)).

Type: int

cmem_num¶

number of the classical register.

Type: int

gate_num¶

number of gates in the quantum circuit.

Type: int

first¶

first gate of the quantum circuit.

Type: object

last¶

last gate of the quantum circuit.

Type: object

tag_table¶

tag table..

Type: object

add_control(qctrl=None)[source]¶

add control qubit to quantum circuit

Parameters: qctrl (int) – control qubit id
Returns: qc_out – quantum circuit after adding control qubit
Return type: instance of QCirc

add_gates(gates=None)[source]¶

add list of gates to the circuit.

Parameters: gates (list of dict) – gates of the quantum circuit gates = [{‘kind’:kind, ‘qid’:qid, ‘phase’:phase, ‘cid’:cid, ‘ctrl’:ctrl}, …] - kind: gate name - qid: qubit id - phase: phase parameter (non-zero only for rotation gates) - cid: classical register id (set only for measurement gate) - ctrl: classical register id for controlling gate operation
Returns: self – circuit after adding gates
Return type: instance of QCirc

Notes

This method changes original quantum circuit.

all_gates_measurement()[source]¶

gates of the qcirc are all measurement

Parameters: None –
Returns: ans – True if all gates are measurement, False if otherwise
Return type: bool

append_gate(kind=None, qid=None, para=None, c=None, ctrl=None, tag=None)[source]¶

append gate to the end of the circuit.

Parameters

kind (int) – kind of gate
qid (list (int)) – list of qubit id
para (list (float), default None) – list of parameters
c (int, default None) – classical register id to store measured data
ctrl (int, default None) – classical register id to controll the gate

Return type

None

clone()[source]¶

clone quantum circuit.

Parameters: None –
Returns: qcirc – quantum circuit
Return type: instance of QCirc

cmem_num¶: Structure/Union member

dump(file_path)[source]¶

dump the circuit

Parameters: file_path (str) – file path of dump file
Return type: None

equivalent(qc, *args, **kwargs)[source]¶

two quantum circuits are equivalent or not (using pyzx’s verify_equality method).

Parameters: None –
Returns: ans
Return type: bool

Notes

Non-unitary gates: measure, reset are not supported.

first¶: Structure/Union member

classmethod from_pyzx(zxqc)[source]¶

get pyzx’s Circuit instance.

Parameters: zxqc (instance of pyzx's Circuit) – quantum circuit
Returns: qc – quantum circuit
Return type: instance of QCirc

Notes

Non-unitary gates: measure, reset are not supported.

classmethod from_qasm(string)[source]¶

get QCirc instance from OpenQASM 2.0 string.

Parameters: None –
Returns: qcirc
Return type: instance of QCirc

Notes

Non-unitary gates (measure, reset) and user customized gates are not supported. Supported gates are ‘x’, ‘y’, ‘z’, ‘h’, ‘s’, ‘sdg’, ‘t’, ‘tdg’, ‘cx’, ‘cz’, ‘ch’, ‘rx’, ‘rz’, ‘crz’.

classmethod from_qasm_file(file_path)[source]¶

get QCirc instance from OpenQASM 2.0 file.

Parameters: file_path (str) – file path name of OpenQASM 2.0 file
Returns: qcirc
Return type: instance of QCirc

Notes

Non-unitary gates (measure, reset) and user customized gates are not supported. Supported gates are ‘x’, ‘y’, ‘z’, ‘h’, ‘s’, ‘sdg’, ‘t’, ‘tdg’, ‘cx’, ‘cz’, ‘ch’, ‘rx’, ‘rz’, ‘crz’.

gate_num¶: Structure/Union member

classmethod generate_random_gates(qubit_num=0, gate_num=0, phase=None, prob=None, **kwargs)[source]¶

generate circuit including random gates.

Parameters

qubit_num (int) – number of qubits
gate_num (int) – numbner of gates
phase (tupple of float) – phases selected randomly
prob (dict) –

{‘x’:prob_x, ‘z’:prob_z, ‘h’:prob_h, ‘s’:prob_s, ‘s_dg’:prob_s_dg,
’t’:prob_t, ‘t_dg’:prob_t_dg, ‘rx’:prob_rx, ‘rz’:prob_rz, ‘cx’:prob_cx, ‘cz’:prob_cz, ‘ch’:prob_ch, ‘crz’:prob_crz}
- prob_x: probability of x
- prob_z: probability of z
- prob_h: probability of h
- prob_s: probability of s
- prob_s_dg: probability of s_dg
- prob_t: probability of t
- prob_t_dg: probability of t_dg
- prob_rx: probability of rx
- prob_rz: probability of rz
- prob_cx: probability of cx
- prob_cz: probability of cz
- prob_ch: probability of ch
- prob_crz: probability of crz

Returns

qcirc – generated circuit

Return type

instance of QCirc

Examples

>>> qc = QCirc.generate_random_gates(qubit_num=5, gate_num=100,
phase_unit=0.25, prob={'h':3, 'cx':7, 'rz':1})

Notes

each probability values are normalized so that the sum of the probabilities is 1.0.
Phase parameters of rotation gates are selected randomly in the element of ‘phase’.

get_gates()[source]¶

get list of gates from the circuit.

Parameters

None –

Returns

gates – gates of the quantum circuit gates = [{‘kind’:kind, ‘qid’:qid, ‘phase’:phase, ‘cid’:cid, ‘ctrl’:ctrl}, …] - kind: gate name - qid: qubit id - phase: phase parameter (non-zero only for rotation gates) - para: [phase, gphase, factor]

gphase means global phase used only when adding control to p gate

cid: classical register id (set only for measurement gate)
ctrl: classical register id to control gate operation

Return type

list of dict

get_params()[source]¶

get parameters for each tag

Parameters: None –
Returns: params – tag and phase dictionary ex) {‘tag1’: phase1, ‘tag2’: phase2, …}
Return type: dict

Examples

>>> qc = QCirc().h(0).rz(0, tag='foo').rx(0, tag='bar')
>>> qc.set_params(params={'foo': 0.2, 'bar': 0.4})
>>> print(qc.get_params())
{'foo': 0.2, 'bar': 0.4}

get_stats()[source]¶

get statistics of the circuit.

Parameters: None –
Returns: stats – {‘qubit_num’:qubit_num, ‘cmem_num’:cmem_num, ‘gate_num’:gate_num, ‘gate_freq’:gate_freq} - qubit_num: number of qubits - cmem_num: number of classical bits - gate_num: number of gates - gate_freq: frequency of gates (Counter)
Return type: dict

get_tag_phase(tag)[source]¶

get parameter (= phase) for the tag

Parameters: tag (str) – tag of phase parameter for parametric quantum circuit.
Returns: phase – rotation angle (unit of angle is PI radian) for the tag.
Return type: float

Examples

>>> qc = QCirc().h(0).rz(0, tag='foo').rx(0, tag='bar')
>>> qc.set_params(params={'foo': 0.2, 'bar': 0.4})
>>> print(qc.get_tag_phase('foo'))
0.2

is_clifford()[source]¶

the quantum circuit is clifford or not

Parameters: None –
Returns: ans – True if the quantum circuit unitary, False if otherwise
Return type: bool

is_equal(qc)[source]¶

eaual or not.

Parameters: qc (instance of QCirc) – quantum circuit (merged)
Returns: qcirc – quantum circuit (result)
Return type: instance of QCirc

is_unitary()[source]¶

the quantum circuit is unitary or not

Parameters: None –
Returns: ans – True if the quantum circuit unitary, False if otherwise
Return type: bool

kind_first()[source]¶

get kind of first gate of the circuit.

Parameters: None –
Returns: kind_list – kind of first quantum gate of quantum circuit
Return type: int

Note

return None if none of gates included

kind_list()[source]¶

get list of kinds from the circuit.

Parameters: None –
Returns: kinds – kinds of the quantum circuit
Return type: list of kind

Note

return None if none of gates included

last¶: Structure/Union member

classmethod load(file_path)[source]¶

load the circuit

Parameters: file_path (str) – file path of dump file
Returns: qcirc – loaded circuit
Return type: instance of QCirc

merge(qc)[source]¶

merge two quantum circuits.

Parameters: qc (instance of QCirc) – quantum circuit (merged)
Returns: qcirc – new quantum circuit (merge result)
Return type: instance of QCirc

merge_mutable(qc)[source]¶

merge a quantum circuit with another one.

Parameters: qc (instance of QCirc) – quantum circuit (merged)
Returns: self – quantum circuit (merge result)
Return type: instance of QCirc

Notes

This method changes original quantum circuit.

multiple(other)[source]¶

integer multiple for quantum circuit

Parameters: other (instance of QCirc / int) – quantum circuit / number
Returns: qc – quantum circuit after multiplication
Return type: instance of QCirc

operate_gate(kind=None, qid=None, cid=None, phase=0.0, gphase=0.0, fac=1.0, tag=None, ctrl=None)[source]¶

operate gate

Parameters

kind (int) – kind of the gate
qid (list) – quantum id list
cid (list) – classical register (memory) id list
phase (float) – phase for rotation gate
gphase (float) – global phase for rotation gate
fac (float) – factor of phase value

Returns

self – quantum circuit

Return type

instance of QCirc

operate_qcirc(qcirc, qctrl=None)[source]¶

operate quantum circuit

Parameters

qcirc (instance of QCirc) – quantum circuit
qctrl (int) – control qubit id

Returns

self – quantum state after executing the quantum circuit

Return type

instance of QState

optimize(*args, **kwargs)[source]¶

optimize the quantum circuit (using pyzx’s full_optimize method).

Parameters: None –
Returns: qc – optimized circuit
Return type: instance of QCirc

Notes

Non-unitary gates: measure, reset are not supported.

pop_gate()[source]¶

pop first gate of the circuit.

Parameters: None –
Returns: gate – tupple of (kind, qid, para, c, ctrl) - kind … kind of gate - qid … qubit id list - para … parameters for rotation - c … classical register ID to store measured data (only for measurement gate) - ctrl … classical register id to controll the gate
Return type: tupple of (int, [int,int], [float,float,float], int, int)

Notes

This method changes original quantum circuit.

qubit_num¶: Structure/Union member

remap(qid=None, cid=None)[source]¶

remap qubit id and cmem id of quantum circuit

Parameters

qid (list (int)) – list of qubit id (quantum register)
cid (list (int)) – list of cmem id (classical memory or classical register)

Returns

qcirc – new quantum circuit after remapping

Return type

instance of QCirc

Examples

>>> qc = QCirc().h(0).cx(0,1).measure(qid=[0,1], cid=[0,1])
>>> qc.show()
q[0] -H-*-M---
q[1] ---X-|-M-
c  =/=====v=v=
2         0 1
>>> qc_new1 = qc.remap(qid=[1,0], cid=[1,0])
>>> qc_new1.show()
q[0] ---X---M-
q[1] -H-*-M-|-
c  =/=====v=v=
2         1 0
>>> qc_new2 = qc.remap(qid=[2,1], cid=[1,0])
>>> qc_new2.show()
q[0] ---------
q[1] ---X---M-
q[2] -H-*-M-|-
c  =/=====v=v=
2         1 0

Notes

Length of the qid must be equal to qubit_num of the original quantum circut. Length of cid must be equal to cmem_num of the original quantum circut. Elements of the qid and the cid must not be duplicated.

save(file_path)[source]¶

save the circuit

Parameters: file_path (str) – file path of dump file
Return type: None

set_params(params)[source]¶

set parameters for each tag

Parameters: params (dict) – tag and phase dictionary ex) {‘tag1’: phase1, ‘tag2’: phase2, …}
Return type: None

Examples

>>> qc = QCirc().h(0).rz(0, tag='foo').rx(0, tag='bar')
>>> qc.set_params(params={'foo': 0.2, 'bar': 0.4})
>>> print(qc)
h 0
rz(0.2) 0
rx(0.4) 0
>>> qc.set_params(params={'foo': 0.3, 'bar': 0.5})
>>> print(qc)
h 0
rz(0.3) 0
rx(0.5) 0

show(width=100)[source]¶

show the circuit

Parameters: width (int, default - 100) – width for line breaks and display long quantum circuit
Return type: None

split_unitary_non_unitary()[source]¶

split two part of the gate.

Parameters: None –
Returns: qc_pair – former part includes only unitary gates and later part includes non-unitary gate (measure or reset) first
Return type: tupple of (QCirc, Qcirc)

tag_table¶: Structure/Union member

to_pyzx()[source]¶

get pyzx’s Circuit instance.

Parameters: None –
Returns: zxqc – quantum circuit
Return type: instance of pyzx’s Circuit

Notes

Non-unitary gates: measure, reset are not supported.

to_qasm()[source]¶

get OpenQASM 2.0 string of the circuit.

Parameters: None –
Returns: qcirc_str
Return type: str

to_qasm_file(file_path)[source]¶

write to OpenQASM 2.0 file.

Parameters: file_path (str) – file path name of OpenQASM 2.0 file
Return type: None

to_string()[source]¶

get string of the circuit (qlazy format).

Parameters: None –
Returns: qcirc_str
Return type: str

qlazy.QCirc.append_qc_canvas(qc_canvas, gates, qubit_num, cmem_num)[source]¶

qlazy.QCirc.init_qc_canvas(qubit_num, cmem_num)[source]¶

qlazy.QCirc.string_to_args(s)[source]¶: convert string to args

qlazy.QObject module¶

Quantum Object

class qlazy.QObject.QObject[source]¶

Bases: object

ccx(q0, q1, q2, ctrl=None)[source]¶

operate CCX gate (toffoli gate, controlled controlled X gate).

Parameters

q0 (int) – qubit id (control qubit).
q1 (int) – qubit id (control qubit).
q2 (int) – qubit id (target qubit).

Returns

self

Return type

instance of QObject

ch(q0, q1, ctrl=None)[source]¶

operate CH gate (controlled H gate).

Parameters

q0 (int) – qubit id (control qubit).
q1 (int) – qubit id (target qubit).

Returns

self

Return type

instance of QObject

cp(q0, q1, phase=0.0, gphase=0.0, fac=1.0, tag=None, ctrl=None)[source]¶

operate CP gate (controlled P gate).

Parameters

q0 (int) – qubit id (control qubit).
q1 (int) – qubit id (target qubit).

Returns

self

Return type

instance of QObject

crx(q0, q1, phase=0.0, gphase=0.0, fac=1.0, tag=None, ctrl=None)[source]¶

operate CRX gate (controlled RX gate).

Parameters

q0 (int) – qubit id (control qubit).
q1 (int) – qubit id (target qubit).
phase (float) – rotation angle (unit of angle is PI radian).

Returns

self

Return type

instance of QObject

cry(q0, q1, phase=0.0, gphase=0.0, fac=1.0, tag=None, ctrl=None)[source]¶

operate CRY gate (controlled RY gate).

Parameters

q0 (int) – qubit id (control qubit).
q1 (int) – qubit id (target qubit).
phase (float) – rotation angle (unit of angle is PI radian).

Returns

self

Return type

instance of QObject

crz(q0, q1, phase=0.0, gphase=0.0, fac=1.0, tag=None, ctrl=None)[source]¶

operate CRZ gate (controlled RZ gate).

Parameters

q0 (int) – qubit id (control qubit).
q1 (int) – qubit id (target qubit).
phase (float) – rotation angle (unit of angle is PI radian).

Returns

self

Return type

instance of QObject

cs(q0, q1, ctrl=None)[source]¶

operate CS gate (controlled S gate).

Parameters

q0 (int) – qubit id (control qubit).
q1 (int) – qubit id (target qubit).

Returns

self

Return type

instance of QObject

cs_dg(q0, q1, ctrl=None)[source]¶

operate CS dagger gate (controlled S dagger gate).

Parameters

q0 (int) – qubit id (control qubit).
q1 (int) – qubit id (target qubit).

Returns

self

Return type

instance of QObject

csw(q0, q1, q2, ctrl=None)[source]¶

operate CSW gate (fredkin gate, controlled swap gate).

Parameters

q0 (int) – qubit id (control qubit).
q1 (int) – qubit id (swap qubit).
q2 (int) – qubit id (swap qubit).

Returns

self

Return type

instance of QObject

ct(q0, q1, ctrl=None)[source]¶

operate CT gate (controlled T gate).

Parameters

q0 (int) – qubit id (control qubit).
q1 (int) – qubit id (target qubit).

Returns

self

Return type

instance of QObject

ct_dg(q0, q1, ctrl=None)[source]¶

operate CT dagger gate (controlled T dagger gate).

Parameters

q0 (int) – qubit id (control qubit).
q1 (int) – qubit id (target qubit).

Returns

self

Return type

instance of QObject

cx(q0, q1, ctrl=None)[source]¶

operate CX gate (controlled X gate, controlled NOT gate, CNOT gate).

Parameters

q0 (int) – qubit id (control qubit).
q1 (int) – qubit id (target qubit).

Returns

self

Return type

instance of QObject

cxr(q0, q1, ctrl=None)[source]¶

operate CXR gate (controlled root X gate).

Parameters

q0 (int) – qubit id (control qubit).
q1 (int) – qubit id (target qubit).

Returns

self

Return type

instance of QObject

cxr_dg(q0, q1, ctrl=None)[source]¶

operate CXR dagger gate (controlled XR dagger gate).

Parameters

q0 (int) – qubit id (control qubit).
q1 (int) – qubit id (target qubit).

Returns

self

Return type

instance of QObject

cy(q0, q1, ctrl=None)[source]¶

operate CY gate (controlled X gate).

Parameters

q0 (int) – qubit id (control qubit).
q1 (int) – qubit id (target qubit).

Returns

self

Return type

instance of QObject

cz(q0, q1, ctrl=None)[source]¶

operate CZ gate (controlled Z gate).

Parameters

q0 (int) – qubit id (control qubit).
q1 (int) – qubit id (target qubit).

Returns

self

Return type

instance of QObject

h(q0, ctrl=None)[source]¶

operate H gate (hadamard gate).

Parameters: q0 (int) – qubit id.
Returns: self
Return type: instance of QObject

iqft(qid)[source]¶

Inverse Quantum Fourier Transform

Parameters: qid (list of int) – qubit id list
Returns: self
Return type: instance of QObject

mcx(qid=None, ctrl=None)[source]¶

operate MCX gate (multi-controlled X gate).

Parameters: qid (list of int) – qubit id list [control, control, … , control, target]
Returns: self
Return type: instance of QObject

measure(qid, cid)[source]¶

add measurement gate (Z-basis).

Parameters

qid (list of int) – qubit id list to measure.
cid (list of int) – classical register id list to store measured result.

Returns

self – quantum circuit after adding

Return type

instance of QCirc

operate(pp=None, ctrl=None, qctrl=None)[source]¶: operate pauli product.

operate_pp(pp=None, ctrl=None, qctrl=None)[source]¶

operate pauli product.

Parameters

pp (instance of PauliProduct) – pauli product to operate
ctrl (int) – contoroll qubit id for controlled pauli product (this option will be removed near future)
qctrl (int) – contoroll qubit id for controlled pauli product

Returns

self – quantum circuit after adding

Return type

instance of QCirc

p(q0, phase=0.0, gphase=0.0, fac=1.0, tag=None, ctrl=None)[source]¶

operate P gate (phase shift gate).

Parameters

q0 (int) – qubit id.
phase (float) – rotation angle (unit of angle is PI radian).

Returns

self

Return type

instance of QObject

Notes

matrix expression is following… | 1.0 0.0 | | 0.0 exp(i*phase*PI) |

qft(qid)[source]¶

Quantum Fourier Transform

Parameters: qid (list of int) – qubit id list
Returns: self
Return type: instance of QObject

reset(qid=None)[source]¶

reset to |00..0> state.

Parameters: qid (list, default - qubit id's list for all of the qubits) – qubit id’s list to reset.
Returns: self – quantum state.
Return type: instance of QObject

Notes

If ‘qid’ is set, specified qubits are reset after measurement. So if the specified qubits are entangled with the remaining qubits, output quantum state is probabilistic. If no qubits are set, all qubits are zero reset.

rx(q0, phase=0.0, gphase=0.0, fac=1.0, tag=None, ctrl=None)[source]¶

operate RX gate (rotation around X-axis).

Parameters

q0 (int) – qubit id.
phase (float) – rotation angle (unit of angle is PI radian).

Returns

self

Return type

instance of QObject

rxx(q0, q1, phase=0.0, gphase=0.0, fac=1.0, tag=None, ctrl=None)[source]¶

operate Rxx gate.

Parameters

q0 (int) – qubit id (control qubit).
q1 (int) – qubit id (target qubit).
phase (float) – rotation angle (unit of angle is PI radian).

Returns

self

Return type

instance of QObject

ry(q0, phase=0.0, gphase=0.0, fac=1.0, tag=None, ctrl=None)[source]¶

operate RY gate (rotation around Y-axis).

Parameters

q0 (int) – qubit id.
phase (float) – rotation angle (unit of angle is PI radian).

Returns

self

Return type

instance of QObject

ryy(q0, q1, phase=0.0, gphase=0.0, fac=1.0, tag=None, ctrl=None)[source]¶

operate Ryy gate.

Parameters

q0 (int) – qubit id (control qubit).
q1 (int) – qubit id (target qubit).
phase (float) – rotation angle (unit of angle is PI radian).

Returns

self

Return type

instance of QObject

rz(q0, phase=0.0, gphase=0.0, fac=1.0, tag=None, ctrl=None)[source]¶

operate RZ gate (rotation around Z-axis).

Parameters

q0 (int) – qubit id.
phase (float) – rotation angle (unit of angle is PI radian).

Returns

self

Return type

instance of QObject

rzz(q0, q1, phase=0.0, gphase=0.0, fac=1.0, tag=None, ctrl=None)[source]¶

operate Rxx gate.

Parameters

q0 (int) – qubit id (control qubit).
q1 (int) – qubit id (target qubit).
phase (float) – rotation angle (unit of angle is PI radian).

Returns

self

Return type

instance of QObject

s(q0, ctrl=None)[source]¶

operate S gate.

Parameters: q0 (int) – qubit id.
Returns: self
Return type: instance of QObject

s_dg(q0, ctrl=None)[source]¶

operate S dagger gate (hermitian conjugate of S gate).

Parameters: q0 (int) – qubit id.
Returns: self
Return type: instance of QObject

sw(q0, q1, ctrl=None)[source]¶

swap gate

Parameters

q0 (int) – qubit id
q1 (int) – qubit id

Returns

self

Return type

instance of QObject

t(q0, ctrl=None)[source]¶

operate T gate.

Parameters: q0 (int) – qubit id.
Returns: self
Return type: instance of QObject

t_dg(q0, ctrl=None)[source]¶

operate T dagger gate (hermitian conjugate of T gate).

Parameters: q0 (int) – qubit id.
Returns: self
Return type: instance of QObject

x(q0, ctrl=None)[source]¶

operate X gate.

Parameters: q0 (int) – qubit id.
Returns: self
Return type: instance of QObject

xr(q0, ctrl=None)[source]¶

operate root X gate.

Parameters: q0 (int) – qubit id.
Returns: self
Return type: instance of QObject

xr_dg(q0, ctrl=None)[source]¶

operate root X dagger gate (hermmitian conjugate of root X gate).

Parameters: q0 (int) – qubit id.
Returns: self
Return type: instance of QObject

y(q0, ctrl=None)[source]¶

operate Y gate.

Parameters: q0 (int) – qubit id.
Returns: self
Return type: instance of QObject

z(q0, ctrl=None)[source]¶

operate Z gate.

Parameters: q0 (int) – qubit id.
Returns: self
Return type: instance of QObject

qlazy.QObject.gray_code(n)[source]¶: gray code generator

qlazy.QState module¶

Quantum State

class qlazy.QState.QState(qubit_num=0, vector=None, seed=None, use_gpu=False, **kwargs)[source]¶

Bases: Structure, QObject

Quantum State

qubit_num¶

qubit number of the quantum state (= log(state_num)).

Type: int

state_num¶

dimension of the quantum state vector (= 2**qubit_num).

Type: int

amp¶

elements of the quantum state vector.

Type: list of complex

classmethod add_method(method)[source]¶

add method (custum gate).

Parameters: method (func) – method (custum gate) to add.

Examples

>>> def bell(self, q0, q1):
>>>     self.h(q0).cx(q0,q1)
>>>     return self
>>> ...
>>> QState.add_method(bell)
>>> qs = QState(qubit_num=2)
>>> qs.bell(0,1)
>>> ...

classmethod add_methods(*methods)[source]¶

add methods (custum gates).

Parameters: methods (func, func, ...) – arguments of methods (custum gates) to add.

Examples

>>> def bell(self, q0, q1):
>>>     self.h(q0).cx(q0,q1)
>>>     return self
>>> ...
>>> def flip(self, q0, q1):
>>>     self.x(q0).x(q1)
>>>     return self
>>> ...
>>> QState.add_methods(bell, flip, ...)
>>> qs = QState(2)
>>> qs.bell(0,1)
>>> qs.flip(0,1)
>>> ...

property amp¶: elements of quantum state vector.

apply(matrix=None, qid=None)[source]¶

apply matrix.

Parameters: matrix (list of list) – matrix to apply.
Returns: self
Return type: instance of QState

Notes

If ‘qid’ isn’t set, dimension of the matrix must be equal to the 2 power of qubit number of the system. If ‘qid’ is set, dimension of the matrix must be equal to the 2 power of ‘qid’ length.

bloch(q=0)[source]¶

get bloch angles.

Parameters

q (int) – qubit id

Returns

theta (float) – bloch angle with Z-axis
phi (float) – bloch angle with X-axis

Notes

the unit of angle is PI radian. for example, 0.5 means 0.5*PI (radian).

buf_id¶: Structure/Union member

buffer_0¶: Structure/Union member

buffer_1¶: Structure/Union member

camp¶: Structure/Union member

clone()[source]¶

get the copy of the quantum state.

Parameters: None –
Returns: qstate – copy of the original quantum state.
Return type: instance of QState

composite(num=1)[source]¶

get the composite state of same quantum states.

Parameters: num (int) – number of quantum states.
Returns: qs – composite quantum state.
Return type: instance of QState

classmethod create_register(num)[source]¶

create registers (qubit id’s) and initialize zero.

Parameters: num (int) – qubit number you want to use.

Examples

>>> qid = QState.create_register(3)
>>> print(qid)
[0,0,0]

classmethod del_all(*qstates)[source]¶

free memory of the all quantum states.

Parameters: qstates (instance of QState,instance of QState,...) – set of QState instances
Return type: None

evolve(observable=None, time=0.0, iteration=0)[source]¶

evolve the quantum state.

Parameters

observable (instance of Observable) – Hamiltonian of the system.
time (float) – period of time.
iter (int) – number of iteration.

Returns

self

Return type

instance of QState

Notes

The ‘iter’ value should be sufficiently larger than the ‘time’ value. This method change the original state.

See also

Obserbable

expect(observable=None)[source]¶

get the expectation value for observable under the quantum state.

Parameters: observable (instance of Observable) – obserbable of the system.
Returns: expect – expect value.
Return type: float

See also

Obserbable

fidelity(qstate, qid=None)[source]¶

get fidelity with the quantum state.

Parameters

qstate (instance of QState) – one of the two quantum states.
qid (list of int) – qubit id’s list.

Returns

fid – fidelity of two quantum states. absolute value of the inner product of two quantum states.

Return type

float

Notes

If ‘qid’ is set, you can get the fidelity for partial quantum state. If the specified quantum system are entangled with the remaining system, output value is probabilistic, while original quantum states do not change.

gbank¶: Structure/Union member

get_amp(qid=None)[source]¶

get the elements of quantum state vector.

Parameters: qid (list of int, default - list of all of the qubit id) – qubit id’s list.
Returns: ret – elements of the quantum state vector.
Return type: numpy.ndarray (complex)

Notes

If ‘qid’ is set, specified qubit state are got after remaining qubits are measured. So if the specified qubits are entangled with the remaining qubits, output quantum state is probabilistic. If no qubits are specified, you get all elements of the quantum state.

get_prob(qid=None)[source]¶

get the probability list of quantum state vector.

Parameters: qid (list of int, default - list of all of the qubit id) – qubit id’s list.
Returns: prob – key - bits string value - probability ex) {‘00’: 0.52, ‘11’: 0.48}
Return type: dict

classmethod init_register(*args)[source]¶

initialize registers (qubit id’s).

Parameters: args (list, list,...) – arguments of qubit registers.
Returns: idx – total qubit number.
Return type: int

Examples

>>> qid_0 = QState.create_register(3)
>>> qid_1 = QState.create_register(2)
>>> print(qid_0, qid_1)
[0,0,0] [0,0]
>>> qnum = QState.init_register(qid_0, qid_1)
>>> print(qnum, qid_0, qid_1)
5 [0,1,2] [3,4]

inpro(qstate, qid=None)[source]¶

get the inner product with quantum state.

Parameters

qstate (instance of QState) – one of the two quantum state.
qid (list of int, default - list of all of the qubit id) – qubit id’s list.

Returns

inp – inner produt (<self|qstate>).

Return type

complex

Notes

If ‘qid’ is set, you can get the inner product for partial quantum state. If the specified quantum system are entangled with the remaining system, output value is probabilistic, while original quantum states do not change.

join(qs_list)[source]¶

get tensor product state of the quantum states’ list.

Parameters: qs_list (list (QState)) – list of quantum states.
Returns: qs_out – tensor product state.
Return type: instance of QState

m(qid=None, shots=1, angle=0.0, phase=0.0)[source]¶

measurement in any direction (default: Z-axis).

Parameters

qid (list of int) – qubit id list to measure.
shots (int, default 1) – number of measurements.
angle (float, default 0.0) – direction of measurement (angle with Z-axis).
phase (float, default 0.0) – direction of measurement (phase around Z-axis).

Returns

md – measurement data.

Return type

instance of MData

Examples

>>> qs = QState(2).h(0).cx(0,1)
>>> md = qs.m()
>>> md.show(shots=100)
direction of measurement: z-axis
frq[00] = 52
frq[11] = 48
last state => 11

See also

MData

mb(qid=None, shots=1)[source]¶: bell measurement

measure(qid=None)[source]¶

one shot measurement in Z-direction.

Parameters: qid (list of int) – qubit id list to measure.
Returns: mval – measurement value.
Return type: str

Examples

>>> qs = QState(qubit_num=2).h(0).cx(0,1)
>>> qs.show()
>>> print(qs.measure(qid=[0,1]))
>>> qs.show()
c[00] = +0.7071+0.0000*i : 0.5000 |++++++
c[01] = +0.0000+0.0000*i : 0.0000 |
c[10] = +0.0000+0.0000*i : 0.0000 |
c[11] = +0.7071+0.0000*i : 0.5000 |++++++
00
c[00] = +1.0000+0.0000*i : 1.0000 |+++++++++++
c[01] = +0.0000+0.0000*i : 0.0000 |
c[10] = +0.0000+0.0000*i : 0.0000 |
c[11] = +0.0000+0.0000*i : 0.0000 |

mx(qid=None, shots=1)[source]¶

X-axis measurement.

Parameters

qid (list of int) – qubit id list to measure.
shots (int, default 1) – number of measurements.

Returns

md – measurement data.

Return type

instance of MData

See also

MData

my(qid=None, shots=1)[source]¶

Y-axis measurement.

Parameters

qid (list of int) – qubit id list to measure.
shots (int, default 1) – number of measurements.

Returns

md – measurement data.

Return type

instance of MData

See also

MData

mz(qid=None, shots=1)[source]¶

Z-axis measurement.

Parameters

qid (list of int) – qubit id list to measure.
shots (int, default 1) – number of measurements.

Returns

md – measurement data.

Return type

instance of MData

See also

MData

operate_gate(kind=None, qid=None, phase=0.0, **kwargs)[source]¶

operate gate

Parameters

kind (int) – kind of the gate
qid (list) – quantum id list
phase (float) – phase for rotation gate

Returns

self – quantum state

Return type

instance of QState

operate_qcirc(qcirc, qctrl=None)[source]¶

operate quantum circuit

Parameters

qcirc (instance of QCirc) – quantum circuit
qctrl (int) – control qubit id

Returns

self – quantum state after executing the quantum circuit

Return type

instance of QState

Notes

The quantum circut must be unintary.

partial(qid=None)[source]¶

get the partial quantum state.

Parameters: qid (list of int, default - list of all of the qubit id) – qubit id’s list to get as a partial quantum system.
Returns: qs – partial quantum state.
Return type: instance of QState

Notes

If ‘qid’ is set, specified partial quantum system are got after remaining system are measured. So if the specified quantum system are entangled with the remaining system, output quantum state is probabilistic. If no qubits are specified, you get the copy of original quantum state.

prob_array¶: Structure/Union member

prob_updated¶: Structure/Union member

qubit_num¶: Structure/Union member

schmidt_coef(qid_0=None, qid_1=None)[source]¶

get schmidt coefficients.

Parameters

qid_0 (list) – subsystem to decomposite.
qid_1 (list) – another subsystem to decomposite.

Returns

coef – schmidt coefficients.

Return type

numpy.ndarray

schmidt_decomp(qid_0=None, qid_1=None)[source]¶

schmidt decomposition.

Parameters

qid_0 (list) – subsystem to decomposite.
qid_1 (list) – another subsystem to decomposite.

Returns

coef (numpy.ndarray) – schmidt coefficients.
qs_0 (list of QState instances) – decomposite quantum state related to ‘qid_0’.
qs_1 (list of QState instances) – decomposite quantum state related to ‘qid_1’.

show(qid=None, nonzero=False, preal=0)[source]¶

show the quantum state (elements of the state vector and probabilities).

Parameters

qid (list of int, default - list of all of the qubit id) – qubit id’s list to show.
nonzero (bool, default False) – if True, only non-zero amplitudes are printed.
preal (int, default 0) – state id to make positive real amplitude. (if -1 is set, do not go out the global phase factor)

Return type

None

Notes

If ‘qid’ is set, it shows the elements of quantum state vector for partial quantum system specified by ‘qid’. If the specified quantum system are entangled with the remaining system, output is probabilistic. If no qubits are specified, it shows the whole quantum state. This method does not change the original quantum state.

Examples

>>> qs = QState(2).h(0).cx(0,1)
>>> qs.show()
c[00] = +0.7071+0.0000*i : 0.5000 |++++++
c[01] = +0.0000+0.0000*i : 0.0000 |
c[10] = +0.0000+0.0000*i : 0.0000 |
c[11] = +0.7071+0.0000*i : 0.5000 |++++++
...
>>> qs.show(qid=[0])
c[0] = +1.0000+0.0000*i : 1.0000 |+++++++++++
c[1] = +0.0000+0.0000*i : 0.0000 |
...
>>> qs.show(nonzero=True)
c[00] = +0.7071+0.0000*i : 0.5000 |++++++
c[11] = +0.7071+0.0000*i : 0.5000 |++++++

state_num¶: Structure/Union member

tenspro(qstate)[source]¶

get the tensor product with quantum state.

Parameters: qstate (instance of QState) – quantum state to get the tensor product.
Returns: qstate_out – tensor produt of ‘self’ and ‘qstate’.
Return type: instance of QState

use_gpu¶: Structure/Union member

qlazy.Result module¶

Result of quantum circuit execution

class qlazy.Result.Result[source]¶

Bases: object

Result of quantum circuit execution

backend¶

backend device of quantum computing

Type: instance of Backend

qubit_num¶

number of qubits

Type: int

cmem_num¶

number of classical bits

Type: int

cid¶

classical register id list to get frequencys.

Type: list

shots¶

number of measurements

Type: int

freqency¶

frequencies of measured value.

Type: instance of Counter

start_time¶

start time to ececute the quantum circuit.

Type: instance of datetime

end_time¶

end time to ececute the quantum circuit.

Type: instance of datetime

elapsed_time¶

elapsed time to ececute the quantum circuit.

Type: float

qstate¶

quantum state after executing circuit.

Type: instance of QState

stabilizer¶

stabilizer state after executing circuit.

Type: instance of Stabilizer

cmem¶

classical memory after executing circuit.

Type: instance of CMem

info¶

result informations relating to the backend device

Type: dict

backend: Backend = None¶

cid: list = None¶

cmem: CMem = None¶

cmem_num: int = None¶

elapsed_time: float = None¶

end_time: datetime = None¶

frequency: Counter = None¶

info: dict = None¶

classmethod load(file_path)[source]¶

load the result

Parameters: file_path (str) – file path of dump file
Returns: result – loaded circuit
Return type: instance of Result

qstate: QState = None¶

qubit_num: int = None¶

save(file_path)[source]¶

save the result

Parameters: file_path (str) – file path of dump file
Return type: None

shots: int = None¶

show(verbose=False)[source]¶

show the result.

Parameters

verbose (bool) – verbose output or not
None –

Return type

None

stabilizer: Stabilizer = None¶

start_time: datetime = None¶

qlazy.Stabilizer module¶

Stabilizer State

class qlazy.Stabilizer.MDataStabilizer(frequency=None, last=None, qid=None, qubit_num=0)[source]¶

Bases: object

Measured Data for Stabilizer

frequency¶

frequencies of measured value.

Type: Counter

last¶

last measured value.

Type: str

qid¶

qubit id’s list.

Type: list of int

qubit_num¶

qubit number of the quantum state (= log(state_num)).

Type: int

class qlazy.Stabilizer.Stabilizer(qubit_num=None, gene_num=None, pp_list=None, seed=None, **kwargs)[source]¶

Bases: Structure, QObject

Stabilizer State

qubit_num¶

number of qubits.

Type: int

gene_num¶

number of generators.

Type: int

classmethod add_method(method)[source]¶

add method (custum gate).

Parameters: method (func) – method (custum gate) to add.

classmethod add_methods(*methods)[source]¶

add methods (custum gates).

Parameters: methods (func, func, ...) – arguments of methods (custum gates) to add.

check_matrix¶: Structure/Union member

clone()[source]¶

get the copy of the quantum state.

Parameters: None –
Returns: stab – copy of the original stabilizer.
Return type: instance of Stabilizer

classmethod del_all(*stabs)[source]¶

free memory of the all stabilizer.

Parameters: stabs (instance of Stabilizer,instance of Stabilizer,...) – set of Stabilizer instances
Return type: None

gene_num¶: Structure/Union member

get_pauli_fac(gene_id)[source]¶

get pauli factor of generator (‘+1’,’-1’,’+i’,’-i’).

Parameters: gene_id (int) – generator id to get.
Returns: pauli_fac_complex – complex facto of the generator (1+0j, 1j, -1+0j, -1j)
Return type: complex

get_pauli_op(gene_id, qubit_id)[source]¶

get pauli operator (‘I’,’X’,’Y’,’Z’).

Parameters

gene_id (int) – generator id to get.
qubit_id (int) – qubit id to get.

Returns

pauli_op_str – pauli operator (‘I’,’X’,’Y’,’Z’)

Return type

str

get_rank()[source]¶: get rank of the stabilizer

get_str()[source]¶: get string of the stabilzer

m(qid=None, shots=1)[source]¶

measurement in Z-direction.

Parameters

qid (list of int) – qubit id list to measure.
shots (int, default 1) – number of measurements.

Returns

md – measurement data.

Return type

instance of MDataStabilizer

Examples

>>> sb = Stabilizer(qubit_num=2).set_all('Z').h(0).cx(0,1)
>>> md = qs.m(qid=[0,1], shots=100)
>>> print(md.freauency)
>>> print(md.last)
Counter({'00':55,'11':45})
11

See also

MDataStabilizer

measure(qid=None)[source]¶

one shot measurement in Z-direction.

Parameters: qid (list of int) – qubit id list to measure.
Returns: mval – measurement value.
Return type: str

Examples

>>> sb = Stabilizer(qubit_num=2).set_all('Z').h(0).cx(0,1)
>>> sb.show()
>>> print(sb.measure(qid=[0,1]))
>>> sb.show()
g[0]:  XX
g[1]:  ZZ
00
g[0]:  ZI
g[1]:  ZZ

mx(qid=None, shots=1)[source]¶

measurement in X-direction.

Parameters

qid (list of int) – qubit id list to measure.
shots (int, default 1) – number of measurements.

Returns

md – measurement data.

Return type

instance of MDataStabilizer

my(qid=None, shots=1)[source]¶

measurement in Y-direction.

Parameters

qid (list of int) – qubit id list to measure.
shots (int, default 1) – number of measurements.

Returns

md – measurement data.

Return type

instance of MDataStabilizer

mz(qid=None, shots=1)[source]¶

measurement in Z-direction.

Parameters

qid (list of int) – qubit id list to measure.
shots (int, default 1) – number of measurements.

Returns

md – measurement data.

Return type

instance of MDataStabilizer

Examples

>>> sb = Stabilizer(2).set_all('Z').h(0).cx(0,1)
>>> md = qs.mz(qid=[0,1], shots=100)
>>> print(md.freauency)
>>> print(md.last)
Counter({'00':55,'11':45})
11

See also

MDataStabilizer

operate(pp=None, ctrl=None, qctrl=None)[source]¶

operate unitary operator to stabilizer.

Parameters

pp (instance of PauliProduct) – pauli product to operate
ctrl (int) – contoroll qubit id for controlled pauli product (this option will be removed near future)
qctrl (int) – contoroll qubit id for controlled pauli product

Returns

self – stabilizer after operation

Return type

instance of Stabilizer

operate_gate(kind=None, qid=None, **kwargs)[source]¶

operate gate

Parameters

kind (int) – kind of the gate
qid (list) – quantum id list

Returns

self – quantum state

Return type

instance of QState

operate_qcirc(qcirc, qctrl=None)[source]¶

operate quantum circuit

Parameters

qcirc (instance of QCirc) – quantum circuit
qctrl (int) – control qubit id

Returns

qs – quantum state after executing the quantum circuit

Return type

instance of QState

Notes

The quantum circut must be clifford.

pauli_factor¶: Structure/Union member

qubit_num¶: Structure/Union member

set_all(pauli_op_str)[source]¶

set all of the qubits same pauli operators.

Parameters: pauli_op_str (str) – string of pauli operator (‘X’,’Y’,’Z’).
Returns: self
Return type: instance of Stabilizer

Examples

>>> sb = Stabilizer(qubit_num=3)
>>> sb.set_all('Z')
>>> sb.show()
g[0]:  ZII
g[1]:  IZI
g[2]:  IIZ

set_pauli_fac(gene_id, pauli_fac_str)[source]¶

set pauli factor of generator (‘+1’,’-1’,’+i’,’-i’).

Parameters: gene_id (int) – generator id to set.
Returns: self
Return type: instance of Stabilizer

set_pauli_op(gene_id, qubit_id, pauli_op_str)[source]¶

set pauli operator (‘I’,’X’,’Y’,’Z’).

Parameters

gene_id (int) – generator id to set.
qubit_id (int) – qubit id to set.

Returns

self

Return type

instance of Stabilizer

show()[source]¶

show the generators of stabilizer.

Parameters: None –
Return type: None

qlazy.config module¶

qlazy.core module¶

qlazy command

qlazy.core.main()[source]¶: execute qlazy command

qlazy.error module¶

exception qlazy.error.QState_Error_AddMethods[source]¶: Bases: Exception

exception qlazy.error.QState_Error_Apply[source]¶: Bases: Exception

exception qlazy.error.QState_Error_Bloch[source]¶: Bases: Exception

exception qlazy.error.QState_Error_Clone[source]¶: Bases: Exception

exception qlazy.error.QState_Error_Evolve[source]¶: Bases: Exception

exception qlazy.error.QState_Error_Expect[source]¶: Bases: Exception

exception qlazy.error.QState_Error_FreeAll[source]¶: Bases: Exception

exception qlazy.error.QState_Error_GetCmp[source]¶: Bases: Exception

exception qlazy.error.QState_Error_Initialize[source]¶: Bases: Exception

exception qlazy.error.QState_Error_InnerProduct[source]¶: Bases: Exception

exception qlazy.error.QState_Error_OperateQcirc[source]¶: Bases: Exception

exception qlazy.error.QState_Error_OperateQgate[source]¶: Bases: Exception

exception qlazy.error.QState_Error_Reset[source]¶: Bases: Exception

exception qlazy.error.QState_Error_Show[source]¶: Bases: Exception

exception qlazy.error.QState_Error_TensorProduct[source]¶: Bases: Exception

exception qlazy.error.QState_NeedMoreArguments[source]¶: Bases: Exception

exception qlazy.error.QState_OutOfBound[source]¶: Bases: Exception

exception qlazy.error.QState_SameQubitID[source]¶: Bases: Exception

exception qlazy.error.QState_TooManyArguments[source]¶: Bases: Exception

exception qlazy.error.QState_UnknownQgateKind[source]¶: Bases: Exception

exception qlazy.error.Stabilizer_Error_AddMethos[source]¶: Bases: Exception

exception qlazy.error.Stabilizer_Error_Clone[source]¶: Bases: Exception

exception qlazy.error.Stabilizer_Error_FreeAll[source]¶: Bases: Exception

exception qlazy.error.Stabilizer_Error_GetPauliFac[source]¶: Bases: Exception

exception qlazy.error.Stabilizer_Error_GetPauliOp[source]¶: Bases: Exception

exception qlazy.error.Stabilizer_Error_GetRank[source]¶: Bases: Exception

exception qlazy.error.Stabilizer_Error_Initialize[source]¶: Bases: Exception

exception qlazy.error.Stabilizer_Error_Measure[source]¶: Bases: Exception

exception qlazy.error.Stabilizer_Error_OperateQcirc[source]¶: Bases: Exception

exception qlazy.error.Stabilizer_Error_OperateQgate[source]¶: Bases: Exception

exception qlazy.error.Stabilizer_Error_SetPauliFac[source]¶: Bases: Exception

exception qlazy.error.Stabilizer_Error_SetPauliOp[source]¶: Bases: Exception

qlazy.gpu module¶

gpu related functions

qlazy.gpu.gpu_preparation()[source]¶: memory allocation and free (dummy)

qlazy.gpu.is_gpu_available()[source]¶: cuda is available or not

qlazy.gpu.is_gpu_supported_lib()[source]¶: this qlazy library supports cuda executoin or not

qlazy.util module¶

various kind of utilities

qlazy.util.check_gpu()[source]¶: NVIDIA GPU is available or not

qlazy.util.densop_check_args(de, kind=None, qid=None)[source]¶: check arguments for densop

qlazy.util.get_lib_ext()[source]¶: get library extension (for Mac OS)

qlazy.util.get_qgate_param_num(kind=None)[source]¶: get parameter number for the quantum gate

qlazy.util.get_qgate_qubit_num(kind=None)[source]¶: get qubit number for the quantum gate

qlazy.util.is_clifford_gate(kind)[source]¶: is the gate clifford?

qlazy.util.is_measurement_gate(kind)[source]¶: is the gate measurement?

qlazy.util.is_non_clifford_gate(kind)[source]¶: is the gate non-clifford?

qlazy.util.is_num(s)[source]¶: is this string numeric or not

qlazy.util.is_reset_gate(kind)[source]¶: is the gate reset?

qlazy.util.is_unitary_gate(kind=None)[source]¶: is the gate unitary?

qlazy.util.qstate_check_args(qs, kind=None, qid=None)[source]¶: check arguments for qstate

qlazy.util.read_config_ini(config_ini_path=None)[source]¶: read config.ini file

qlazy.util.reverse_bit_order(vec_in)[source]¶: reverse bit order of the state vector

Module contents¶

class qlazy.Backend(product=None, device=None)[source]¶

Bases: object

Backend device of quantum computing

product¶

product name of the backend (‘qlazy’ or ‘qulacs’ or ‘ibmq’)

Type: str

device¶

device name of the product

Type: str

config_braket¶

config for amazon braket backend {‘backet_name’: str, ‘poll_timeout_seconds’: int}

Type: dict

Notes

If you use amazon braket backend (braket_local, braket_aws, braket_ionq, braket_rigetti, braket_oqc), you must have config.ini file in your ‘~/.qlazy/’ directory, and discribe like following example …

Example

>>> bk = Backend(product='qlazy', device='stabilizer_simulator')
>>> bk = Backend(product='qulacs', device='gpu_simulator')
>>> bk = Backend(product='ibmq', device='least_busy')
>>> bk = Backend(product='braket_rigetti', device='aspen_11') # read ~/.qlazy/config.ini
...
$ cat ~/.qlazy/config.ini
[backend_braket]
backet_name = amazon-braket-xxxx # set your s3 backet name
...
$ cat ~/.qlazy/config.ini
[backend_braket]
backet_name = amazon-braket-xxxx # set your s3 backet name
poll_timeout_seconds = 86400  # set 1-day (default: 5-days)

classmethod devices(product)[source]¶: get devices list for the product

expect(qcirc=None, observable=None, shots=None, precise=False, init=None)[source]¶

run the quantum circuit.

Parameters

qcirc (instance of QCirc) – quantum circuit.
observable (instance of Observable) – obserbable considerd.
shots (int, default - None) – number of measurements for estimating the expectation value.
precise (bool, default - False) – precise calculation (only qlazy and qulacs) or estimation by measurements.
init (instance of QState, MPState) – initial quantum state

Returns

expval – expectation value

Return type

complex

Examples

>>> # simple example
>>> from qlazy import QCirc, Backend
>>> from qlazy.Observable import X,Y,Z
>>> bk = Backend(product='qlazy', device='qstate_simulator')
>>> ob = Z(0)*X(1)
>>> qc = QCirc().h(0).cx(0,1)
>>> exp = bk.expect(qcirc=qc, shots=10000, observable=ob)
>>> print(exp.real)
>>> 0.0074

classmethod ibmq_devices()[source]¶: get ibmq’s devices list

classmethod products()[source]¶: get products list

classmethod qlazy_devices()[source]¶: get qlazy’s devices list

classmethod qulacs_devices()[source]¶: get qulacs’s devices list

run(qcirc=None, shots=1, cid=None, out_state=False, init=None, **kwargs)[source]¶

run the quantum circuit.

Parameters

qcirc (instance of QCirc) – quantum circuit.
shots (int, default 1) – number of measurements.
cid (list, default None) – classical register id list to count frequency.
out_state (bool, default False) – output classical and quantum information after execting circuit. (only for qlazy’s qstate and stabilizer simulator)
init (instance of QState, Stabilizer, MPState) – initial quantum state

Returns

result – measurement result.

Return type

incetance of Result

Examples

>>> # simple example
>>> from qlazy import QCirc, Backend
>>> bk = Backend(product='qlazy', device='qstate_simulator')
>>> qc = QCirc().h(0).cx(0,1).measure(qid=[0,1], cid=[0,1])
>>> result = bk.run(qcirc=qc, shots=100)
>>> print(result.frequency)
Counter({'00': 51, '11': 49})
>>> ...
>>> # control quantum gate by measured results
>>> from qlazy import QCirc, Backend
>>> bk = Backend(product='qlazy', device='qstate_simulator')
>>> qc = QCirc.h(0)
>>> qc.cx(0,1).measure(qid=[0],cid=[0])
>>> qc.x(0, ctrl=0).x(1, ctrl=0).measure(qid=[0,1], cid=[0,1])
>>> result = bk.run(qcirc=qc, shots=100)
>>> print(result.frequency)
Counter({'00': 100})

class qlazy.CMem(cmem_num, **kwargs)[source]¶

Bases: Structure

Classical Memory

cmem_num¶

number of the classical register (classical memory size).

Type: int

bit_array¶

bit array of classical memory.

Type: list (int)

bit_array¶: Structure/Union member

property bits¶: bit list of classical memory.

clone()[source]¶

get the copy of the classical memory.

Parameters: None –
Returns: cmem – copy of the original classical memory.
Return type: instance of CMem

cmem_num¶: Structure/Union member

get_bits()[source]¶

get bit list of the classical memory.

Parameters: None –
Returns: bits – bits array of the classical memory
Return type: numpy.ndarray (int)

set_bits(bits)[source]¶

set bit list to the classical memory.

Parameters: bits (list) – bits array of the classical memory
Return type: None

class qlazy.DensOp(qubit_num=0, qstate=None, prob=None, matrix=None, **kwargs)[source]¶

Bases: Structure, QObject

Density Operator

row¶

dimension of density operator (= 2**qubit_num).

Type: int

col¶

dimension of density operator (= 2**qubit_num).

Type: int

element¶

matrix elements of density operator.

Type: list of list of complex

add(densop=None)[source]¶

add the density operator.

Parameters: densop (instance of DensOp) – density operator to add.
Returns: self
Return type: instance of DensOp

Notes

This method change the original density operator.

classmethod add_method(method)[source]¶

add method (custum gate).

Parameters: method (func) – method (custum gate) to add.

Examples

>>> def bell(self, q0, q1):
>>>     self.h(q0).cx(q0,q1)
>>> ...
>>> DensOp.add_method(bell)
>>> qs = DensOp(qubit_num=2)
>>> qs.bell(0,1)
>>> ...

classmethod add_methods(*methods)[source]¶

add methods (custum gates).

Parameters: methods (func, func, ...) – arguments of methods (custum gates) to add.

Examples

>>> def bell(self, q0, q1):
>>>     self.h(q0).cx(q0,q1)
>>>     return self
>>> ...
>>> def flip(self, q0, q1):
>>>     self.x(q0).x(q1)
>>>     return self
>>> ...
>>> DensOp.add_methods(bell, flip, ...)
>>> de = DensOp(qubit=2)
>>> de.bell(0,1)
>>> de.flip(0,1)
>>> ...

amp_dump(q, prob=0.0)[source]¶

execute the quantum channel of amplitude dumping.

Parameters

q (int) – qubit id to execute.
prob (float) – probability of the quantum channel.

Returns

self

Return type

instance of DensOp

apply(matrix=None, qid=None, dire='both')[source]¶

apply the matrix to density operator. (= [matrix] * [self] * [dagger of matrix])

Parameters: matrix (list of list) – matrix to apply.
Return type: None

Notes

If ‘qid’ isn’t set, dimension of the matrix must be equal to dimension of the density operator. If ‘qid’ is set, dimension of the matrix must be equal to the 2 power of ‘qid’ length.

bit_flip(q, prob=0.0)[source]¶

execute the quantum channel of bit flip.

Parameters

q (int) – qubit id to execute.
prob (float) – probabillity of the quantum channel.

Returns

self

Return type

instance of DensOp

bit_phase_flip(q, prob=0.0)[source]¶

execute the quantum channel of bit and phase flip.

Parameters

q (int) – qubit id to execute.
prob (float) – probability of the quantum channel.

Returns

self

Return type

instance of DensOp

buf_id¶: Structure/Union member

buffer_0¶: Structure/Union member

buffer_1¶: Structure/Union member

clone()[source]¶

get the copy of density operator.

Parameters: None –
Returns: densop – copy of the original density operator.
Return type: instance of DensOp

col¶: Structure/Union member

composite(num=0)[source]¶

get the composite density operator of same density operators.

Parameters: num (int) – number of density operators..
Returns: de – composite density operator.
Return type: instance of DensOp

cond_entropy(qid_0=None, qid_1=None)[source]¶

get the conditional entropy.

Parameters

qid_0 (list of int) – qubit id’s list (sub-system) to calculate the entropy.
qid_1 (list of int) – qubit id’s list (sub-system) to calculate the entropy.

Returns

ent – conditianal entropy (S(qid_0|qid_1)).

Return type

float

classmethod create_register(num)[source]¶

create registers (qubit id’s list) and initialize zero.

Parameters: num (int) – qubit number you want to use.
Returns: qid – qubit id’s list.
Return type: list of int

Examples

>>> qid = DensOp.create_register(3)
>>> print(qid)
[0,0,0]

classmethod del_all(*densops)[source]¶

free memory of the all density operators.

Parameters: densops (instance of DensOp,instance of DensOp,...) – set of DensOp instances
Return type: None

depolarize(q, prob=0.0)[source]¶

execute the quantum channel of depolarize.

Parameters

q (int) – qubit id to execute.
prob (float) – probability of the quantum channel.

Returns

self

Return type

instance of DensOp

distance(densop=None, qid=None)[source]¶

get the trace distance with the density operator.

Parameters

densop (instance of DensOp) – density operator to get the trace distance.
qid (list of int, default - all of the qubit id's list) – qubit id’s list.

Returns

dis – trace distance.

Return type

float

property element¶: matrix elements of density operator.

elm¶: Structure/Union member

entropy(qid=None)[source]¶

get the von neumann entropy (or entanglement entropy).

Parameters: qid (list of int, default - list all of the qubit id) – qubit id’s list (sub-system) to calculate the entropy.
Returns: ent – von neumann entropy.
Return type: float

expect(matrix=None)[source]¶

get the expectation value of matrix under this density operator.

Parameters: matrix (list of list of complex) – matrix expression of hermitian operator.
Returns: value – expectation value.
Return type: float

Notes

‘matrix’ must be hermitian, and its dimension is equal to the dimension of density operator.

fidelity(densop=None, qid=None)[source]¶

get the fidelity with density operator.

Parameters

densop (instance of DensOp) – density operators to get fidelity.
qid (list of int, default - all of the qubit id's list) – qubit id’s list.

Returns

fid – fidelity of two density operators.

Return type

float

gbank¶: Structure/Union member

get_elm(qid=None)[source]¶

get the matrix elements of density operator.

Parameters: qid (list of int, default - list of all of the qubit id) – qubit id’s list.
Returns: elm – elements of the density matrix.
Return type: list of complex

Notes

If ‘qid’ is set, matrix elements of specified density operator are got after partial trace for remaining qubits. If no qubits are specified, you get all matrix elements of the density operator.

classmethod init_register(*args)[source]¶

initialize registers (qubit id’s list).

Parameters: args (list, list,...) – arguments of qubit registers.
Returns: idx – total qubit number.
Return type: int

Examples

>>> qid_0 = DensOp.create_register(3)
>>> qid_1 = DensOp.create_register(2)
>>> print(qid_0, qid_1)
[0,0,0] [0,0]
>>> qnum = DensOp.init_register(qid_0, qid_1)
>>> print(qnum, qid_0, qid_1)
5 [0,1,2] [3,4]

instrument(kraus=None, qid=None, measured_value=None)[source]¶

instrument to the density operator

Parameters

kraus (list of list of comprex) – Kraus operators.
qid (list) – qubit id’s list to measure.
measured_value (int) – index of measurement (in the case of selective measurement).

Returns

self

Return type

instance of DensOp

Notes

If ‘measured_value’ is set, selective measurement of the index corresponding to ‘measured_value’ is done (but not normalize). If ‘measured_value’ is not set, non-selective measurement is done (only operator sum for the Kraus operators are executed). This method does change the original density operator.

join(de_list)[source]¶

get tensor product state (density operator) of the density operators’ list.

Parameters: de_list (list (DensOp)) – list of density operators.
Returns: de_out – tensor product state (density operator).
Return type: instance of DensOp

static mat_norm(mat)[source]¶: norm of the matrix

static mat_spectrum(mat)[source]¶: spectrum of the hermitian matrix

static mat_sqrt(mat)[source]¶: square root of the matrix

classmethod mix(densop=None, prob=None)[source]¶

linear sum of the density operators.

Parameters

densop (list of instances of DensOp) – densitiy operators.
prob (list of float) – probabilities (coefficients of the linear sum).

mul(factor=1.0)[source]¶

multiply the density operator by factor.

Parameters: factor (float, default 1.0) – number to multiply.
Returns: self
Return type: instance of DensOp

Notes

This method change the original density operator.

mutual_info(qid_0=None, qid_1=None)[source]¶

get the mutual information.

Parameters

qid_0 (list of int) – qubit id’s list (sub-system) to calculate the mutual information.
qid_1 (list of int) – qubit id’s list (sub-system) to calculate the mutual information.

Returns

ent – mutual information (S(qid_0:qid_1)).

Return type

float

operate_gate(kind=None, qid=None, phase=0.0, **kwargs)[source]¶

operate gate

Parameters

kind (int) – kind of the gate
qid (list) – quantum id list
phase (float) – phase for rotation gate

Returns

self – quantum state

Return type

instance of DensOp

operate_qcirc(qcirc, qctrl=None)[source]¶

operate quantum circuit

Parameters

qcirc (instance of QCirc) – quantum circuit
qctrl (int) – control qubit id

Returns

self – quantum state after executing the quantum circuit

Return type

instance of DensOp

Notes

The quantum circut must be unintary.

partial(qid=None)[source]¶

get the density operator for partial system.

Parameters: qid (list of int) – qubit id’s list to show.
Returns: densop – density operator for partial system (= partial trace for remaining system).
Return type: instance of DensOp

patrace(qid=None)[source]¶

get the partial trace of density operator.

Parameters: qid (list of int) – qubit id’s list to show.
Returns: densop – density operator after partial trace.
Return type: instance of DensOp

phase_dump(q, prob=0.0)[source]¶

execute the quantum channel of phase dumping.

Parameters

q (int) – qubit id to execute.
prob (float) – probability of the quantum channel.

Returns

self

Return type

instance of DensOp

phase_flip(q, prob=0.0)[source]¶

execute the quantum channel of phase flip.

Parameters

q (int) – qubit id to execute.
prob (float) – probability of the quantum channel.

Returns

self

Return type

instance of DensOp

probability(kraus=None, povm=None, qid=None)[source]¶

get the probabilities for measuring operators. (Kraus or POVM operators).

Parameters

kraus (list of list of comprex) – Kraus operators.
povm (list of list of comprex) – POVM operators.
qid (list) – qubit id’s list to measure.

Returns

prob – probabilities for measuring operators.

Return type

list of float

Notes

Either ‘kraus’ or ‘povm’ must be set. If ‘qid’ is not set, all of the qubits are measured, the dimention of Kraus or POVM operator must be equal to the dimension of density operator. If ‘qid’ is set, the part of qubits are measured, the dimension of Kraus or POVM operator must be equal to the 2 power of ‘qid’ length. This method does not change the original density operator.

relative_entropy(densop=None)[source]¶

get the relative entropy.

Parameters: densop (instance of DensOp) – density operator to get the relative entropy.
Returns: ent – relative entropy.
Return type: float

row¶: Structure/Union member

show(qid=None, nonzero=False)[source]¶

show the elements of density operator.

Parameters

qid (list of int, default - list of all of the qubit id) – qubit id’s list to show.
nonzero (bool, default False) – if True, only non-zero elements are printed.

Return type

None

Notes

If ‘qid’ is set, it shows the matrix elements of density operator for partial quantum system specified by ‘qid’. If ‘qid’ isn’t set, it shows the matrix elements of whole quantum system.

Examples

>>> de = DensOp(qubit_num=1)
>>> ...
>>> de.show()
elm[0][0] = +0.5000+0.0000*i : 0.2500 |++++
elm[0][1] = +0.0000+0.0000*i : 0.0000 |
elm[1][0] = +0.0000+0.0000*i : 0.0000 |
elm[1][1] = +0.5000+0.0000*i : 0.2500 |++++
...
>>> de.show(nonzero=True)
elm[0][0] = +0.5000+0.0000*i : 0.2500 |++++
elm[1][1] = +0.5000+0.0000*i : 0.2500 |++++

spectrum()[source]¶

get the spectrum.

Parameters

None –

Returns

qstate (list of QState) – list of the quantum state basis.
prob (list of float) – list of coefficients for each quantum states basis.

sqtrace()[source]¶

get the square trace of density operator.

Parameters: None –
Returns: sqtrace – square trace of the density operator.
Return type: float

tenspro(densop)[source]¶

get the tensor product with density operator.

Parameters: densop (instance of DensOp) – density operator to get the tensor product..
Returns: densop_out – tensor produt of ‘self’ and ‘densop’.
Return type: instance of DensOp

trace()[source]¶

get the trace of density operator.

Parameters: None –
Returns: trace – trace of the density operator.
Return type: float

von_neumann_entropy()[source]¶

get the von neumann entropy (or entanglement entropy).

Parameters: None –
Returns: ent – von neumann entropy.
Return type: float

class qlazy.MPState(qubit_num=0, bits_str=None, tensors=None, max_truncation_err=1e-06, **kwargs)[source]¶

Bases: FiniteMPS, QObject

Matrix Product State

qubit_num¶

number of qubits (number of nodes)

Type: int

bond_dimensions¶

list of bond dimensions

Type: list (int)

max_truncation_err¶

maximum of truncation error

Type: float

tensors¶

list of 3-rank tensors for the matrix product

Type: list (np.ndarray)

property amp¶: elements of quantum state vector.

clone()[source]¶

get the copy of the matrix product state.

Parameters: None –
Returns: mps – copy of the original matrix product state.
Return type: instance of MPState

classmethod del_all(*mpstates)[source]¶

free memory of the all matrix product states.

Parameters: mpstates (instance of MPState,instance of MPState,...) – set of MPState instances
Return type: None

expect(observable=None)[source]¶

get the expectation value for observable under the matrix product state.

Parameters: observable (instance of Observable) – obserbable of the system.
Returns: expect – expect value.
Return type: complex

See also

Obserbable

fidelity(mps, qid=None)[source]¶

get fidelity with the matrix product state.

Parameters

mps (instance of MPState) – one of the two matrix product states.
qid (list of int) – qubit id’s list.

Returns

fid – fidelity of the two matrix product states. absolute value of the inner product of two matrix product states.

Return type

float

Notes

If ‘qid’ is set, you can get the fidelity for partial quantum state. If the specified quantum system are entangled with the remaining system, output value is probabilistic, while original quantum states do not change.

get_amp(qid=None)[source]¶

get the elements of quantum state vector.

Parameters: qid (list of int, default - list of all of the qubit id) – qubit id’s list.
Returns: ret – elements of the quantum state vector.
Return type: numpy.ndarray (complex)

Notes

If ‘qid’ is set, specified qubit state are got after remaining qubits are measured. So if the specified qubits are entangled with the remaining qubits, output quantum state is probabilistic. If no qubits are specified, you get all elements of the quantum state.

inpro(mps, qid=None)[source]¶

get the inner product with matrix product state.

Parameters

mps (instance of MPState) – one of the two matrix product state.
qid (list of int, default - list of all of the qubit id) – qubit id’s list.

Returns

inp – inner produt (<self|mps>).

Return type

complex

Notes

If ‘qid’ is set, you can get the inner product for partial quantum state. If the specified quantum system are entangled with the remaining system, output value is probabilistic, while original quantum states do not change.

m(qid=None, shots=1)[source]¶

measurement in Z-direction

Parameters

qid (list of int) – qubit id list to measure.
shots (int, default 1) – number of measurements.

Returns

md – measurement data.

Return type

instance of MDataMPState

See also

MDataMPState

property max_truncation_err¶

measure(qid=None)[source]¶

one shot measurement in Z-direction.

Parameters: qid (list of int) – qubit id list to measure.
Returns: mval – measurement value.
Return type: str

Examples

>>> mps = MPState(qubit_num=2).h(0).cx(0,1)
>>> mps.show()
>>> print(mps.measure(qid=[0,1]))
>>> mps.show()
c[00] = +0.7071+0.0000*i : 0.5000 |++++++
c[01] = +0.0000+0.0000*i : 0.0000 |
c[10] = +0.0000+0.0000*i : 0.0000 |
c[11] = +0.7071+0.0000*i : 0.5000 |++++++
00
c[00] = +1.0000+0.0000*i : 1.0000 |+++++++++++
c[01] = +0.0000+0.0000*i : 0.0000 |
c[10] = +0.0000+0.0000*i : 0.0000 |
c[11] = +0.0000+0.0000*i : 0.0000 |

operate_1qubit_gate(gate_str, q, para=0.0)[source]¶

operate 1-qubit gate.

Parameters

gate_str (str) – gate stiring (ex. ‘x’,’y’,’z’,’h’,’s’, ..)
q0 (int) – qubit id.
para (float) – angle for rotation gate (unit of angle is PI radian).

Returns

self

Return type

instance of MPState

operate_2qubit_gate(gate_str, q0, q1, para=0.0)[source]¶

operate 2-qubit gate.

Parameters

gate_str (str) – gate stiring (ex. ‘cx’,’cy’,’cz’,’ch’,’crz’, ..)
q0 (int) – qubit id.
q1 (int) – qubit id.
para (float) – angle for rotation gate (unit of angle is PI radian).

Returns

self

Return type

instance of MPState

operate_gate(kind=None, qid=None, phase=0.0, **kwargs)[source]¶

operate gate

Parameters

kind (int) – kind of the gate
qid (list) – quantum id list
phase (float) – phase for rotation gate

Returns

self – quantum state

Return type

instance of MPState

operate_qcirc(qcirc, qctrl=None)[source]¶

operate quantum circuit

Parameters

qcirc (instance of QCirc) – quantum circuit
qctrl (int) – control qubit id

Returns

self – quantum state after executing the quantum circuit

Return type

instance of MPState

Notes

The quantum circut must be unintary.

property qubit_num¶

reset_qubits(qid=None)[source]¶

reset to |00..0> state.

Parameters: qid (list, default - qubit id's list for all of the qubits) – qubit id’s list to reset.
Returns: self – matrix product state.
Return type: instance of MPState

Notes

If ‘qid’ is set, specified qubits are reset after measurement. So if the specified qubits are entangled with the remaining qubits, output quantum state is probabilistic. If no qubits are set, all qubits are zero reset.

show(qid=None, nonzero=False, preal=0)[source]¶

show the quantum state (elements of the state vector and probabilities).

Parameters

qid (list of int, default - list of all of the qubit id) – qubit id’s list to show.
nonzero (bool, default False) – if True, only non-zero amplitudes are printed.
preal (int, default 0) – state id to make positive real amplitude. (if -1 is set, do not go out the global phase factor)

Return type

None

Notes

If ‘qid’ is set, it shows the elements of quantum state vector for partial quantum system specified by ‘qid’. If the specified quantum system are entangled with the remaining system, output is probabilistic. If no qubits are specified, it shows the whole quantum state. This method does not change the original quantum state.

Examples

>>> mps = MPState(qubit_num=2).h(0).cx(0,1)
>>> mps.show()
c[00] = +0.7071+0.0000*i : 0.5000 |++++++
c[01] = +0.0000+0.0000*i : 0.0000 |
c[10] = +0.0000+0.0000*i : 0.0000 |
c[11] = +0.7071+0.0000*i : 0.5000 |++++++
...
>>> mps.show(qid=[0])
c[0] = +1.0000+0.0000*i : 1.0000 |+++++++++++
c[1] = +0.0000+0.0000*i : 0.0000 |
...
>>> mps.show(nonzero=True)
c[00] = +0.7071+0.0000*i : 0.5000 |++++++
c[11] = +0.7071+0.0000*i : 0.5000 |++++++

class qlazy.Observable(string=None)[source]¶

Bases: object

Observable for quantum many-body spin system.

base¶

observable

Type: instance of ObservableBase

string¶

string of observable description ex) “-2.0+Z_0*Z_1+X_0+X_1” for 2-qubit system

Type: str

weighted_pp_list¶

weighted pauli product list

Type: list of dict ({‘weight’:weight, ‘pp’:pauli_product})

qubit_num¶

total qubit number

Type: int

add_wpp(weight=1.0, pp=None)[source]¶

add the weighted pauli product to the list (self.weighted_pp_list).

Parameters

weight (float) – weight value correspond to the pauli product
pp (instance of PauliProduct) – pauli product

Returns

self – observable after adding weighted pauli product

Return type

instance of Ovservable

property base¶

clone()[source]¶

clone observable.

Parameters: None –
Returns: ob – observable
Return type: instance of Observable

get_idx_weight(pp)[source]¶

get index and weight value correspond to the pauli product.

Parameters

pp (instance of PauliProduct) – pauli product

Returns

idx (int) – index number of the list (self.weighted_pp_list) correspond to the pauli product
weight (float) – weight value correspond to the pauli product

get_observable_base()[source]¶

get ObservableBase instance.

Parameters: None –
Returns: ob_base – observable
Return type: instance of ObservableBase

get_qubit_num()[source]¶

get the total qubit number considerd

Parameters: None –
Returns: qubit_num – total qubit number considerd by the observable.
Return type: inst

get_string()[source]¶

get string of observable.

Parameters: None –
Returns: s – string of observable
Return type: str

get_weighted_pp_list(string)[source]¶

get weighted pauli product list.

Parameters: string (str) – string of observable
Returns: weighted_pp_list – weighted pauli product list
Return type: list of dict (weight:pauli_product)

is_hermitian()[source]¶

hermitian or not

Parameters: None –
Returns: ans – is the observable hermitian or not
Return type: bool

property qubit_num¶

recalc_weight()[source]¶

recalculate the weights of weighted_pp_list: (weight <= weight * pp.factor, pp.factor <= 1.0)

Parameters: None –
Returns: ans – is the observable hermitian or not
Return type: bool

property string¶

class qlazy.ObservableBase(string=None, **kwargs)[source]¶

Bases: Structure

Observable for quantum many-body spin system.

array_num¶: Structure/Union member

spin_num¶: Structure/Union member

spro_array¶: Structure/Union member

class qlazy.PauliProduct(pauli_str, qid=None, factor=1 + 0j)[source]¶

Bases: object

Pauli Product

qid¶

list of qubit id.

Type: list of int

pauli_list¶

list of pauli operators.

Type: list of str

factor¶

factor of pauli product.

Type: complex

get_binary_rep(qubit_num=None)[source]¶

get binary representation of pauli product.

Parameters: qubit_num (int, default - max(self.qid)+1) – qubit number of binary representation.
Returns: binary_rep – output binary representation of the pauli product.
Return type: list of int

Examples

>>> pp = PauliProduct(pauli_str="XYZ", qid=[0,1,2])
>>> print(pp.get_binary_rep())
[1,1,0,0,1,1]

get_qubit_num()[source]¶

get the total qubit number considerd

Parameters: None –
Returns: qubit_num – total qubit number considerd by the pauli product.
Return type: inst

is_commute(pp)[source]¶

is pauli product commute to other pauli product or not.

Parameters: pp (instance of PauliProduct) – pauli product
Returns: ans – commute (True) or anti-commute (False)
Return type: bool

tenspro(pp)[source]¶

get tensor product with other pauli product.

Parameters: pp (instance of PauliProduct) – pauli product
Returns: pp_out – output pauli product
Return type: instance of PauliProduct

class qlazy.QCirc(**kwargs)[source]¶

Bases: Structure, QObject

Quantum Circuit

qubit_num¶

qubit number of the quantum state (= log(state_num)).

Type: int

cmem_num¶

number of the classical register.

Type: int

gate_num¶

number of gates in the quantum circuit.

Type: int

first¶

first gate of the quantum circuit.

Type: object

last¶

last gate of the quantum circuit.

Type: object

tag_table¶

tag table..

Type: object

add_control(qctrl=None)[source]¶

add control qubit to quantum circuit

Parameters: qctrl (int) – control qubit id
Returns: qc_out – quantum circuit after adding control qubit
Return type: instance of QCirc

add_gates(gates=None)[source]¶

add list of gates to the circuit.

Parameters: gates (list of dict) – gates of the quantum circuit gates = [{‘kind’:kind, ‘qid’:qid, ‘phase’:phase, ‘cid’:cid, ‘ctrl’:ctrl}, …] - kind: gate name - qid: qubit id - phase: phase parameter (non-zero only for rotation gates) - cid: classical register id (set only for measurement gate) - ctrl: classical register id for controlling gate operation
Returns: self – circuit after adding gates
Return type: instance of QCirc

Notes

This method changes original quantum circuit.

all_gates_measurement()[source]¶

gates of the qcirc are all measurement

Parameters: None –
Returns: ans – True if all gates are measurement, False if otherwise
Return type: bool

append_gate(kind=None, qid=None, para=None, c=None, ctrl=None, tag=None)[source]¶

append gate to the end of the circuit.

Parameters

kind (int) – kind of gate
qid (list (int)) – list of qubit id
para (list (float), default None) – list of parameters
c (int, default None) – classical register id to store measured data
ctrl (int, default None) – classical register id to controll the gate

Return type

None

clone()[source]¶

clone quantum circuit.

Parameters: None –
Returns: qcirc – quantum circuit
Return type: instance of QCirc

cmem_num¶: Structure/Union member

dump(file_path)[source]¶

dump the circuit

Parameters: file_path (str) – file path of dump file
Return type: None

equivalent(qc, *args, **kwargs)[source]¶

two quantum circuits are equivalent or not (using pyzx’s verify_equality method).

Parameters: None –
Returns: ans
Return type: bool

Notes

Non-unitary gates: measure, reset are not supported.

first¶: Structure/Union member

classmethod from_pyzx(zxqc)[source]¶

get pyzx’s Circuit instance.

Parameters: zxqc (instance of pyzx's Circuit) – quantum circuit
Returns: qc – quantum circuit
Return type: instance of QCirc

Notes

Non-unitary gates: measure, reset are not supported.

classmethod from_qasm(string)[source]¶

get QCirc instance from OpenQASM 2.0 string.

Parameters: None –
Returns: qcirc
Return type: instance of QCirc

Notes

Non-unitary gates (measure, reset) and user customized gates are not supported. Supported gates are ‘x’, ‘y’, ‘z’, ‘h’, ‘s’, ‘sdg’, ‘t’, ‘tdg’, ‘cx’, ‘cz’, ‘ch’, ‘rx’, ‘rz’, ‘crz’.

classmethod from_qasm_file(file_path)[source]¶

get QCirc instance from OpenQASM 2.0 file.

Parameters: file_path (str) – file path name of OpenQASM 2.0 file
Returns: qcirc
Return type: instance of QCirc

Notes

Non-unitary gates (measure, reset) and user customized gates are not supported. Supported gates are ‘x’, ‘y’, ‘z’, ‘h’, ‘s’, ‘sdg’, ‘t’, ‘tdg’, ‘cx’, ‘cz’, ‘ch’, ‘rx’, ‘rz’, ‘crz’.

gate_num¶: Structure/Union member

classmethod generate_random_gates(qubit_num=0, gate_num=0, phase=None, prob=None, **kwargs)[source]¶

generate circuit including random gates.

Parameters

qubit_num (int) – number of qubits
gate_num (int) – numbner of gates
phase (tupple of float) – phases selected randomly
prob (dict) –

{‘x’:prob_x, ‘z’:prob_z, ‘h’:prob_h, ‘s’:prob_s, ‘s_dg’:prob_s_dg,
’t’:prob_t, ‘t_dg’:prob_t_dg, ‘rx’:prob_rx, ‘rz’:prob_rz, ‘cx’:prob_cx, ‘cz’:prob_cz, ‘ch’:prob_ch, ‘crz’:prob_crz}
- prob_x: probability of x
- prob_z: probability of z
- prob_h: probability of h
- prob_s: probability of s
- prob_s_dg: probability of s_dg
- prob_t: probability of t
- prob_t_dg: probability of t_dg
- prob_rx: probability of rx
- prob_rz: probability of rz
- prob_cx: probability of cx
- prob_cz: probability of cz
- prob_ch: probability of ch
- prob_crz: probability of crz

Returns

qcirc – generated circuit

Return type

instance of QCirc

Examples

>>> qc = QCirc.generate_random_gates(qubit_num=5, gate_num=100,
phase_unit=0.25, prob={'h':3, 'cx':7, 'rz':1})

Notes

each probability values are normalized so that the sum of the probabilities is 1.0.
Phase parameters of rotation gates are selected randomly in the element of ‘phase’.

get_gates()[source]¶

get list of gates from the circuit.

Parameters

None –

Returns

gates – gates of the quantum circuit gates = [{‘kind’:kind, ‘qid’:qid, ‘phase’:phase, ‘cid’:cid, ‘ctrl’:ctrl}, …] - kind: gate name - qid: qubit id - phase: phase parameter (non-zero only for rotation gates) - para: [phase, gphase, factor]

gphase means global phase used only when adding control to p gate

cid: classical register id (set only for measurement gate)
ctrl: classical register id to control gate operation

Return type

list of dict

get_params()[source]¶

get parameters for each tag

Parameters: None –
Returns: params – tag and phase dictionary ex) {‘tag1’: phase1, ‘tag2’: phase2, …}
Return type: dict

Examples

>>> qc = QCirc().h(0).rz(0, tag='foo').rx(0, tag='bar')
>>> qc.set_params(params={'foo': 0.2, 'bar': 0.4})
>>> print(qc.get_params())
{'foo': 0.2, 'bar': 0.4}

get_stats()[source]¶

get statistics of the circuit.

Parameters: None –
Returns: stats – {‘qubit_num’:qubit_num, ‘cmem_num’:cmem_num, ‘gate_num’:gate_num, ‘gate_freq’:gate_freq} - qubit_num: number of qubits - cmem_num: number of classical bits - gate_num: number of gates - gate_freq: frequency of gates (Counter)
Return type: dict

get_tag_phase(tag)[source]¶

get parameter (= phase) for the tag

Parameters: tag (str) – tag of phase parameter for parametric quantum circuit.
Returns: phase – rotation angle (unit of angle is PI radian) for the tag.
Return type: float

Examples

>>> qc = QCirc().h(0).rz(0, tag='foo').rx(0, tag='bar')
>>> qc.set_params(params={'foo': 0.2, 'bar': 0.4})
>>> print(qc.get_tag_phase('foo'))
0.2

is_clifford()[source]¶

the quantum circuit is clifford or not

Parameters: None –
Returns: ans – True if the quantum circuit unitary, False if otherwise
Return type: bool

is_equal(qc)[source]¶

eaual or not.

Parameters: qc (instance of QCirc) – quantum circuit (merged)
Returns: qcirc – quantum circuit (result)
Return type: instance of QCirc

is_unitary()[source]¶

the quantum circuit is unitary or not

Parameters: None –
Returns: ans – True if the quantum circuit unitary, False if otherwise
Return type: bool

kind_first()[source]¶

get kind of first gate of the circuit.

Parameters: None –
Returns: kind_list – kind of first quantum gate of quantum circuit
Return type: int

Note

return None if none of gates included

kind_list()[source]¶

get list of kinds from the circuit.

Parameters: None –
Returns: kinds – kinds of the quantum circuit
Return type: list of kind

Note

return None if none of gates included

last¶: Structure/Union member

classmethod load(file_path)[source]¶

load the circuit

Parameters: file_path (str) – file path of dump file
Returns: qcirc – loaded circuit
Return type: instance of QCirc

merge(qc)[source]¶

merge two quantum circuits.

Parameters: qc (instance of QCirc) – quantum circuit (merged)
Returns: qcirc – new quantum circuit (merge result)
Return type: instance of QCirc

merge_mutable(qc)[source]¶

merge a quantum circuit with another one.

Parameters: qc (instance of QCirc) – quantum circuit (merged)
Returns: self – quantum circuit (merge result)
Return type: instance of QCirc

Notes

This method changes original quantum circuit.

multiple(other)[source]¶

integer multiple for quantum circuit

Parameters: other (instance of QCirc / int) – quantum circuit / number
Returns: qc – quantum circuit after multiplication
Return type: instance of QCirc

operate_gate(kind=None, qid=None, cid=None, phase=0.0, gphase=0.0, fac=1.0, tag=None, ctrl=None)[source]¶

operate gate

Parameters

kind (int) – kind of the gate
qid (list) – quantum id list
cid (list) – classical register (memory) id list
phase (float) – phase for rotation gate
gphase (float) – global phase for rotation gate
fac (float) – factor of phase value

Returns

self – quantum circuit

Return type

instance of QCirc

operate_qcirc(qcirc, qctrl=None)[source]¶

operate quantum circuit

Parameters

qcirc (instance of QCirc) – quantum circuit
qctrl (int) – control qubit id

Returns

self – quantum state after executing the quantum circuit

Return type

instance of QState

optimize(*args, **kwargs)[source]¶

optimize the quantum circuit (using pyzx’s full_optimize method).

Parameters: None –
Returns: qc – optimized circuit
Return type: instance of QCirc

Notes

Non-unitary gates: measure, reset are not supported.

pop_gate()[source]¶

pop first gate of the circuit.

Parameters: None –
Returns: gate – tupple of (kind, qid, para, c, ctrl) - kind … kind of gate - qid … qubit id list - para … parameters for rotation - c … classical register ID to store measured data (only for measurement gate) - ctrl … classical register id to controll the gate
Return type: tupple of (int, [int,int], [float,float,float], int, int)

Notes

This method changes original quantum circuit.

qubit_num¶: Structure/Union member

remap(qid=None, cid=None)[source]¶

remap qubit id and cmem id of quantum circuit

Parameters

qid (list (int)) – list of qubit id (quantum register)
cid (list (int)) – list of cmem id (classical memory or classical register)

Returns

qcirc – new quantum circuit after remapping

Return type

instance of QCirc

Examples

>>> qc = QCirc().h(0).cx(0,1).measure(qid=[0,1], cid=[0,1])
>>> qc.show()
q[0] -H-*-M---
q[1] ---X-|-M-
c  =/=====v=v=
2         0 1
>>> qc_new1 = qc.remap(qid=[1,0], cid=[1,0])
>>> qc_new1.show()
q[0] ---X---M-
q[1] -H-*-M-|-
c  =/=====v=v=
2         1 0
>>> qc_new2 = qc.remap(qid=[2,1], cid=[1,0])
>>> qc_new2.show()
q[0] ---------
q[1] ---X---M-
q[2] -H-*-M-|-
c  =/=====v=v=
2         1 0

Notes

Length of the qid must be equal to qubit_num of the original quantum circut. Length of cid must be equal to cmem_num of the original quantum circut. Elements of the qid and the cid must not be duplicated.

save(file_path)[source]¶

save the circuit

Parameters: file_path (str) – file path of dump file
Return type: None

set_params(params)[source]¶

set parameters for each tag

Parameters: params (dict) – tag and phase dictionary ex) {‘tag1’: phase1, ‘tag2’: phase2, …}
Return type: None

Examples

>>> qc = QCirc().h(0).rz(0, tag='foo').rx(0, tag='bar')
>>> qc.set_params(params={'foo': 0.2, 'bar': 0.4})
>>> print(qc)
h 0
rz(0.2) 0
rx(0.4) 0
>>> qc.set_params(params={'foo': 0.3, 'bar': 0.5})
>>> print(qc)
h 0
rz(0.3) 0
rx(0.5) 0

show(width=100)[source]¶

show the circuit

Parameters: width (int, default - 100) – width for line breaks and display long quantum circuit
Return type: None

split_unitary_non_unitary()[source]¶

split two part of the gate.

Parameters: None –
Returns: qc_pair – former part includes only unitary gates and later part includes non-unitary gate (measure or reset) first
Return type: tupple of (QCirc, Qcirc)

tag_table¶: Structure/Union member

to_pyzx()[source]¶

get pyzx’s Circuit instance.

Parameters: None –
Returns: zxqc – quantum circuit
Return type: instance of pyzx’s Circuit

Notes

Non-unitary gates: measure, reset are not supported.

to_qasm()[source]¶

get OpenQASM 2.0 string of the circuit.

Parameters: None –
Returns: qcirc_str
Return type: str

to_qasm_file(file_path)[source]¶

write to OpenQASM 2.0 file.

Parameters: file_path (str) – file path name of OpenQASM 2.0 file
Return type: None

to_string()[source]¶

get string of the circuit (qlazy format).

Parameters: None –
Returns: qcirc_str
Return type: str

class qlazy.QState(qubit_num=0, vector=None, seed=None, use_gpu=False, **kwargs)[source]¶

Bases: Structure, QObject

Quantum State

qubit_num¶

qubit number of the quantum state (= log(state_num)).

Type: int

state_num¶

dimension of the quantum state vector (= 2**qubit_num).

Type: int

amp¶

elements of the quantum state vector.

Type: list of complex

classmethod add_method(method)[source]¶

add method (custum gate).

Parameters: method (func) – method (custum gate) to add.

Examples

>>> def bell(self, q0, q1):
>>>     self.h(q0).cx(q0,q1)
>>>     return self
>>> ...
>>> QState.add_method(bell)
>>> qs = QState(qubit_num=2)
>>> qs.bell(0,1)
>>> ...

classmethod add_methods(*methods)[source]¶

add methods (custum gates).

Parameters: methods (func, func, ...) – arguments of methods (custum gates) to add.

Examples

>>> def bell(self, q0, q1):
>>>     self.h(q0).cx(q0,q1)
>>>     return self
>>> ...
>>> def flip(self, q0, q1):
>>>     self.x(q0).x(q1)
>>>     return self
>>> ...
>>> QState.add_methods(bell, flip, ...)
>>> qs = QState(2)
>>> qs.bell(0,1)
>>> qs.flip(0,1)
>>> ...

property amp¶: elements of quantum state vector.

apply(matrix=None, qid=None)[source]¶

apply matrix.

Parameters: matrix (list of list) – matrix to apply.
Returns: self
Return type: instance of QState

Notes

If ‘qid’ isn’t set, dimension of the matrix must be equal to the 2 power of qubit number of the system. If ‘qid’ is set, dimension of the matrix must be equal to the 2 power of ‘qid’ length.

bloch(q=0)[source]¶

get bloch angles.

Parameters

q (int) – qubit id

Returns

theta (float) – bloch angle with Z-axis
phi (float) – bloch angle with X-axis

Notes

the unit of angle is PI radian. for example, 0.5 means 0.5*PI (radian).

buf_id¶: Structure/Union member

buffer_0¶: Structure/Union member

buffer_1¶: Structure/Union member

camp¶: Structure/Union member

clone()[source]¶

get the copy of the quantum state.

Parameters: None –
Returns: qstate – copy of the original quantum state.
Return type: instance of QState

composite(num=1)[source]¶

get the composite state of same quantum states.

Parameters: num (int) – number of quantum states.
Returns: qs – composite quantum state.
Return type: instance of QState

classmethod create_register(num)[source]¶

create registers (qubit id’s) and initialize zero.

Parameters: num (int) – qubit number you want to use.

Examples

>>> qid = QState.create_register(3)
>>> print(qid)
[0,0,0]

classmethod del_all(*qstates)[source]¶

free memory of the all quantum states.

Parameters: qstates (instance of QState,instance of QState,...) – set of QState instances
Return type: None

evolve(observable=None, time=0.0, iteration=0)[source]¶

evolve the quantum state.

Parameters

observable (instance of Observable) – Hamiltonian of the system.
time (float) – period of time.
iter (int) – number of iteration.

Returns

self

Return type

instance of QState

Notes

The ‘iter’ value should be sufficiently larger than the ‘time’ value. This method change the original state.

See also

Obserbable

expect(observable=None)[source]¶

get the expectation value for observable under the quantum state.

Parameters: observable (instance of Observable) – obserbable of the system.
Returns: expect – expect value.
Return type: float

See also

Obserbable

fidelity(qstate, qid=None)[source]¶

get fidelity with the quantum state.

Parameters

qstate (instance of QState) – one of the two quantum states.
qid (list of int) – qubit id’s list.

Returns

fid – fidelity of two quantum states. absolute value of the inner product of two quantum states.

Return type

float

Notes

If ‘qid’ is set, you can get the fidelity for partial quantum state. If the specified quantum system are entangled with the remaining system, output value is probabilistic, while original quantum states do not change.

gbank¶: Structure/Union member

get_amp(qid=None)[source]¶

get the elements of quantum state vector.

Parameters: qid (list of int, default - list of all of the qubit id) – qubit id’s list.
Returns: ret – elements of the quantum state vector.
Return type: numpy.ndarray (complex)

Notes

If ‘qid’ is set, specified qubit state are got after remaining qubits are measured. So if the specified qubits are entangled with the remaining qubits, output quantum state is probabilistic. If no qubits are specified, you get all elements of the quantum state.

get_prob(qid=None)[source]¶

get the probability list of quantum state vector.

Parameters: qid (list of int, default - list of all of the qubit id) – qubit id’s list.
Returns: prob – key - bits string value - probability ex) {‘00’: 0.52, ‘11’: 0.48}
Return type: dict

classmethod init_register(*args)[source]¶

initialize registers (qubit id’s).

Parameters: args (list, list,...) – arguments of qubit registers.
Returns: idx – total qubit number.
Return type: int

Examples

>>> qid_0 = QState.create_register(3)
>>> qid_1 = QState.create_register(2)
>>> print(qid_0, qid_1)
[0,0,0] [0,0]
>>> qnum = QState.init_register(qid_0, qid_1)
>>> print(qnum, qid_0, qid_1)
5 [0,1,2] [3,4]

inpro(qstate, qid=None)[source]¶

get the inner product with quantum state.

Parameters

qstate (instance of QState) – one of the two quantum state.
qid (list of int, default - list of all of the qubit id) – qubit id’s list.

Returns

inp – inner produt (<self|qstate>).

Return type

complex

Notes

If ‘qid’ is set, you can get the inner product for partial quantum state. If the specified quantum system are entangled with the remaining system, output value is probabilistic, while original quantum states do not change.

join(qs_list)[source]¶

get tensor product state of the quantum states’ list.

Parameters: qs_list (list (QState)) – list of quantum states.
Returns: qs_out – tensor product state.
Return type: instance of QState

m(qid=None, shots=1, angle=0.0, phase=0.0)[source]¶

measurement in any direction (default: Z-axis).

Parameters

qid (list of int) – qubit id list to measure.
shots (int, default 1) – number of measurements.
angle (float, default 0.0) – direction of measurement (angle with Z-axis).
phase (float, default 0.0) – direction of measurement (phase around Z-axis).

Returns

md – measurement data.

Return type

instance of MData

Examples

>>> qs = QState(2).h(0).cx(0,1)
>>> md = qs.m()
>>> md.show(shots=100)
direction of measurement: z-axis
frq[00] = 52
frq[11] = 48
last state => 11

See also

MData

mb(qid=None, shots=1)[source]¶: bell measurement

measure(qid=None)[source]¶

one shot measurement in Z-direction.

Parameters: qid (list of int) – qubit id list to measure.
Returns: mval – measurement value.
Return type: str

Examples

>>> qs = QState(qubit_num=2).h(0).cx(0,1)
>>> qs.show()
>>> print(qs.measure(qid=[0,1]))
>>> qs.show()
c[00] = +0.7071+0.0000*i : 0.5000 |++++++
c[01] = +0.0000+0.0000*i : 0.0000 |
c[10] = +0.0000+0.0000*i : 0.0000 |
c[11] = +0.7071+0.0000*i : 0.5000 |++++++
00
c[00] = +1.0000+0.0000*i : 1.0000 |+++++++++++
c[01] = +0.0000+0.0000*i : 0.0000 |
c[10] = +0.0000+0.0000*i : 0.0000 |
c[11] = +0.0000+0.0000*i : 0.0000 |

mx(qid=None, shots=1)[source]¶

X-axis measurement.

Parameters

qid (list of int) – qubit id list to measure.
shots (int, default 1) – number of measurements.

Returns

md – measurement data.

Return type

instance of MData

See also

MData

my(qid=None, shots=1)[source]¶

Y-axis measurement.

Parameters

qid (list of int) – qubit id list to measure.
shots (int, default 1) – number of measurements.

Returns

md – measurement data.

Return type

instance of MData

See also

MData

mz(qid=None, shots=1)[source]¶

Z-axis measurement.

Parameters

qid (list of int) – qubit id list to measure.
shots (int, default 1) – number of measurements.

Returns

md – measurement data.

Return type

instance of MData

See also

MData

operate_gate(kind=None, qid=None, phase=0.0, **kwargs)[source]¶

operate gate

Parameters

kind (int) – kind of the gate
qid (list) – quantum id list
phase (float) – phase for rotation gate

Returns

self – quantum state

Return type

instance of QState

operate_qcirc(qcirc, qctrl=None)[source]¶

operate quantum circuit

Parameters

qcirc (instance of QCirc) – quantum circuit
qctrl (int) – control qubit id

Returns

self – quantum state after executing the quantum circuit

Return type

instance of QState

Notes

The quantum circut must be unintary.

partial(qid=None)[source]¶

get the partial quantum state.

Parameters: qid (list of int, default - list of all of the qubit id) – qubit id’s list to get as a partial quantum system.
Returns: qs – partial quantum state.
Return type: instance of QState

Notes

If ‘qid’ is set, specified partial quantum system are got after remaining system are measured. So if the specified quantum system are entangled with the remaining system, output quantum state is probabilistic. If no qubits are specified, you get the copy of original quantum state.

prob_array¶: Structure/Union member

prob_updated¶: Structure/Union member

qubit_num¶: Structure/Union member

schmidt_coef(qid_0=None, qid_1=None)[source]¶

get schmidt coefficients.

Parameters

qid_0 (list) – subsystem to decomposite.
qid_1 (list) – another subsystem to decomposite.

Returns

coef – schmidt coefficients.

Return type

numpy.ndarray

schmidt_decomp(qid_0=None, qid_1=None)[source]¶

schmidt decomposition.

Parameters

qid_0 (list) – subsystem to decomposite.
qid_1 (list) – another subsystem to decomposite.

Returns

coef (numpy.ndarray) – schmidt coefficients.
qs_0 (list of QState instances) – decomposite quantum state related to ‘qid_0’.
qs_1 (list of QState instances) – decomposite quantum state related to ‘qid_1’.

show(qid=None, nonzero=False, preal=0)[source]¶

show the quantum state (elements of the state vector and probabilities).

Parameters

qid (list of int, default - list of all of the qubit id) – qubit id’s list to show.
nonzero (bool, default False) – if True, only non-zero amplitudes are printed.
preal (int, default 0) – state id to make positive real amplitude. (if -1 is set, do not go out the global phase factor)

Return type

None

Notes

If ‘qid’ is set, it shows the elements of quantum state vector for partial quantum system specified by ‘qid’. If the specified quantum system are entangled with the remaining system, output is probabilistic. If no qubits are specified, it shows the whole quantum state. This method does not change the original quantum state.

Examples

>>> qs = QState(2).h(0).cx(0,1)
>>> qs.show()
c[00] = +0.7071+0.0000*i : 0.5000 |++++++
c[01] = +0.0000+0.0000*i : 0.0000 |
c[10] = +0.0000+0.0000*i : 0.0000 |
c[11] = +0.7071+0.0000*i : 0.5000 |++++++
...
>>> qs.show(qid=[0])
c[0] = +1.0000+0.0000*i : 1.0000 |+++++++++++
c[1] = +0.0000+0.0000*i : 0.0000 |
...
>>> qs.show(nonzero=True)
c[00] = +0.7071+0.0000*i : 0.5000 |++++++
c[11] = +0.7071+0.0000*i : 0.5000 |++++++

state_num¶: Structure/Union member

tenspro(qstate)[source]¶

get the tensor product with quantum state.

Parameters: qstate (instance of QState) – quantum state to get the tensor product.
Returns: qstate_out – tensor produt of ‘self’ and ‘qstate’.
Return type: instance of QState

use_gpu¶: Structure/Union member

class qlazy.Result[source]¶

Bases: object

Result of quantum circuit execution

backend¶

backend device of quantum computing

Type: instance of Backend

qubit_num¶

number of qubits

Type: int

cmem_num¶

number of classical bits

Type: int

cid¶

classical register id list to get frequencys.

Type: list

shots¶

number of measurements

Type: int

freqency¶

frequencies of measured value.

Type: instance of Counter

start_time¶

start time to ececute the quantum circuit.

Type: instance of datetime

end_time¶

end time to ececute the quantum circuit.

Type: instance of datetime

elapsed_time¶

elapsed time to ececute the quantum circuit.

Type: float

qstate¶

quantum state after executing circuit.

Type: instance of QState

stabilizer¶

stabilizer state after executing circuit.

Type: instance of Stabilizer

cmem¶

classical memory after executing circuit.

Type: instance of CMem

info¶

result informations relating to the backend device

Type: dict

backend: Backend = None¶

cid: list = None¶

cmem: CMem = None¶

cmem_num: int = None¶

elapsed_time: float = None¶

end_time: datetime = None¶

frequency: Counter = None¶

info: dict = None¶

classmethod load(file_path)[source]¶

load the result

Parameters: file_path (str) – file path of dump file
Returns: result – loaded circuit
Return type: instance of Result

qstate: QState = None¶

qubit_num: int = None¶

save(file_path)[source]¶

save the result

Parameters: file_path (str) – file path of dump file
Return type: None

shots: int = None¶

show(verbose=False)[source]¶

show the result.

Parameters

verbose (bool) – verbose output or not
None –

Return type

None

stabilizer: Stabilizer = None¶

start_time: datetime = None¶

class qlazy.Stabilizer(qubit_num=None, gene_num=None, pp_list=None, seed=None, **kwargs)[source]¶

Bases: Structure, QObject

Stabilizer State

qubit_num¶

number of qubits.

Type: int

gene_num¶

number of generators.

Type: int

classmethod add_method(method)[source]¶

add method (custum gate).

Parameters: method (func) – method (custum gate) to add.

classmethod add_methods(*methods)[source]¶

add methods (custum gates).

Parameters: methods (func, func, ...) – arguments of methods (custum gates) to add.

check_matrix¶: Structure/Union member

clone()[source]¶

get the copy of the quantum state.

Parameters: None –
Returns: stab – copy of the original stabilizer.
Return type: instance of Stabilizer

classmethod del_all(*stabs)[source]¶

free memory of the all stabilizer.

Parameters: stabs (instance of Stabilizer,instance of Stabilizer,...) – set of Stabilizer instances
Return type: None

gene_num¶: Structure/Union member

get_pauli_fac(gene_id)[source]¶

get pauli factor of generator (‘+1’,’-1’,’+i’,’-i’).

Parameters: gene_id (int) – generator id to get.
Returns: pauli_fac_complex – complex facto of the generator (1+0j, 1j, -1+0j, -1j)
Return type: complex

get_pauli_op(gene_id, qubit_id)[source]¶

get pauli operator (‘I’,’X’,’Y’,’Z’).

Parameters

gene_id (int) – generator id to get.
qubit_id (int) – qubit id to get.

Returns

pauli_op_str – pauli operator (‘I’,’X’,’Y’,’Z’)

Return type

str

get_rank()[source]¶: get rank of the stabilizer

get_str()[source]¶: get string of the stabilzer

m(qid=None, shots=1)[source]¶

measurement in Z-direction.

Parameters

qid (list of int) – qubit id list to measure.
shots (int, default 1) – number of measurements.

Returns

md – measurement data.

Return type

instance of MDataStabilizer

Examples

>>> sb = Stabilizer(qubit_num=2).set_all('Z').h(0).cx(0,1)
>>> md = qs.m(qid=[0,1], shots=100)
>>> print(md.freauency)
>>> print(md.last)
Counter({'00':55,'11':45})
11

See also

MDataStabilizer

measure(qid=None)[source]¶

one shot measurement in Z-direction.

Parameters: qid (list of int) – qubit id list to measure.
Returns: mval – measurement value.
Return type: str

Examples

>>> sb = Stabilizer(qubit_num=2).set_all('Z').h(0).cx(0,1)
>>> sb.show()
>>> print(sb.measure(qid=[0,1]))
>>> sb.show()
g[0]:  XX
g[1]:  ZZ
00
g[0]:  ZI
g[1]:  ZZ

mx(qid=None, shots=1)[source]¶

measurement in X-direction.

Parameters

qid (list of int) – qubit id list to measure.
shots (int, default 1) – number of measurements.

Returns

md – measurement data.

Return type

instance of MDataStabilizer

my(qid=None, shots=1)[source]¶

measurement in Y-direction.

Parameters

qid (list of int) – qubit id list to measure.
shots (int, default 1) – number of measurements.

Returns

md – measurement data.

Return type

instance of MDataStabilizer

mz(qid=None, shots=1)[source]¶

measurement in Z-direction.

Parameters

qid (list of int) – qubit id list to measure.
shots (int, default 1) – number of measurements.

Returns

md – measurement data.

Return type

instance of MDataStabilizer

Examples

>>> sb = Stabilizer(2).set_all('Z').h(0).cx(0,1)
>>> md = qs.mz(qid=[0,1], shots=100)
>>> print(md.freauency)
>>> print(md.last)
Counter({'00':55,'11':45})
11

See also

MDataStabilizer

operate(pp=None, ctrl=None, qctrl=None)[source]¶

operate unitary operator to stabilizer.

Parameters

pp (instance of PauliProduct) – pauli product to operate
ctrl (int) – contoroll qubit id for controlled pauli product (this option will be removed near future)
qctrl (int) – contoroll qubit id for controlled pauli product

Returns

self – stabilizer after operation

Return type

instance of Stabilizer

operate_gate(kind=None, qid=None, **kwargs)[source]¶

operate gate

Parameters

kind (int) – kind of the gate
qid (list) – quantum id list

Returns

self – quantum state

Return type

instance of QState

operate_qcirc(qcirc, qctrl=None)[source]¶

operate quantum circuit

Parameters

qcirc (instance of QCirc) – quantum circuit
qctrl (int) – control qubit id

Returns

qs – quantum state after executing the quantum circuit

Return type

instance of QState

Notes

The quantum circut must be clifford.

pauli_factor¶: Structure/Union member

qubit_num¶: Structure/Union member

set_all(pauli_op_str)[source]¶

set all of the qubits same pauli operators.

Parameters: pauli_op_str (str) – string of pauli operator (‘X’,’Y’,’Z’).
Returns: self
Return type: instance of Stabilizer

Examples

>>> sb = Stabilizer(qubit_num=3)
>>> sb.set_all('Z')
>>> sb.show()
g[0]:  ZII
g[1]:  IZI
g[2]:  IIZ

set_pauli_fac(gene_id, pauli_fac_str)[source]¶

set pauli factor of generator (‘+1’,’-1’,’+i’,’-i’).

Parameters: gene_id (int) – generator id to set.
Returns: self
Return type: instance of Stabilizer

set_pauli_op(gene_id, qubit_id, pauli_op_str)[source]¶

set pauli operator (‘I’,’X’,’Y’,’Z’).

Parameters

gene_id (int) – generator id to set.
qubit_id (int) – qubit id to set.

Returns

self

Return type

instance of Stabilizer

show()[source]¶

show the generators of stabilizer.

Parameters: None –
Return type: None