Quantum channels and noise models

Kraus channel

class graphix.channels.KrausChannel(kraus_data)

quantum channel class in the Kraus representation. Defined by Kraus operators \(K_i\) with scalar prefactors coef) \(c_i\), where the channel act on density matrix as \(\rho' = \sum_i K_i^\dagger \rho K_i\). The data should satisfy \(\sum K_i^\dagger K_i = I\)

nqubit

number of qubits acted on by the Kraus operators

Type

int

size

number of Kraus operators (== Choi rank)

Type

int

kraus_ops

the data in format array_like(dict): [{coef: scalar, operator: array_like}, {coef: scalar, operator: array_like}, …]

Type

array_like(dict())

Returns

containing the corresponding Kraus operators

Return type

Channel object

__init__(kraus_data)

Parameters

kraus_data (array_like) – array of Kraus operator data. array_like(dict): [{coef: scalar, operator: array_like}, {parameter: scalar, operator: array_like}, …] only works for square Kraus operators

Raises

ValueError – If empty array_like is provided.

graphix.channels.dephasing_channel(prob: float) → KrausChannel

single-qubit dephasing channel, \((1-p) \rho + p Z \rho Z\)

Parameters

prob (float) – The probability associated to the channel

Returns

containing the corresponding Kraus operators

Return type

graphix.channel.KrausChannel object

graphix.channels.depolarising_channel(prob: float) → KrausChannel

single-qubit depolarizing channel

\[(1-p) \rho + \frac{p}{3} (X \rho X + Y \rho Y + Z \rho Z) = (1 - 4 \frac{p}{3}) \rho + 4 \frac{p}{3} id\]

Parameters

prob (float) – The probability associated to the channel

graphix.channels.pauli_channel(px: float, py: float, pz: float) → KrausChannel

single-qubit pauli channel,

\[(1-p_X-p_Y-p_Z) \rho + p_X X \rho X + p_Y Y \rho Y + p_Z Z \rho Z)\]

graphix.channels.two_qubit_depolarising_channel(prob: float) → KrausChannel

two-qubit depolarising channel.

\[\mathcal{E} (\rho) = (1-p) \rho + \frac{p}{15} \sum_{P_i \in \{id, X, Y ,Z\}^{\otimes 2}/(id \otimes id)}P_i \rho P_i\]

Parameters

prob (float) – The probability associated to the channel

Returns

containing the corresponding Kraus operators

Return type

graphix.channel.KrausChannel object

graphix.channels.two_qubit_depolarising_tensor_channel(prob: float) → KrausChannel

two-qubit tensor channel of single-qubit depolarising channels with same probability. Kraus operators:

\[\Big\{ \sqrt{(1-p)} id, \sqrt{(p/3)} X, \sqrt{(p/3)} Y , \sqrt{(p/3)} Z \Big\} \otimes \Big\{ \sqrt{(1-p)} id, \sqrt{(p/3)} X, \sqrt{(p/3)} Y , \sqrt{(p/3)} Z \Big\}\]

Parameters

prob (float) – The probability associated to the channel

Returns

containing the corresponding Kraus operators

Return type

graphix.channel.KrausChannel object

Noise model classes

class graphix.noise_models.noise_model.NoiseModel

Abstract base class for all noise models.

abstract __init__()

abstract byproduct_x()

apply noise to qubits that happens in the X gate process

abstract byproduct_z()

apply noise to qubits that happens in the Z gate process

abstract clifford()

apply noise to qubits that happens in the Clifford gate process

abstract confuse_result()

assign wrong measurement result

abstract entangle()

apply noise to qubits that happens in the CZ gate process

abstract measure()

apply noise to qubits that happens in the measurement process

abstract prepare_qubit()

return qubit to be added with preparation errors.

abstract tick_clock()

notion of time in real devices - this is where we apply effect of T1 and T2. we assume commands that lie between ‘T’ commands run simultaneously on the device.

class graphix.noise_models.noiseless_noise_model.NoiselessNoiseModel

Noiseless noise model for testing. Only return the identity channel.

Parameters

NoiseModel (class) – Parent abstract class class:graphix.noise_model.NoiseModel

__init__()

byproduct_x()

apply noise to qubits after X gate correction

byproduct_z()

apply noise to qubits after Z gate correction

clifford()

apply noise to qubits that happens in the Clifford gate process

confuse_result(cmd)

assign wrong measurement result

entangle()

return noise model to qubits that happens after the CZ gats

measure()

apply noise to qubit to be measured.

prepare_qubit()

return the channel to apply after clean single-qubit preparation. Here just identity.

tick_clock()

notion of time in real devices - this is where we apply effect of T1 and T2. we assume commands that lie between ‘T’ commands run simultaneously on the device.