qat.quops.QuantumChannelKraus

class qat.quops.QuantumChannelKraus(kraus_operators, name='', check_trace_preserving: bool = False, check_trace_reducing: bool = False)

Implementation of a quantum channel with the Kraus representation

\[\mathcal{E}(\rho)=\sum_{k=0}^{K-1} E_k \rho E_k^\dagger\]

with \(E_k\) the Kraus operators.

Parameters

• kraus_operators (list<np.array>) – list of Kraus operators

• name (string, optional) – name. Defaults to “”.

• check_trace_preserving (bool) – If True, check for trace preservation of the Kraus operators. Default to False.

• check_trace_reducing (bool) – If True, check if Kraus operators are physical. Default to False.

Two channels in the Kraus representation can be composed with the * operator:

import numpy as np
from qat.quops import QuantumChannelKraus

p1, p2 = 0.2, 0.15
chan1 = QuantumChannelKraus([np.sqrt(1. - p1) * np.eye(2), np.array([[0., np.sqrt(p1)], [0., 0.]])
chan2 = QuantumChannelKraus([np.sqrt(1. - p2) * np.eye(2), np.array([[0., np.sqrt(p2)], [0., 0.]])

chan3 = chan1 * chan2

print(chan3.kraus_operators)

  File "<stdin>", line 6
    chan2 = QuantumChannelKraus([np.sqrt(1. - p2) * np.eye(2), np.array([[0., np.sqrt(p2)], [0., 0.]])
    ^
SyntaxError: invalid syntax

kraus_operators

the list of Kraus operators \(\lbrace E_k \rbrace_{k}\)

Type

list<np.ndarray>

name

name

Type

string

kraus_rank

Kraus rank \(K\) (number of Kraus operators)

Type

int

apply_to(density_matrix, qbits=None, old_method=True, n_threads=1, weights=None)

Apply the quantum channel to the density matrix

Parameters

• density_matrix (matrix) – the density matrix (sparse or dense repr)

• qbits (list<int>, optional) – list of qubits in density_matrix to apply quantum channel to. Defaults to None, in which case: direct matrix product (sizes have to match)

• old_method (bool) – whether to allocate kronecker (True) or not.

• n_threads (int) – number of threads to use

Returns

the resulting density matrix

Return type

matrix

apply_to_vector(index, qbits, psi, full_kronecker=True)

Apply one Kraus operator to a state vector E[index]*psi

Parameters

• index (int) – index of the Kraus operator

• qbits (list) – list of qubits to apply Kraus operator to

• psi (list) – state vector

• full_kronecker (bool, optional) – whether to use an efficient kronecker product. Defaults to True.

Returns

the resulting state vector

kraus_rank()

Returns

the Kraus rank of the quantum channel

to_chi(matrix_basis=None)

Convert to Chi matrix representations

Parameters

matrix_basis (list(np.array), optional) – matrix basis. Defaults to None, in which case take canonical basis.

Returns

QuantumChannelChi

to_choi()

Convert to Choi representation

Returns

QuantumChannelChoi

to_ptm()

Convert to PTM representation

Returns

QuantumChannelPTM