mimiqcircuits.operations.noisechannel.kraus

Functions

is_valid_power_of_2(n)

Check if a number is a power of 2.

Classes

Kraus(E[, rtol])

Kraus(kmatrices).

class mimiqcircuits.operations.noisechannel.kraus.Kraus(E, rtol=1e-12)

Bases: krauschannel

Kraus(kmatrices).

Custom N-qubit Kraus channel specified by a list of 2^N x 2^N Kraus matrices.

A Kraus channel is defined by:

\[\mathcal{E}(\rho) = \sum_k E_k \rho E_k^\dagger,\]

where \(E_k\) are Kraus matrices that need to fulfill \(\sum_k E_k^\dagger E_k = I\).

If the Kraus matrices are all proportional to unitaries, use MixedUnitary() instead.

The Kraus matrices are defined in the computational basis in the usual textbook order (the first qubit corresponds to the left-most qubit). For 1 qubit, we have \(|0\rangle\), \(|1\rangle\). For 2 qubits, we have \(|00\rangle\), \(|01\rangle\), \(|10\rangle\), \(|11\rangle\).

Note: Currently, only 1 and 2-qubit custom Kraus channels are supported.

See also

MixedUnitary GateCustom

Parameters:

kmatrices (list) – List of \(2^N \times 2^N\) complex matrices. The number of qubits is equal to \(N\).

Examples

>>> from mimiqcircuits import *
>>> from symengine import *
>>> c = Circuit()
>>> c.push(Kraus([Matrix([[1, 0], [0, sqrt(0.9)]]), Matrix([[0, sqrt(0.1)], [0, 0]])]), 0)
1-qubit circuit with 1 instruction:
└── Kraus(Operator([[1, 0], [0, 0.948683298050514]]), Operator([[0, 0.316227766016838], [0, 0]])) @ q[0]

Kraus Matrices

>>> g=Kraus([Matrix([[1, 0], [0, sqrt(0.9)]]), Matrix([[0, sqrt(0.1)], [0, 0]])])
>>> g.krausmatrices()
[[1.0, 0]
[0, 0.948683298050514]
, [0, 0.316227766016838]
[0, 0]
]

# Example 2: Kraus with Projector0 and Projector1

>>> c = Circuit()
>>> c.push(Kraus([Projector0(), Projector1()]), 0)
1-qubit circuit with 1 instruction:
└── Kraus(P₀(1), P₁(1)) @ q[0]

# Example 3: Kraus with a matrix and Projector1

>>> c = Circuit()
>>> c.push(Kraus([Matrix([[1, 0], [0, 0]]), Projector1()]), 0)
1-qubit circuit with 1 instruction:
└── Kraus(Operator([[1, 0], [0, 0]]), P₁(1)) @ q[0]

__init__(E, rtol=1e-12)

evaluate(values)

Evaluates symbolic parameters in Kraus matrices using a dictionary of values.

Parameters:

values (dict) – A dictionary where keys are symbolic variables and values are the corresponding numerical values.

Returns:

A new Kraus instance with evaluated matrices.

Return type:

Kraus

krausoperators()

Returns the Kraus operators.

__str__()

String representation, listing either AbstractOperators or matrix slices.

unwrappedkrausmatrices()

Returns the unwrapped Kraus matrices.