Kraus

class Kraus(data, input_dims=None, output_dims=None)

Bases: qiskit.quantum_info.operators.channel.quantum_channel.QuantumChannel

Kraus representation of a quantum channel.

For a quantum channel \(\mathcal{E}\), the Kraus representation is given by a set of matrices \([A_0,...,A_{K-1}]\) such that the evolution of a DensityMatrix \(\rho\) is given by

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

A general operator map \(\mathcal{G}\) can also be written using the generalized Kraus representation which is given by two sets of matrices \([A_0,...,A_{K-1}]\), \([B_0,...,A_{B-1}]\) such that

\[\mathcal{G}(\rho) = \sum_{i=0}^{K-1} A_i \rho B_i^\dagger\]

See reference [1] for further details.

References

1. C.J. Wood, J.D. Biamonte, D.G. Cory, Tensor networks and graphical calculus for open quantum systems, Quant. Inf. Comp. 15, 0579-0811 (2015). arXiv:1111.6950 [quant-ph]

Initialize a quantum channel Kraus operator.

Parameters

• (QuantumCircuit or (data) – Instruction or BaseOperator or matrix): data to initialize superoperator.

• input_dims (tuple) – the input subsystem dimensions. [Default: None]

• output_dims (tuple) – the output subsystem dimensions. [Default: None]

Raises

QiskitError – if input data cannot be initialized as a a list of Kraus matrices.

Additional Information:

If the input or output dimensions are None, they will be automatically determined from the input data. If the input data is a list of Numpy arrays of shape (2**N, 2**N) qubit systems will be used. If the input does not correspond to an N-qubit channel, it will assign a single subsystem with dimension specified by the shape of the input.

Methods

adjoint	Return the adjoint quantum channel.
compose	Return the operator composition with another Kraus.
conjugate	Return the conjugate quantum channel.
copy	Make a deep copy of current operator.
dot	Return the right multiplied operator self * other.
expand	Return the reverse-order tensor product with another Kraus.
input_dims	Return tuple of input dimension for specified subsystems.
is_cp	Test if Choi-matrix is completely-positive (CP)
is_cptp	Return True if completely-positive trace-preserving.
is_tp	Test if a channel is trace-preserving (TP)
is_unitary	Return True if QuantumChannel is a unitary channel.
output_dims	Return tuple of output dimension for specified subsystems.
power	Return the power of the quantum channel.
reshape	Return a shallow copy with reshaped input and output subsystem dimensions.
tensor	Return the tensor product with another Kraus.
to_instruction	Convert to a Kraus or UnitaryGate circuit instruction.
to_operator	Try to convert channel to a unitary representation Operator.
transpose	Return the transpose quantum channel.

Attributes

atol = 1e-08

data

Return list of Kraus matrices for channel.

dim

Return tuple (input_shape, output_shape).

num_qubits

Return the number of qubits if a N-qubit operator or None otherwise.

qargs

Return the qargs for the operator.

rtol = 1e-05

settings

Return operator settings.