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Kraus

class Kraus(data, input_dims=None, output_dims=None)[소스]

기반 클래스: 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.

참조

  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.

매개변수
  • or (data (QuantumCircuit) – 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]

예외 발생

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 settings.