Choi¶

class Choi(data, input_dims=None, output_dims=None)[source]¶

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

Choi-matrix representation of a Quantum Channel.

The Choi-matrix representation of a quantum channel \(\mathcal{E}\) is a matrix

\[\Lambda = \sum_{i,j} |i\rangle\!\langle j|\otimes \mathcal{E}\left(|i\rangle\!\langle j|\right)\]

Evolution of a DensityMatrix \(\rho\) with respect to the Choi-matrix is given by

\[\mathcal{E}(\rho) = \mbox{Tr}_{1}\left[\Lambda (\rho^T \otimes \mathbb{I})\right]\]

where \(\mbox{Tr}_1\) is the partial_trace() over subsystem 1.

See reference [1] for further details.

References

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 Choi matrix 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 Choi matrix.

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 Numpy array of shape (4**N, 4**N) qubit systems will be used. If the input operator is not an N-qubit operator, 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 Choi.
`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 Choi.
`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 (CPTP).
`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 Choi.
`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

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