# Choi¶

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

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

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 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.

 Choi.atol The default absolute tolerance parameter for float comparisons. Choi.data Return data. Choi.dim Return tuple (input_shape, output_shape). Choi.num_qubits Return the number of qubits if a N-qubit operator or None otherwise. Choi.qargs Return the qargs for the operator. Choi.rtol The relative tolerance parameter for float comparisons.
 Choi.__call__(qargs) Return a clone with qargs set Choi.__mul__(other) Choi.add(other) Return the linear operator self + other. Return the adjoint of the operator. Choi.compose(other[, qargs, front]) Return the composed quantum channel self @ other. Return the conjugate of the QuantumChannel. Make a deep copy of current operator. Choi.dot(other[, qargs]) Return the right multiplied operator self * other. Choi.expand(other) Return the tensor product channel other ⊗ self. Choi.input_dims([qargs]) Return tuple of input dimension for specified subsystems. Choi.is_cp([atol, rtol]) Test if Choi-matrix is completely-positive (CP) Choi.is_cptp([atol, rtol]) Return True if completely-positive trace-preserving (CPTP). Choi.is_tp([atol, rtol]) Test if a channel is completely-positive (CP) Choi.is_unitary([atol, rtol]) Return True if QuantumChannel is a unitary channel. Choi.multiply(other) Return the linear operator other * self. Choi.output_dims([qargs]) Return tuple of output dimension for specified subsystems. The matrix power of the channel. Choi.reshape([input_dims, output_dims]) Return a shallow copy with reshaped input and output subsystem dimensions. Choi.set_atol(value) Set the class default absolute tolerance parameter for float comparisons. Choi.set_rtol(value) Set the class default relative tolerance parameter for float comparisons. Choi.subtract(other) Return the linear operator self - other. Choi.tensor(other) Return the tensor product channel self ⊗ other. Convert to a Kraus or UnitaryGate circuit instruction. Try to convert channel to a unitary representation Operator. Return the transpose of the QuantumChannel. Choi.__call__(qargs) Return a clone with qargs set Choi.__mul__(other)