Choi

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

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

• 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]

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.

Attributes

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.

Methods

Choi.__call__(qargs)	Return a clone with qargs set
Choi.__mul__(other)
Choi.add(other)	Return the linear operator self + other.
Choi.adjoint()	Return the adjoint of the operator.
Choi.compose(other[, qargs, front])	Return the composed quantum channel self @ other.
Choi.conjugate()	Return the conjugate of the QuantumChannel.
Choi.copy()	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.
Choi.power(n)	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.
Choi.to_instruction()	Convert to a Kraus or UnitaryGate circuit instruction.
Choi.to_operator()	Try to convert channel to a unitary representation Operator.
Choi.transpose()	Return the transpose of the QuantumChannel.
Choi.__call__(qargs)	Return a clone with qargs set
Choi.__mul__(other)