Chi

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

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

Pauli basis Chi-matrix representation of a quantum channel.

The Chi-matrix representation of an \(n\)-qubit quantum channel \(\mathcal{E}\) is a matrix \(\chi\) such that the evolution of a DensityMatrix \(\rho\) is given by

\[\mathcal{E}(ρ) = \sum_{i, j} \chi_{i,j} P_i ρ P_j\]

where \([P_0, P_1, ..., P_{4^{n}-1}]\) is the \(n\)-qubit Pauli basis in lexicographic order. It is related to the Choi representation by a change of basis of the Choi-matrix into the Pauli basis.

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 Chi-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 is not an N-qubit channel or cannot be initialized as a Chi-matrix.

Additional Information:

If the input or output dimensions are None, they will be automatically determined from the input data. The Chi matrix representation is only valid for N-qubit channels.

Methods

adjoint	Return the adjoint quantum channel.
compose	Return the operator composition with another Chi.
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 Chi.
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 Chi.
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 data.

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.