SuperOp¶

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

Superoperator representation of a quantum channel.

The Superoperator representation of a quantum channel \(\mathcal{E}\) is a matrix \(S\) such that the evolution of a DensityMatrix \(\rho\) is given by

\[|\mathcal{E}(\rho)\rangle\!\rangle = S |\rho\rangle\!\rangle\]

where the double-ket notation \(|A\rangle\!\rangle\) denotes a vector formed by stacking the columns of the matrix \(A\) (column-vectorization).

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 Superoperator 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 superoperator.

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

`SuperOp.atol`	The default absolute tolerance parameter for float comparisons.
`SuperOp.data`	Return data.
`SuperOp.dim`	Return tuple (input_shape, output_shape).
`SuperOp.num_qubits`	Return the number of qubits if a N-qubit operator or None otherwise.
`SuperOp.qargs`	Return the qargs for the operator.
`SuperOp.rtol`	The relative tolerance parameter for float comparisons.

Methods

`SuperOp.__call__`(qargs)	Return a clone with qargs set
`SuperOp.__mul__`(other)
`SuperOp.add`(other)	Return the linear operator self + other.
`SuperOp.adjoint`()	Return the adjoint of the operator.
`SuperOp.compose`(other[, qargs, front])	Return the composed quantum channel self @ other.
`SuperOp.conjugate`()	Return the conjugate of the QuantumChannel.
`SuperOp.copy`()	Make a deep copy of current operator.
`SuperOp.dot`(other[, qargs])	Return the right multiplied operator self * other.
`SuperOp.expand`(other)	Return the tensor product channel other ⊗ self.
`SuperOp.input_dims`([qargs])	Return tuple of input dimension for specified subsystems.
`SuperOp.is_cp`([atol, rtol])	Test if Choi-matrix is completely-positive (CP)
`SuperOp.is_cptp`([atol, rtol])	Return True if completely-positive trace-preserving (CPTP).
`SuperOp.is_tp`([atol, rtol])	Test if a channel is completely-positive (CP)
`SuperOp.is_unitary`([atol, rtol])	Return True if QuantumChannel is a unitary channel.
`SuperOp.multiply`(other)	Return the linear operator other * self.
`SuperOp.output_dims`([qargs])	Return tuple of output dimension for specified subsystems.
`SuperOp.power`(n)	Return the compose of a QuantumChannel with itself n times.
`SuperOp.reshape`([input_dims, output_dims])	Return a shallow copy with reshaped input and output subsystem dimensions.
`SuperOp.set_atol`(value)	Set the class default absolute tolerance parameter for float comparisons.
`SuperOp.set_rtol`(value)	Set the class default relative tolerance parameter for float comparisons.
`SuperOp.subtract`(other)	Return the linear operator self - other.
`SuperOp.tensor`(other)	Return the tensor product channel self ⊗ other.
`SuperOp.to_instruction`()	Convert to a Kraus or UnitaryGate circuit instruction.
`SuperOp.to_operator`()	Try to convert channel to a unitary representation Operator.
`SuperOp.transpose`()	Return the transpose of the QuantumChannel.
`SuperOp.__call__`(qargs)	Return a clone with qargs set
`SuperOp.__mul__`(other)