SuperOp¶

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

Bases: QuantumChannel

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.

প্যারামিটার

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]

রেইজেস

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.

Methods

`adjoint`	Return the adjoint quantum channel.
`compose`	Return the operator composition with another SuperOp.
`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 SuperOp.
`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 SuperOp.
`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 settings.