qiskit.quantum_info.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

(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 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.

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

Initialize a quantum channel Superoperator 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 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

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

Attributes

`atol`	The default absolute tolerance parameter for float comparisons.
`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`	The relative tolerance parameter for float comparisons.

add(other)¶

Return the linear operator self + other.

DEPRECATED: use operator + other instead.

Parameters: other (BaseOperator) – an operator object.
Returns: the operator self + other.
Return type: BaseOperator

adjoint()¶: Return the adjoint of the operator.

property atol¶: The default absolute tolerance parameter for float comparisons.

compose(other, qargs=None, front=False)[source]¶

Return the composed quantum channel self @ other.

Parameters

other (QuantumChannel) – a quantum channel.
qargs (list or None) – a list of subsystem positions to apply other on. If None apply on all subsystems [default: None].
front (bool) – If True compose using right operator multiplication, instead of left multiplication [default: False].

Returns

The quantum channel self @ other.

Return type

SuperOp

Raises

QiskitError – if other has incompatible dimensions.

Additional Information:: Composition (@) is defined as left matrix multiplication for SuperOp matrices. That is that A @ B is equal to B * A. Setting front=True returns right matrix multiplication A * B and is equivalent to the dot() method.

conjugate()[source]¶: Return the conjugate of the QuantumChannel.

copy()¶: Make a deep copy of current operator.

property data¶: Return data.

property dim¶: Return tuple (input_shape, output_shape).

dot(other, qargs=None)¶

Return the right multiplied operator self * other.

Parameters

other (BaseOperator) – an operator object.
qargs (list or None) – a list of subsystem positions to apply other on. If None apply on all subsystems [default: None].

Returns

The operator self * other.

Return type

BaseOperator

Raises

QiskitError – if other cannot be converted to an operator, or has incompatible dimensions for specified subsystems.

expand(other)[source]¶

Return the tensor product channel other ⊗ self.

Parameters: other (QuantumChannel) – a quantum channel.
Returns: the tensor product channel other ⊗ self as a SuperOp object.
Return type: SuperOp
Raises: QiskitError – if other cannot be converted to a channel.

input_dims(qargs=None)¶: Return tuple of input dimension for specified subsystems.

is_cp(atol=None, rtol=None)¶: Test if Choi-matrix is completely-positive (CP)

is_cptp(atol=None, rtol=None)¶: Return True if completely-positive trace-preserving (CPTP).

is_tp(atol=None, rtol=None)¶: Test if a channel is completely-positive (CP)

is_unitary(atol=None, rtol=None)¶: Return True if QuantumChannel is a unitary channel.

multiply(other)¶

Return the linear operator other * self.

DEPRECATED: use other * operator instead.

Parameters: other (complex) – a complex number.
Returns: the linear operator other * self.
Return type: BaseOperator
Raises: NotImplementedError – if subclass does not support multiplication.

property num_qubits¶: Return the number of qubits if a N-qubit operator or None otherwise.

output_dims(qargs=None)¶: Return tuple of output dimension for specified subsystems.

power(n)[source]¶

Return the compose of a QuantumChannel with itself n times.

Parameters: n (int) – compute the matrix power of the superoperator matrix.
Returns: the n-times composition channel as a SuperOp object.
Return type: SuperOp
Raises: QiskitError – if the input and output dimensions of the QuantumChannel are not equal, or the power is not an integer.

property qargs¶: Return the qargs for the operator.

reshape(input_dims=None, output_dims=None)¶

Return a shallow copy with reshaped input and output subsystem dimensions.

Arg:

input_dims (None or tuple): new subsystem input dimensions.: If None the original input dims will be preserved [Default: None].
output_dims (None or tuple): new subsystem output dimensions.: If None the original output dims will be preserved [Default: None].

Returns: returns self with reshaped input and output dimensions.
Return type: BaseOperator
Raises: QiskitError – if combined size of all subsystem input dimension or subsystem output dimensions is not constant.

property rtol¶: The relative tolerance parameter for float comparisons.

classmethod set_atol(value)¶

Set the class default absolute tolerance parameter for float comparisons.

DEPRECATED: use operator.atol = value instead

classmethod set_rtol(value)¶

Set the class default relative tolerance parameter for float comparisons.

DEPRECATED: use operator.rtol = value instead

subtract(other)¶

Return the linear operator self - other.

DEPRECATED: use operator - other instead.

Parameters: other (BaseOperator) – an operator object.
Returns: the operator self - other.
Return type: BaseOperator

tensor(other)[source]¶

Return the tensor product channel self ⊗ other.

Parameters: other (QuantumChannel) – a quantum channel.
Returns: the tensor product channel self ⊗ other as a SuperOp object.
Return type: SuperOp
Raises: QiskitError – if other cannot be converted to a channel.

to_instruction()¶

Convert to a Kraus or UnitaryGate circuit instruction.

If the channel is unitary it will be added as a unitary gate, otherwise it will be added as a kraus simulator instruction.

Returns: A kraus instruction for the channel.
Return type: qiskit.circuit.Instruction
Raises: QiskitError – if input data is not an N-qubit CPTP quantum channel.

to_operator()¶: Try to convert channel to a unitary representation Operator.

transpose()[source]¶: Return the transpose of the QuantumChannel.