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SuperOp

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

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Superoperator representation of a quantum channel.

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

E(ρ) ⁣=Sρ ⁣|\mathcal{E}(\rho)\rangle\!\rangle = S |\rho\rangle\!\rangle

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

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 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

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.


Methods

__call__

SuperOp.__call__(qargs)

Return a clone with qargs set

__mul__

SuperOp.__mul__(other)

add

SuperOp.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

SuperOp.adjoint()

Return the adjoint of the operator.

compose

SuperOp.compose(other, qargs=None, front=False)

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

SuperOp.conjugate()

Return the conjugate of the QuantumChannel.

copy

SuperOp.copy()

Make a deep copy of current operator.

dot

SuperOp.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

SuperOp.expand(other)

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

SuperOp.input_dims(qargs=None)

Return tuple of input dimension for specified subsystems.

is_cp

SuperOp.is_cp(atol=None, rtol=None)

Test if Choi-matrix is completely-positive (CP)

is_cptp

SuperOp.is_cptp(atol=None, rtol=None)

Return True if completely-positive trace-preserving (CPTP).

is_tp

SuperOp.is_tp(atol=None, rtol=None)

Test if a channel is completely-positive (CP)

is_unitary

SuperOp.is_unitary(atol=None, rtol=None)

Return True if QuantumChannel is a unitary channel.

multiply

SuperOp.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.

output_dims

SuperOp.output_dims(qargs=None)

Return tuple of output dimension for specified subsystems.

power

SuperOp.power(n)

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.

reshape

SuperOp.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.

set_atol

classmethod SuperOp.set_atol(value)

Set the class default absolute tolerance parameter for float comparisons.

set_rtol

classmethod SuperOp.set_rtol(value)

Set the class default relative tolerance parameter for float comparisons.

subtract

SuperOp.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

SuperOp.tensor(other)

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

SuperOp.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

SuperOp.to_operator()

Try to convert channel to a unitary representation Operator.

transpose

SuperOp.transpose()

Return the transpose of the QuantumChannel.

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