Stinespring

class qiskit.quantum_info.Stinespring(data, input_dims=None, output_dims=None)

ベースクラス: QuantumChannel

Stinespring representation of a quantum channel.

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

\[\mathcal{E}(ρ) = \mbox{Tr}_2\left[A ρ A^\dagger\right]\]

where \(\mbox{Tr}_2\) is the partial_trace() over subsystem 2.

A general operator map \(\mathcal{G}\) can also be written using the generalized Stinespring representation which is given by two matrices \(A\), \(B\) such that

\[\mathcal{G}(ρ) = \mbox{Tr}_2\left[A ρ B^\dagger\right]\]

See reference [1] for further details.

参照

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 Stinespring operator.

パラメータ:

• 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]

例外:

QiskitError – if input data cannot be initialized as a a list of Kraus matrices.

Additional Information:

If the input or output dimensions are None, they will be automatically determined from the input data. This can fail for the Stinespring operator if the output dimension cannot be automatically determined.

Attributes

atol = 1e-08

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.

Methods

adjoint()

Return the adjoint quantum channel.

注釈

This is equivalent to the matrix Hermitian conjugate in the SuperOp representation ie. for a channel \(\mathcal{E}\), the SuperOp of the adjoint channel \(\mathcal{{E}}^\dagger\) is \(S_{\mathcal{E}^\dagger} = S_{\mathcal{E}}^\dagger\).

戻り値の型:

Self

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

Return the operator composition with another Stinespring.

パラメータ:

• other (Stinespring) – a Stinespring object.

• qargs (list or None) – Optional, 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].

戻り値:

The composed Stinespring.

戻り値の型:

Stinespring

例外:

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

注釈

Composition (&) by default is defined as left matrix multiplication for matrix operators, while @ (equivalent to dot()) is defined as right matrix multiplication. That is that A & B == A.compose(B) is equivalent to B @ A == B.dot(A) when A and B are of the same type.

Setting the front=True kwarg changes this to right matrix multiplication and is equivalent to the dot() method A.dot(B) == A.compose(B, front=True).

conjugate()

Return the conjugate quantum channel.

注釈

This is equivalent to the matrix complex conjugate in the SuperOp representation ie. for a channel \(\mathcal{E}\), the SuperOp of the conjugate channel \(\overline{{\mathcal{{E}}}}\) is \(S_{\overline{\mathcal{E}^\dagger}} = \overline{S_{\mathcal{E}}}\).

copy()

Make a deep copy of current operator.

dot(other, qargs=None)

Return the right multiplied operator self * other.

パラメータ:

• other (Operator) – an operator object.

• qargs (list or None) – Optional, a list of subsystem positions to apply other on. If None apply on all subsystems (default: None).

戻り値:

The right matrix multiplied Operator.

戻り値の型:

Operator

注釈

The dot product can be obtained using the @ binary operator. Hence a.dot(b) is equivalent to a @ b.

expand(other)

Return the reverse-order tensor product with another Stinespring.

パラメータ:

other (Stinespring) – a Stinespring object.

戻り値:

the tensor product \(b \otimes a\), where \(a\)

is the current Stinespring, and \(b\) is the other Stinespring.

戻り値の型:

Stinespring

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)

戻り値の型:

bool

is_cptp(atol=None, rtol=None)

Return True if completely-positive trace-preserving.

is_tp(atol=None, rtol=None)

Test if a channel is trace-preserving (TP)

戻り値の型:

bool

is_unitary(atol=None, rtol=None)

Return True if QuantumChannel is a unitary channel.

戻り値の型:

bool

output_dims(qargs=None)

Return tuple of output dimension for specified subsystems.

power(n)

Return the power of the quantum channel.

パラメータ:

n (float) – the power exponent.

戻り値:

the channel \(\mathcal{{E}} ^n\).

戻り値の型:

SuperOp

例外:

QiskitError – if the input and output dimensions of the SuperOp are not equal.

注釈

For non-positive or non-integer exponents the power is defined as the matrix power of the SuperOp representation ie. for a channel \(\mathcal{{E}}\), the SuperOp of the powered channel \(\mathcal{{E}}^\n\) is \(S_{{\mathcal{{E}}^n}} = S_{{\mathcal{{E}}}}^n\).

reshape(input_dims=None, output_dims=None, num_qubits=None)

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

パラメータ:

• 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].

• num_qubits (None or int) – reshape to an N-qubit operator [Default: None].

戻り値:

returns self with reshaped input and output dimensions.

戻り値の型:

BaseOperator

例外:

QiskitError – if combined size of all subsystem input dimension or subsystem output dimensions is not constant.

tensor(other)

Return the tensor product with another Stinespring.

パラメータ:

other (Stinespring) – a Stinespring object.

戻り値:

the tensor product \(a \otimes b\), where \(a\)

is the current Stinespring, and \(b\) is the other Stinespring.

戻り値の型:

Stinespring

注釈

The tensor product can be obtained using the ^ binary operator. Hence a.tensor(b) is equivalent to a ^ b.

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.

戻り値:

A kraus instruction for the channel.

戻り値の型:

qiskit.circuit.Instruction

例外:

QiskitError – if input data is not an N-qubit CPTP quantum channel.

to_operator()

Try to convert channel to a unitary representation Operator.

戻り値の型:

Operator

transpose()

Return the transpose quantum channel.

注釈

This is equivalent to the matrix transpose in the SuperOp representation, ie. for a channel \(\mathcal{E}\), the SuperOp of the transpose channel \(\mathcal{{E}}^T\) is \(S_{mathcal{E}^T} = S_{\mathcal{E}}^T\).