Stinespring

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

Bases : 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.

Références

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.

Paramètres:

• 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]

Lève:

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.

Note

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 \(S_{\mathcal{E}^\dagger} = S_{\mathcal{E}}^\dagger\).

Type renvoyé:

Self

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

Return the operator composition with another Stinespring.

Paramètres:

• 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].

Renvoie:

The composed Stinespring.

Type renvoyé:

Stinespring

Lève:

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

Note

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.

Note

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.

Paramètres:

• 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).

Renvoie:

The right matrix multiplied Operator.

Type renvoyé:

Operator

Note

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.

Paramètres:

other (Stinespring) – a Stinespring object.

Renvoie:

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

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

Type renvoyé:

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)

Type renvoyé:

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)

Type renvoyé:

bool

is_unitary(atol=None, rtol=None)

Return True if QuantumChannel is a unitary channel.

Type renvoyé:

bool

output_dims(qargs=None)

Return tuple of output dimension for specified subsystems.

power(n)

Return the power of the quantum channel.

Paramètres:

n (float) – the power exponent.

Renvoie:

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

Type renvoyé:

SuperOp

Lève:

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

Note

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.

Paramètres:

• 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].

Renvoie:

returns self with reshaped input and output dimensions.

Type renvoyé:

BaseOperator

Lève:

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.

Paramètres:

other (Stinespring) – a Stinespring object.

Renvoie:

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

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

Type renvoyé:

Stinespring

Note

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.

Renvoie:

A kraus instruction for the channel.

Type renvoyé:

qiskit.circuit.Instruction

Lève:

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

to_operator()

Try to convert channel to a unitary representation Operator.

Type renvoyé:

Operator

transpose()

Return the transpose quantum channel.

Note

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 \(S_{mathcal{E}^T} = S_{\mathcal{E}}^T\).