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 is a rectangular matrix such that the evolution of a DensityMatrix is given by
where is the partial_trace() over subsystem 2.
A general operator map can also be written using the generalized Stinespring representation which is given by two matrices , such that
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 Stinespring operator.
Parameters
- data (QuantumCircuit |circuit.instruction.Instruction | BaseOperator | np.ndarray) – data to initialize superoperator.
- input_dims (int |tuple | None) – the input subsystem dimensions.
- output_dims (int |tuple | None) – the output subsystem dimensions.
Raises
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
Default value: 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
Default value: 1e-05
settings
Return settings.
Methods
adjoint
adjoint()
Return the adjoint quantum channel.
This is equivalent to the matrix Hermitian conjugate in the SuperOp representation ie. for a channel , the SuperOp of the adjoint channel is .
Return type
Self
compose
compose(other, qargs=None, front=False)
Return the operator composition with another Stinespring.
Parameters
- 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].
Returns
The composed Stinespring.
Return type
Raises
QiskitError – if other cannot be converted to an operator, or has incompatible dimensions for specified subsystems.
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
conjugate()
Return the conjugate quantum channel.
This is equivalent to the matrix complex conjugate in the SuperOp representation ie. for a channel , the SuperOp of the conjugate channel is .
copy
dot
dot(other, qargs=None)
Return the right multiplied operator self * other.
Parameters
- 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).
Returns
The right matrix multiplied Operator.
Return type
The dot product can be obtained using the @ binary operator. Hence a.dot(b) is equivalent to a @ b.
expand
expand(other)
Return the reverse-order tensor product with another Stinespring.
Parameters
other (Stinespring) – a Stinespring object.
Returns
the tensor product , where
is the current Stinespring, and is the other Stinespring.
Return type
input_dims
is_cp
is_cp(atol=None, rtol=None)
Test if Choi-matrix is completely-positive (CP)
Parameters
Return type
is_cptp
is_tp
is_unitary
is_unitary(atol=None, rtol=None)
Return True if QuantumChannel is a unitary channel.
Parameters
Return type
output_dims
power
power(n)
Return the power of the quantum channel.
Parameters
n (float) – the power exponent.
Returns
the channel .
Return type
Raises
QiskitError – if the input and output dimensions of the SuperOp are not equal.
For non-positive or non-integer exponents the power is defined as the matrix power of the SuperOp representation ie. for a channel , the SuperOp of the powered channel is .
reshape
reshape(input_dims=None, output_dims=None, num_qubits=None)
Return a shallow copy with reshaped input and output subsystem dimensions.
Parameters
- 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].
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.
tensor
tensor(other)
Return the tensor product with another Stinespring.
Parameters
other (Stinespring) – a Stinespring object.
Returns
the tensor product , where
is the current Stinespring, and is the other Stinespring.
Return type
The tensor product can be obtained using the ^ binary operator. Hence a.tensor(b) is equivalent to a ^ b.
to_instruction
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
Raises
QiskitError – if input data is not an N-qubit CPTP quantum channel.
to_operator
transpose
transpose()
Return the transpose quantum channel.
This is equivalent to the matrix transpose in the SuperOp representation, ie. for a channel , the SuperOp of the transpose channel is .