qiskit.quantum_info.Stinespring
class Stinespring(data, input_dims=None, output_dims=None)
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
- **(**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 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.
__init__
__init__(data, input_dims=None, output_dims=None)
Initialize a quantum channel Stinespring 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 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.
Methods
__init__(data[, input_dims, output_dims]) | Initialize a quantum channel Stinespring 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 quantum channel 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. |
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) | The matrix power of the channel. |
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
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
adjoint()
Return the adjoint of the operator.
atol
The default absolute tolerance parameter for float comparisons.
compose
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
Raises
QiskitError – if other cannot be converted to a Stinespring or 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
conjugate()
Return the conjugate of the QuantumChannel.
copy
copy()
Make a deep copy of current operator.
data
Return data.
dim
Return tuple (input_shape, output_shape).
dot
dot(other, qargs=None)
Return the right multiplied 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].
Returns
The quantum channel self * other.
Return type
Raises
QiskitError – if other cannot be converted to a Stinespring or has incompatible dimensions.
expand
expand(other)
Return the tensor product channel other ⊗ self.
Parameters
other (QuantumChannel) – a quantum channel subclass.
Returns
the tensor product channel other ⊗ self as a Stinespring object.
Return type
Raises
QiskitError – if other cannot be converted to a channel.
input_dims
input_dims(qargs=None)
Return tuple of input dimension for specified subsystems.
is_cp
is_cp(atol=None, rtol=None)
Test if Choi-matrix is completely-positive (CP)
is_cptp
is_cptp(atol=None, rtol=None)
Return True if completely-positive trace-preserving.
is_tp
is_tp(atol=None, rtol=None)
Test if a channel is completely-positive (CP)
is_unitary
is_unitary(atol=None, rtol=None)
Return True if QuantumChannel is a unitary channel.
multiply
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.
num_qubits
Return the number of qubits if a N-qubit operator or None otherwise.
output_dims
output_dims(qargs=None)
Return tuple of output dimension for specified subsystems.
power
power(n)
The matrix power of the channel.
Parameters
n (int) – compute the matrix power of the superoperator matrix.
Returns
the matrix power of the SuperOp converted to a Stinespring channel.
Return type
Raises
QiskitError – if the input and output dimensions of the QuantumChannel are not equal, or the power is not an integer.
qargs
Return the qargs for the operator.
reshape
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.
rtol
The relative tolerance parameter for float comparisons.
set_atol
classmethod set_atol(value)
Set the class default absolute tolerance parameter for float comparisons.
DEPRECATED: use operator.atol = value instead
set_rtol
classmethod set_rtol(value)
Set the class default relative tolerance parameter for float comparisons.
DEPRECATED: use operator.rtol = value instead
subtract
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
tensor(other)
Return the tensor product channel self ⊗ other.
Parameters
other (QuantumChannel) – a quantum channel subclass.
Returns
the tensor product channel other ⊗ self as a Stinespring object.
Return type
Raises
QiskitError – if other cannot be converted to a channel.
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
to_operator()
Try to convert channel to a unitary representation Operator.
transpose
transpose()
Return the transpose of the QuantumChannel.