Kraus
Kraus(data, input_dims=None, output_dims=None)
Bases: qiskit.quantum_info.operators.channel.quantum_channel.QuantumChannel
Kraus representation of a quantum channel.
For a quantum channel , the Kraus representation is given by a set of matrices such that the evolution of a DensityMatrix
is given by
A general operator map can also be written using the generalized Kraus representation which is given by two sets of 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](opens in a new tab)
Initialize a quantum channel Kraus 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. If the input data is a list of Numpy arrays of shape (2**N, 2**N) qubit systems will be used. If the input does not correspond to an N-qubit channel, it will assign a single subsystem with dimension specified by the shape of the input.
Methods
adjoint
Kraus.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 .
compose
Kraus.compose(other, qargs=None, front=False)
Return the operator composition with another Kraus.
Parameters
- other (Kraus) – a Kraus 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 Kraus.
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 dot()
is defined as right matrix multiplication. That is that A & B == A.compose(B)
is equivalent to 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
Kraus.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
Kraus.copy()
Make a deep copy of current operator.
dot
Kraus.dot(other, qargs=None)
expand
Kraus.expand(other)
input_dims
Kraus.input_dims(qargs=None)
Return tuple of input dimension for specified subsystems.
is_cp
Kraus.is_cp(atol=None, rtol=None)
Test if Choi-matrix is completely-positive (CP)
is_cptp
Kraus.is_cptp(atol=None, rtol=None)
Return True if completely-positive trace-preserving.
is_tp
Kraus.is_tp(atol=None, rtol=None)
Test if a channel is trace-preserving (TP)
is_unitary
Kraus.is_unitary(atol=None, rtol=None)
Return True if QuantumChannel is a unitary channel.
output_dims
Kraus.output_dims(qargs=None)
Return tuple of output dimension for specified subsystems.
power
Kraus.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
Kraus.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
Kraus.tensor(other)
to_instruction
Kraus.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
Kraus.to_operator()
Try to convert channel to a unitary representation Operator.
transpose
Kraus.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 .
Attributes
atol
= 1e-08
data
Return list of Kraus matrices for channel.
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.