Choi
class Choi(data, input_dims=None, output_dims=None)
Bases: qiskit.quantum_info.operators.channel.quantum_channel.QuantumChannel
Choi-matrix representation of a Quantum Channel.
The Choi-matrix representation of a quantum channel is a matrix
Evolution of a DensityMatrix
with respect to the Choi-matrix is given by
where is the partial_trace()
over subsystem 1.
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 Choi matrix operator.
Parameters
- 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]
Raises
QiskitError – if input data cannot be initialized as a Choi matrix.
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 Numpy array of shape (4**N, 4**N) qubit systems will be used. If the input operator is not an N-qubit operator, it will assign a single subsystem with dimension specified by the shape of the input.
Methods
adjoint
Choi.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
Choi.compose(other, qargs=None, front=False)
Return the operator composition with another Choi.
Parameters
- other (Choi) – a Choi 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 Choi.
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
Choi.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
Choi.copy()
Make a deep copy of current operator.
dot
Choi.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
Choi.expand(other)
Return the reverse-order tensor product with another Choi.
Parameters
other (Choi) – a Choi object.
Returns
the tensor product , where
is the current Choi, and is the other Choi.
Return type
input_dims
Choi.input_dims(qargs=None)
Return tuple of input dimension for specified subsystems.
is_cp
Choi.is_cp(atol=None, rtol=None)
Test if Choi-matrix is completely-positive (CP)
is_cptp
Choi.is_cptp(atol=None, rtol=None)
Return True if completely-positive trace-preserving (CPTP).
is_tp
Choi.is_tp(atol=None, rtol=None)
Test if a channel is trace-preserving (TP)
is_unitary
Choi.is_unitary(atol=None, rtol=None)
Return True if QuantumChannel is a unitary channel.
output_dims
Choi.output_dims(qargs=None)
Return tuple of output dimension for specified subsystems.
power
Choi.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
Choi.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
Choi.tensor(other)
Return the tensor product with another Choi.
Parameters
other (Choi) – a Choi object.
Returns
the tensor product , where
is the current Choi, and is the other Choi.
Return type
The tensor product can be obtained using the ^
binary operator. Hence a.tensor(b)
is equivalent to a ^ b
.
to_instruction
Choi.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
Choi.to_operator()
Try to convert channel to a unitary representation Operator.
transpose
Choi.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
Default value: 1e-08
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
Default value: 1e-05
settings
Return settings.