PTM
class PTM(data, input_dims=None, output_dims=None)
Pauli Transfer Matrix (PTM) representation of a Quantum Channel.
The PTM representation of an -qubit quantum channel is an -qubit SuperOp defined with respect to vectorization in the Pauli basis instead of column-vectorization. The elements of the PTM are given by
where is the -qubit Pauli basis in lexicographic order.
Evolution of a DensityMatrix with respect to the PTM is given by
where denotes vectorization in the Pauli basis .
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 PTM quantum channel 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 is not an N-qubit channel or cannot be initialized as a PTM.
Additional Information:
If the input or output dimensions are None, they will be automatically determined from the input data. The PTM representation is only valid for N-qubit channels.
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.
Methods
__call__
PTM.__call__(qargs)
Return a clone with qargs set
__mul__
PTM.__mul__(other)
add
PTM.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
PTM.adjoint()
Return the adjoint of the operator.
compose
PTM.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 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
PTM.conjugate()
Return the conjugate of the QuantumChannel.
copy
PTM.copy()
Make a deep copy of current operator.
dot
PTM.dot(other, qargs=None)
Return the right multiplied operator self * other.
Parameters
- other (BaseOperator) – an operator object.
- qargs (list or None) – a list of subsystem positions to apply other on. If None apply on all subsystems [default: None].
Returns
The operator self * other.
Return type
BaseOperator
Raises
QiskitError – if other cannot be converted to an operator, or has incompatible dimensions for specified subsystems.
expand
PTM.expand(other)
Return the tensor product channel other ⊗ self.
Parameters
other (QuantumChannel) – a quantum channel.
Returns
the tensor product channel other ⊗ self as a PTM object.
Return type
Raises
QiskitError – if other cannot be converted to a channel.
input_dims
PTM.input_dims(qargs=None)
Return tuple of input dimension for specified subsystems.
is_cp
PTM.is_cp(atol=None, rtol=None)
Test if Choi-matrix is completely-positive (CP)
is_cptp
PTM.is_cptp(atol=None, rtol=None)
Return True if completely-positive trace-preserving (CPTP).
is_tp
PTM.is_tp(atol=None, rtol=None)
Test if a channel is completely-positive (CP)
is_unitary
PTM.is_unitary(atol=None, rtol=None)
Return True if QuantumChannel is a unitary channel.
multiply
PTM.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.
output_dims
PTM.output_dims(qargs=None)
Return tuple of output dimension for specified subsystems.
power
PTM.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 PTM channel.
Return type
Raises
QiskitError – if the input and output dimensions of the QuantumChannel are not equal, or the power is not an integer.
reshape
PTM.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.
set_atol
classmethod PTM.set_atol(value)
Set the class default absolute tolerance parameter for float comparisons.
set_rtol
classmethod PTM.set_rtol(value)
Set the class default relative tolerance parameter for float comparisons.
subtract
PTM.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
PTM.tensor(other)
Return the tensor product channel self ⊗ other.
Parameters
other (QuantumChannel) – a quantum channel.
Returns
the tensor product channel self ⊗ other as a PTM object.
Return type
Raises
QiskitError – if other cannot be converted to a channel.
to_instruction
PTM.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
PTM.to_operator()
Try to convert channel to a unitary representation Operator.
transpose
PTM.transpose()
Return the transpose of the QuantumChannel.