PTM¶

class PTM(data, input_dims=None, output_dims=None)[source]¶

Bases: qiskit.quantum_info.operators.channel.quantum_channel.QuantumChannel

Pauli Transfer Matrix (PTM) representation of a Quantum Channel.

The PTM representation of an \(n\)-qubit quantum channel \(\mathcal{E}\) is an \(n\)-qubit SuperOp \(R\) defined with respect to vectorization in the Pauli basis instead of column-vectorization. The elements of the PTM \(R\) are given by

\[R_{i,j} = \mbox{Tr}\left[P_i \mathcal{E}(P_j) \right]\]

where \([P_0, P_1, ..., P_{4^{n}-1}]\) is the \(n\)-qubit Pauli basis in lexicographic order.

Evolution of a DensityMatrix \(\rho\) with respect to the PTM is given by

\[|\mathcal{E}(\rho)\rangle\!\rangle_P = S_P |\rho\rangle\!\rangle_P\]

where \(|A\rangle\!\rangle_P\) denotes vectorization in the Pauli basis \(\langle i | A\rangle\!\rangle_P = \mbox{Tr}[P_i A]\).

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

(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 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.

Methods

`adjoint`	Return the adjoint quantum channel.
`compose`	Return the operator composition with another PTM.
`conjugate`	Return the conjugate quantum channel.
`copy`	Make a deep copy of current operator.
`dot`	Return the right multiplied operator self * other.
`expand`	Return the reverse-order tensor product with another PTM.
`input_dims`	Return tuple of input dimension for specified subsystems.
`is_cp`	Test if Choi-matrix is completely-positive (CP)
`is_cptp`	Return True if completely-positive trace-preserving (CPTP).
`is_tp`	Test if a channel is trace-preserving (TP)
`is_unitary`	Return True if QuantumChannel is a unitary channel.
`output_dims`	Return tuple of output dimension for specified subsystems.
`power`	Return the power of the quantum channel.
`reshape`	Return a shallow copy with reshaped input and output subsystem dimensions.
`tensor`	Return the tensor product with another PTM.
`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 quantum channel.

Attributes

atol = 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 = 1e-05¶

settings¶: Return operator settings.