# 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.

Références

1. 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.

Paramètres
• (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]

Lève

QiskitError – if input data is not an N-qubit channel or cannot be initialized as a PTM.

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.