qat.quops.QuantumChannelPTM

class qat.quops.QuantumChannelPTM(ptm, name='')

A quantum channel in its Pauli transfer matrix (PTM) representation.

\[R_{ij}^{(\mathcal{E})}\equiv\frac{1}{d}\mathrm{Tr}\left[\boldsymbol{P}_{i}\mathcal{E}(\boldsymbol{P}_{j})\right]\]

with \(d=2^{n_\mathrm{qubits}}\).

Parameters

• ptm (np.array) – the PTM matrix

• name (string, optional) – the name of the channel. Defaults to empty string.

matrix

the PTM matrix \(R_{ij}^{(\mathcal{E})}\)

Type

np.array

name

the name of the channel

Type

str

arity

the arity of the gate

Type

int

apply_to(density_matrix, qbits)

Applies the channel to a density matrix

Assumes density_matrix has shape 4, 4, …, 4 (with nqbits 4s)

Parameters

• density_matrix (np.array) – density matrix as a tensor of shape (4, 4, … 4)

• qbits (list<int>) – qbits on which gate is applied

Returns

(np.array) density matrix as tensor

property matrix

The PTM matrix

property ptm

The PTM matrix (deprecated)

property tensor

Return the PTM as a tensor

to_choi()

Convert to Choi representation

Returns

QuantumChannelChoi

to_kraus(force=False)

Convert to Kraus representation

Parameters

force (bool, optional) – if True, force convertion if chi matrix is not PSD. Default to False.

Note

Convertion goes through PTM -> Chi -> Kraus

Returns

QuantumChannelKraus