qat.quops.metrics.get_average_process_fidelity

qat.quops.metrics.get_average_process_fidelity(chan1, chan2=None, use_formula=True)

Compute the average fidelity between two processes

\[F_{\mathrm{ave}}(\mathcal{E},\mathcal{F}) \equiv \int \mathrm{d}\rho F\left( \mathcal{E}(\rho) \mathcal{F}(\rho) \right)\]

with \(F\) the fidelity as defined in get_state_fidelity().

Parameters

• chan1 (QuantumChannel[PTM|Kraus|Choi]) – the first channel \(\mathcal{E}\)

• chan2 (QuantumChannel[PTM|Kraus|Choi], optional) – the second channel \(\mathcal{F}\). Defaults to None (identity).

Returns

the average process fidelity

Return type

float

Warning

Works only if chan2 is a unitary process.

Reference:

Phys. Rev. A 71, 062310

Note

The Choi matrices fidelity uses (A. Gilchrist)[https://arxiv.org/abs/quant-ph/0408063] fidelity definition, while while the Pauli transfer matrix definition uses a different vfidelity convention relying on the Hilebrt-Schmidt scalar product.