unitarity_to_rb_decay

forest.benchmarking.randomized_benchmarking.unitarity_to_rb_decay(unitarity, dimension) → float

Converts a unitarity decay to a standard RB decay under the assumption that no unitary errors present.

Proposition 8. in [ECN] gives the unitarity u as an upper bound of a function of the average gate error r and the dimension d:

\[u >= (1 - d r/(d-1))^2\]

This upper bound is saturated when no unitary errors are present, i.e. the noise is purely stochastic, like in the case of depolarizing noise. We can use this saturated equality to upper bound the standard RB decay. This allows comparison of measured unitarity and RB decays. We might hope that the gates are well calibrated and finely controlled so that the RB decay is very close to the upper bound given by the unitarity passed into this function.

Parameters:

• unitarity – The measured decay parameter in a unitarity measurement
• dimension – The dimension of the Hilbert space, 2**num_qubits

Returns:

The upper bound on RB decay, saturated if no unitary errors are present, Proposition 8 of [ECN]