pygsti.tools.rbtools.p_to_r

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pygsti.tools.rbtools.p_to_r#

p_to_r(p, d, rtype='EI')#

Converts an RB decay constant (p) to the RB error rate (r).

Here p is (normally) obtained from fitting data to A + Bp^m. There are two ‘types’ of RB error rate corresponding to different rescalings of 1 - p. These are the entanglement infidelity (EI) type r and the average gate infidelity (AGI) type r. The EI-type r is given by:

r = (d^2 - 1)(1 - p)/d^2,

where d is the dimension of the system (i.e., 2^n for n qubits). The AGI-type r is given by

r = (d - 1)(1 - p)/d.

For RB on gates whereby every gate is followed by an n-qubit uniform depolarizing channel (the most idealized RB scenario) then the EI-type (AGI-type) r corresponds to the EI (AGI) of the depolarizing channel to the identity channel.

The default (EI) is the convention used in direct RB, and is perhaps the most well-motivated as then r corresponds to the error probability of the gates (in the idealized pauli-errors scenario). AGI is the convention used throughout Clifford RB theory.

Parameters:

  • p (float) – Fit parameter p from P_m = A + B*p**m.

  • d (int) – Number of dimensions of the Hilbert space

  • rtype ({'EI','AGI'}, optional) – The RB error rate rescaling convention.

Returns:

r – The RB error rate

Return type:

float

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