Table 1 Individual error contributions for QIRB

From: Measuring error rates of mid-circuit measurements

P

Contribution to rΩ

\(\ne {\mathbb{I}}\)

pL(a, P, b)

\(={\mathbb{I}}\)

2[panti(a) + panti(b) − 2panti(a)panti(b)]pL(a, P, b)

  1. Here we report the contribution to rΩ by the error (a, P, b) occurring in layer L. Entries were calculated by determining the probability of each error causing a state transition. An error’s contribution to rΩ depends upon three factors: (i) the probability pL(a, P, b) of the error occurring; (ii) if \(P={\mathbb{I}}\); and (iii) the probabilities panti(a) and panti(b) of X⊗a and X⊗b anti-commuting with a random \({s}_{{{{\rm{meas}}}}}^{{{{\rm{pre}}}}}\) and \({s}_{{{{\rm{meas}}}}}^{{{{\rm{post}}}}}\), respectively. Because, on average, three-quarters of the entries of \({s}_{{{{\rm{meas}}}}}^{{{{\rm{pre}}}}}\) and \({s}_{{{{\rm{meas}}}}}^{{{{\rm{post}}}}}\) are Pauli-Z operators and one-quarter of their entries are I, computing panti(a) and panti(b) is a bit harder. Supplementary Note 4 contains more details on how to perform these calculations.
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