Subsystem surface and compass code sensitivities to non-identical infidelity distributions on heavy-hex lattice

TL;DR

This study investigates how non-uniform and outlier error distributions affect the logical error rates of subsystem surface and compass codes, revealing that average error rates depend mainly on mean infidelity, with limited sensitivity to higher moments.

Contribution

It provides a numerical analysis of the impact of non-identical error distributions on quantum error correction performance, highlighting the limited influence of outliers and the benefits of location-aware decoding.

Findings

Logical error rate depends mainly on average infidelity, not higher moments.

Error rate saturates with errors at a few 'bad' locations.

Location-aware decoders modestly improve logical error rates.

Abstract

Logical qubits encoded into a quantum code exhibit improved error rates when the physical error rates are sufficiently low, below the pseudothreshold. Logical error rates and pseudothresholds can be estimated for specific circuits and noise models, and these estimates provide approximate goals for qubit performance. However, estimates often assume uniform error rates, while real devices have static and/or dynamic distributions of non-identical error rates and may exhibit outliers. These distributions make it more challenging to evaluate, compare, and rank the expected performance of quantum processors. We numerically investigate how the logical error rate depends on parameters of the noise distribution for the subsystem surface code and the compass code on a subdivided hexagonal lattice. Three notable observations are found: (1) the average logical error rate depends on the average of the physical qubit infidelity distribution without sensitivity to higher moments (e.g., variance or outliers) for a wide parameter range; (2) the logical error rate saturates as errors increase at one or a few "bad" locations; and (3) a decoder that is aware of location specific error rates modestly improves the logical error rate. We discuss the implications of these results in the context of several different practical sources of outliers and non-uniform qubit error rates.