Thresholds for correcting errors, erasures, and faulty syndrome measurements in degenerate quantum codes

TL;DR

This paper introduces a new method for establishing lower bounds on fault-tolerance thresholds in degenerate quantum codes, improving upon previous bounds by analytically combining various error probabilities.

Contribution

It provides explicit analytic expressions for threshold bounds applicable to quantum LDPC codes with logarithmic or larger distances, enhancing fault-tolerance analysis.

Findings

Threshold bounds are parametrically better than previous percolation-based bounds.

Explicit formulas for combining error probabilities in quantum LDPC codes.

Applicable to codes with sublinear distance scaling.

Abstract

We suggest a technique for constructing lower (existence) bounds for the fault-tolerant threshold to scalable quantum computation applicable to degenerate quantum codes with sublinear distance scaling. We give explicit analytic expressions combining probabilities of erasures, depolarizing errors, and phenomenological syndrome measurement errors for quantum LDPC codes with logarithmic or larger distances. These threshold estimates are parametrically better than the existing analytical bound based on percolation.