Thresholds for post-selected quantum error correction from statistical mechanics

TL;DR

This paper explores the use of post-selection in quantum error correction, employing statistical mechanics to analytically determine thresholds and phases, thereby enhancing scalable quantum computing strategies.

Contribution

It introduces a statistical mechanical framework to analyze post-selected quantum error correction, providing analytic thresholds and phase characterization for surface codes.

Findings

Identification of regimes where post-selection improves QEC performance

Derivation of analytic expressions for logical and abort thresholds

Discovery of four thermodynamic phases in post-selected QEC

Abstract

We identify regimes where post-selection can be used scalably in quantum error correction (QEC) to improve performance. We use statistical mechanical models to analytically quantify the performance and thresholds of post-selected QEC, with a focus on the surface code. Based on the non-equilibrium magnetization of these models, we identify a simple heuristic technique for post-selection that does not require a decoder. Along with performance gains, this heuristic allows us to derive analytic expressions for post-selected conditional logical thresholds and abort thresholds of surface codes. We find that such post-selected QEC is characterised by four distinct thermodynamic phases, and detail the implications of this phase space for practical, scalable quantum computation.