Thresholds for post-selected quantum error correction from statistical mechanics

• URL: http://arxiv.org/abs/2410.07598v3
• Date: Thu, 18 Sep 2025 23:51:07 GMT
• Title: Thresholds for post-selected quantum error correction from statistical mechanics
• Authors: Lucas H. English, Dominic J. Williamson, Stephen D. Bartlett,
• Abstract summary: We identify regimes where post-selection can be used scalably in quantum error correction (QEC)<n>We use statistical mechanical models to analytically quantify the performance and thresholds of post-selected QEC.<n>We find that such post-selected QEC is characterised by four distinct thermodynamic phases.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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