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arXiv · 2410.07598

Thresholds for post-selected quantum error correction from statistical mechanics

Lucas H. English·Dominic J. Williamson·Stephen D. Bartlett
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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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Lucas H. English, Dominic J. Williamson, Stephen D. Bartlett. 2024-10-10. Thresholds for post-selected quantum error correction from statistical mechanics. https://doi.org/10.1103/nh49-52y2

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