Thresholds for Postselected Quantum Error Correction from Statistical Mechanics

We identify regimes where postselection 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 postselected QEC, with a focus on the surface code. Based on the nonequilibrium magnetization of these models, we identify a simple heuristic technique for postselection that determines whether to abort without requiring a decoder. Along with performance gains, this heuristic allows us to derive analytic expressions for postselected conditional logical thresholds and abort thresholds of surface codes. We find that such postselected QEC is characterized by four distinct thermodynamic phases and detail the implications of this phase space for practical, scalable quantum computation.