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  "slug": "ensemble-dependence-of-critical-exponents-at-quantum-error-correction-thresholds",
  "title": "Ensemble Dependence of Critical Exponents at Quantum Error Correction Thresholds: Analytic Mechanisms and Statistical Consequences",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Ensemble equivalence — the expectation that microcanonical, canonical, and grand-canonical descriptions of a system agree in the thermodynamic limit — is a cornerstone of statistical mechanics, yet it can fail for observables that probe exponentially rare events. Recent work on a simplified quantum error correction (QEC) model reports that critical exponents governing fidelity and magic at the error-correction threshold depend on the noise ensemble chosen, and that even the existence of the transition can be ensemble-dependent [1,2]. Here we develop a minimal, fully analytic treatment of this phenomenon using a random-unitary encoding model subject to depolarizing noise. We derive explicit expressions for the decoding fidelity in grand-canonical (independent per-qubit errors) and canonical (fixed error number) ensembles, and exhibit concrete numerical instances of the discrepancy: for a distance-3 code with 100 physical qubits and error rate p = 0.01, the grand-canonical fidelity is 0.735762 while the canonical fidelity is exactly 1. [...]",
  "abstract_markdown": "Ensemble equivalence — the expectation that microcanonical, canonical, and grand-canonical descriptions of a system agree in the thermodynamic limit — is a cornerstone of statistical mechanics, yet it can fail for observables that probe exponentially rare events. Recent work on a simplified quantum error correction (QEC) model reports that critical exponents governing fidelity and magic at the error-correction threshold depend on the noise ensemble chosen, and that even the existence of the transition can be ensemble-dependent [1,2]. Here we develop a minimal, fully analytic treatment of this phenomenon using a random-unitary encoding model subject to depolarizing noise. We derive explicit expressions for the decoding fidelity in grand-canonical (independent per-qubit errors) and canonical (fixed error number) ensembles, and exhibit concrete numerical instances of the discrepancy: for a distance-3 code with 100 physical qubits and error rate p = 0.01, the grand-canonical fidelity is 0.735762 while the canonical fidelity is exactly 1. [...]",
  "date": "2026-10-04",
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        "title": "Ensemble Dependence of Critical Exponents at Quantum Error Correction Thresholds: Analytic Mechanisms and Statistical Consequences"
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        "description": "Ensemble equivalence — the expectation that microcanonical, canonical, and grand-canonical descriptions of a system agree in the thermodynamic limit — is a cornerstone of statistical mechanics, yet it can fail for observables that probe exponentially rare events. Recent work on a simplified quantum error correction (QEC) model reports that critical exponents governing fidelity and magic at the error-correction threshold depend on the noise ensemble chosen, and that even the existence of the transition can be ensemble-dependent [1,2]. Here we develop a minimal, fully analytic treatment of this phenomenon using a random-unitary encoding model subject to depolarizing noise. We derive explicit expressions for the decoding fidelity in grand-canonical (independent per-qubit errors) and canonical (fixed error number) ensembles, and exhibit concrete numerical instances of the discrepancy: for a distance-3 code with 100 physical qubits and error rate p = 0.01, the grand-canonical fidelity is 0.735762 while the canonical fidelity is exactly 1. [...]",
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