Statistical mechanics of quantum error correcting codes

2020/07/31 by Yaodong Li, Matthew P. A. Fisher · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Computer science #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Statistical physics #cond-mat.dis-nn #cond-mat.stat-mech #quant-ph

paper · pdf · doi:10.1103/physrevb.103.104306

published as Phys. Rev. B 103, 104306 (2021) · 22 pages, 8 figures. v2: fixed .bbl file, new footnote 12. v3: updated references and acknowledgements. v4: fixed typos; published version

arxiv created 2021/03/24 · openalex publication_date 2021/03/24 · arxiv updated 2021/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Random quantum dynamics generates quantum error correcting codes that are robust against observers and errors. Here, the authors describe a simple physical picture of such codes, mapping characteristic code properties to the statistical mechanics of fluctuating ``entanglement domain walls''. The error correcting criterion is understood as a decoupling condition of domain walls, which leads to a universal scaling law of the ``code distance''.

Citations

• Entanglement in the stabilizer formalism
• Error Correction in Quantum Communication
• Detecting Topological Order in a Ground State Wave Function
• Improved simulation of stabilizer circuits
• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
• Good Quantum Error-Correcting Codes Exist
• Black holes as mirrors: quantum information in random subsystems
• Fault-tolerant quantum computation by anyons
• Coarse-grained dynamics of operator and state entanglement
• Dynamical Purification Phase Transition Induced by Quantum Measurements
• The private classical capacity and quantum capacity of a quantum channel
• Approximate quantum error correction
• Quantum Computation and Quantum Information
• Measurement-Driven Phase Transition within a Volume-Law Entangled Phase
• Stabilizer Codes and Quantum Error Correction

Cited by

• Universality of Entanglement Transitions from Stroboscopic to Continuous Measurements
• Quantum criticality in the nonunitary dynamics of (2+1)-dimensional free fermions
• Sachdev-Ye-Kitaev circuits for braiding and charging Majorana zero modes
• Spin stiffness and resilience phase transition in a noisy toric-rotor code