Quantum error correction with degenerate codes for correlated noise

2010/07/31 by Giulio Chiribella, Michele Dall'Arno, Michele Dall’Arno +4
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Computer science #Degenerate energy levels #Discrete mathematics #Error detection and correction #Image (mathematics) #Mathematical analysis #Mathematics #Noise (video) #Physics #Probability of error #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum computer #Quantum error correction #Quantum mechanics #Quantum noise #Quantum-Dot Cellular Automata #Statistical physics #Upper and lower bounds #quant-ph

paper · pdf · doi:10.1103/physreva.83.052305

published as Phys. Rev. A 83, 052305 (2011) · 5 pages, published version

openalex publication_date 2011/05/09 · arxiv created 2011/05/16 · arxiv updated 2015/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We introduce a quantum packing bound on the minimal resources required by nondegenerate error-correction codes for any kind of noise. We prove that degenerate codes can outperform nondegenerate ones in the presence of correlated noise, by exhibiting examples where the quantum packing bound is violated.

Citations

• How to Correct Small Quantum Errors
• Non-Markovian dynamics of double quantum dot charge qubits due to acoustic phonons
• Quantum-state engineering with Josephson-junction devices
• Complementarity of private and correctable subsystems in quantum cryptography and error correction
• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• Probabilistic theories with purification
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