Learning Encodings by Maximizing State Distinguishability: Variational Quantum Error Correction

2025/06/13 by Nico Meyer, Meyer, Nico, Christopher Mutschler +5 · 2 citations
Computer Science · #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Neural Networks and Reservoir Computing #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2506.11552

openalex publication_date 2025/06/13 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

Quantum error correction is crucial for protecting quantum information against decoherence. Traditional codes like the surface code require substantial overhead, making them impractical for near-term, early fault-tolerant devices. We propose a novel objective function for tailoring error correction codes to specific noise structures by maximizing the distinguishability between quantum states after a noise channel, ensuring efficient recovery operations. We formalize this concept with the distinguishability loss function, serving as a machine learning objective to discover resource-efficient encoding circuits optimized for given noise characteristics. We implement this methodology using variational techniques, termed variational quantum error correction (VarQEC). Our approach yields codes with desirable theoretical and practical properties and outperforms standard codes in various scenarios. We also provide proof-of-concept demonstrations on IBM and IQM hardware devices, highlighting the practical relevance of our procedure.

Citations

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• Stabilizer Codes and Quantum Error Correction
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• Perfect Quantum Error Correction Code
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• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• On the limited memory BFGS method for large scale optimization
• Completely positive maps and entropy inequalities

Cited by

• Correcting quantum errors one gradient step at a time
• Real-time adaptive quantum error correction by model-free multi-agent learning

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