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Entropy
Volume 28
Issue 7
10.3390/e28070726
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Article

Information-Theoretic Framework for Quantum State Purification and Error Correction via Symmetric Subspace Projection

by
Jiaqi Tang
1 and
Mu-Jiang-Shan Wang
2,*
1
School of Computer Science and Technology, Guangdong University of Technology, Guangzhou 510006, China
2
Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
*
Author to whom correspondence should be addressed.
Entropy 2026, 28(7), 726; https://doi.org/10.3390/e28070726 (registering DOI)
Submission received: 18 April 2026 / Revised: 17 June 2026 / Accepted: 19 June 2026 / Published: 24 June 2026
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Abstract

The severe susceptibility of qubits to environmental noise remains the primary obstacle to practical quantum computing. To overcome this, we introduce a purification-assisted quantum error-correction (QEC) framework that embeds a symmetric subspace projection module between the encoding and physical layers. Acting as an information-theoretic noise-entropy filter, it compresses von Neumann entropy before encoding. Under depolarizing noise, a three-copy scheme elevates the surface-code threshold from 1.1% to a 2.0% noiseless bound (~1.6% at circuit level). Our iterative purification-assisted error-correction (IPEC) algorithm dynamically modulates purification depth via syndrome feedback, delivering a 46-fold logical error reduction for surface codes (d = 7) at a 1.0% physical error rate.
Keywords: quantum state purification; quantum error correction; symmetric subspace projection; fault-tolerant threshold; iterative purification-assisted error-correction algorithm; coherent information; stabilizer codes quantum state purification; quantum error correction; symmetric subspace projection; fault-tolerant threshold; iterative purification-assisted error-correction algorithm; coherent information; stabilizer codes

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MDPI and ACS Style

Tang, J.; Wang, M.-J.-S. Information-Theoretic Framework for Quantum State Purification and Error Correction via Symmetric Subspace Projection. Entropy 2026, 28, 726. https://doi.org/10.3390/e28070726

AMA Style

Tang J, Wang M-J-S. Information-Theoretic Framework for Quantum State Purification and Error Correction via Symmetric Subspace Projection. Entropy. 2026; 28(7):726. https://doi.org/10.3390/e28070726

Chicago/Turabian Style

Tang, Jiaqi, and Mu-Jiang-Shan Wang. 2026. "Information-Theoretic Framework for Quantum State Purification and Error Correction via Symmetric Subspace Projection" Entropy 28, no. 7: 726. https://doi.org/10.3390/e28070726

APA Style

Tang, J., & Wang, M.-J.-S. (2026). Information-Theoretic Framework for Quantum State Purification and Error Correction via Symmetric Subspace Projection. Entropy, 28(7), 726. https://doi.org/10.3390/e28070726

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