Structure Theorem for Quantum Replacer Codes

2025/05/10 by Chitambar, Eric, Hagen, Sarah, Kribs, David W. +2
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2505.06659

Abstract

Quantum replacer codes are codes that can be protected from errors induced by a given set of quantum replacer channels, an important class of quantum channels that includes the erasures of subsets of qubits that arise in quantum error correction. We prove a structure theorem for such codes that synthesizes a variety of special cases with earlier theoretical work in quantum error correction. We present several examples and applications of the theorem, including a mix of new observations and results together with some subclasses of codes revisited from this new perspective.

Citations

• Optimizing quantum error correction protocols with erasure qubits
• Hybrid quantum systems with artificial atoms in solid state
• Quantum Data-Syndrome Codes: Subsystem and Impure Code Constructions
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Related

• Quantum stabilizer codes and beyond
• An Introduction to Quantum Error Correction
• Quantum Error Correcting Subsystem Codes From Two Classical Linear Codes
• Stabilizer Codes and Quantum Error Correction
• An Introduction to Error-Correcting Codes: From Classical to Quantum