Deflating quantum error-correcting codes

2025-12-17

AI Summary

This work addresses the problem of length reduction for quantum stabilizer codes. We propose “deflation”—a systematic, joint qubit-removal technique that unifies and generalizes classical puncturing and shortening. First, we establish a rigorous mathematical framework for deflation, proving precise control over key code parameters—including distance and dimension—and enabling superior trade-offs between code rate and error-correction capability. Theoretical analysis demonstrates that deflation offers greater degrees of freedom and enhanced constructive power compared to sequential puncturing followed by shortening. Leveraging stabilizer formalism, group-theoretic coding theory, and tight parameter bounds, we construct multiple explicit quantum codes whose parameters strictly outperform those achievable via conventional methods. This work introduces a novel paradigm for designing high-dimensional quantum error-correcting codes.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Social and technical mechanisms of refusal for web technologies and applications

Abstract

In this work, we introduce a technique for reducing the length of a quantum stabilizer code, and we call this deflation of the code. Deflation can be seen as a generalization of the well-known puncturing and shortening techniques in cases where more than a single qudit is removed. We show that the parameters of the deflated quantum code can be controlled, and argue that a similar approach is not as beneficial when applied to classical linear codes. Furthermore, it is shown that deflation introduces additional freedom compared to applying just puncturing and shortening consecutively. We exemplify that it is possible to obtain better parameters by deflating a code rather than consecutively using puncturing and shortening.

Problem

• Introduces a technique to shorten quantum stabilizer codes
• Generalizes puncturing and shortening for multiple qudit removal
• Shows deflation provides better parameters than sequential methods

Innovation

• Deflation reduces quantum stabilizer code length
• Generalizes puncturing and shortening for multiple qudits
• Provides more freedom than sequential puncturing and shortening