Quantum Error Correction Codes: Topological Optimization

Jincheng Zhang

Published Sep 5, 2026• 0 citations

Abstract

This paper investigates the application of topological optimization techniques to quantum error correction codes. The core claim is that optimizing the topological structure of quantum error correction codes can significantly reduce error correction resource consumption and enhance the resilience of quantum computations. This is achieved through the utilization of topological optimization algorithms to identify optimal sub-graph structures within the topological network of a quantum error correction code, minimizing resource usage while maintaining sufficient error correction capability. We present a novel approach to quantum error correction design, moving beyond traditional code selection and offering a framework for dynamic code adaptation. The theoretical framework incorporates concepts from graph theory, linear algebra, and quantum information theory. The primary objective is to demonstrate a method for systematically reducing the overhead associated with quantum error correction, a critical step towards building fault-tolerant quantum computers. Our approach focuses on minimizing the number of physical qubits required to encode a logical qubit, a key metric for evaluating the efficiency of any quantum error correction scheme. The results indicate a substantial potential for optimization, suggesting a path toward more practical and scalable quantum computation.

DOI: 10.5281/zenodo.22315407

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