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Topological Quantum Computing Error Correction Code Optimization Algorithms

Jincheng Zhang

Published Sep 7, 2026• 0 citations
Publisher

Abstract

This paper investigates the optimization of error correction codes specifically tailored for topological quantum computing. Recognizing the unique challenges posed by error propagation within topological networks, we propose a novel approach centered on analyzing and mitigating error transmission pathways. The core of our method involves constructing a topological quantum computing model and simulating error propagation dynamics. Utilizing an optimization algorithm, we systematically adjust the parameters of the error correction code, aiming to reduce the velocity of error propagation and ultimately enhance the overall resilience of the topological quantum computation. We demonstrate the potential of this approach to significantly improve the fault tolerance of topological quantum computers. The primary mathematical framework revolves around the concept of topological entanglement entropy and its application in quantifying error propagation rates. The key equations used are: (Ei, t) representing the energy of a qubit at time t, (γij) representing the coupling strength between qubits i and j, (Pij) representing the probability of error propagation between qubits i and j, (Hij) representing the Hamiltonian operator governing the interaction between qubits i and j, (ρi) representing the density matrix of qubit i, and (Si) representing the topological entanglement entropy of qubit i. The optimization algorithm, a variant of the genetic algorithm, is defined as: (αij, βij) where αij and βij represent the parameters to be optimized, and the objective function is defined as minimizing (Pij) for all pairs of qubits i and j. The overall error correction fidelity is quantified as: (F) = 1 - (∑i Pi), where Pi is the probability of error for qubit i. This work contributes to the development of robust and scalable topological quantum computing architectures.

DOI
10.5281/zenodo.22573634

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This paper investigates the application of topological optimization techniques to enhance quantum error correction (QEC) coding. Traditional QEC schemes often face limitations in terms of redundancy and scalability. We propose a novel approach utilizing topological optimization to design the physical topology of QEC architectures, specifically focusing on qubit connectivity. The core claim is that through this optimization process, we can significantly improve both the error correction performance and the scalability of QEC codes. The underlying mechanism involves leveraging algorithms to iteratively refine the topological structure, minimizing unnecessary connections and maximizing the efficiency of the encoding process. The results demonstrate a potential pathway towards more robust and scalable quantum computers by fundamentally altering the design space for QEC. We present a theoretical framework and explore key considerations for implementing this approach, highlighting its potential to overcome the current constraints in QEC design. Our methodology provides a novel strategy for optimizing qubit interactions within a QEC system.
Quantum error correction (QEC) remains a critical challenge for the practical realization of quantum computation. Traditional QEC approaches often rely on pre-defined error correction codes and fixed topological structures, which may not be optimal for all quantum systems and noise environments. This paper proposes a novel framework for quantum error correction that leverages adaptive topological optimization. The core idea is to dynamically adjust the error correction topology in real-time, based on feedback from the quantum system, to maximize information transmission efficiency and resilience to noise. We construct a quantum error correction network where each physical qubit is associated with multiple logical qubits, forming a topological code. Utilizing quantum measurement and control techniques, we monitor the coherence and noise levels of the qubits, alongside the effectiveness of the error correction code. A quantum feedback control algorithm then dynamically modifies the topological connections, minimizing the impact of noise and enhancing the correction efficiency. This adaptive approach offers a significant improvement over static QEC methods, promising more robust and efficient quantum communication and computation in challenging environments. The theoretical framework presented demonstrates the potential for achieving significantly improved performance through real-time topology optimization.