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Refining quantum fidelity: approaches in quantum error correction

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Abstract

Quantum fidelity is a cornerstone metric for evaluating the accuracy and reliability of quantum information processes, particularly in noise- and error-prone environments. This study presents a comprehensive exploration of refined approaches to quantum fidelity within the framework of quantum error correction (QEC). Central to our analysis is the role of fidelity in preserving quantum states and mitigating the impact of noise across QEC codes such as the Steane code and Shor code. By leveraging density matrices, which encapsulate the statistical and quantum coherence properties of quantum systems, we conduct a mode analysis with respect to the off-diagonal elements, unveiling their critical influence on state preservation and error resilience. A key focus is the interpolation parameter \( p \), which governs the transition from a maximally mixed state to the actual quantum state. Comparative analysis across fidelity computation techniques highlights the superior performance of methods such as 2x sqrtm, 3x svd, and eigvals, while methods like sqrtmh eigvalsh and sqrtm svd exhibit slower fidelity growth in these regions. The Steane QEC code demonstrates enhanced robustness over the Shor code, particularly under noisy conditions, showcasing its ability to maintain quantum state integrity. This study underscores the pivotal role of density matrices in optimizing QEC protocols, enabling precise fidelity evaluation, and ensuring the scalability and reliability of quantum technologies. This research improved the development of next-generation quantum computing and communication infrastructures.

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Authors and Affiliations

  1. Department of Electronics Engineering, Indian Institute of Technology (Banaras Hindu University), IIT (BHU), Varanasi, Uttar Pradesh, 221005, India

    Vikram Singh Thakur & Atul Kumar

  2. Department of Computer Science, Munster Technological University, Bishopstown, Cork, T12 P928, Ireland

    Kapal Dev

  3. Institute of Intelligent Systems, University of Johannesburg, Auckland Park 2006, South Africa

    Kapal Dev

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  1. Vikram Singh Thakur
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  2. Atul Kumar
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Correspondence to Vikram Singh Thakur.

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Thakur, V.S., Kumar, A. & Dev, K. Refining quantum fidelity: approaches in quantum error correction. Quantum Inf Process 24, 190 (2025). https://doi.org/10.1007/s11128-025-04809-3

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