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  • Open Access

Designing quantum error correction codes for practical spin qudit systems

Sumin Lim and Arzhang Ardavan

  • CAESR, Department of Physics, University of Oxford, The Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom

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Phys. Rev. A 112, 022418 – Published 12 August, 2025

DOI: https://doi.org/10.1103/7q6l-d4qh

Abstract

The implementation of practical error correction protocols is essential for deployment of quantum information technologies. Ways of exploiting high-spin nuclei, which have multilevel quantum resources, have attracted interest in this context because they offer additional Hilbert space dimensions in a spatially compact and theoretically efficient structure. We present a quantitative analysis of the performance of a spin-qudit-based error-correctable quantum memory, with reference to the actual Hamiltonians of several potential candidate systems. First, the ideal code-word implemented on a spin-7/2 nucleus, which provides first-order Pauli-X, Y and Z error correction, has intrinsic infidelity due to mixed eigenstates under realistic conditions. We confirm that expansion to a spin-9/2 system with tailored code words can compensate for this infidelity. Second, we claim that electric field fluctuations, which are inevitable in real systems, should also be considered as a noise source, and we illustrate an encoding and decoding scheme for a multi-spin-qudit-based error correction code that can simultaneously compensate for both electric- and magnetic-field perturbations. Such strategies are important as we move beyond the current noisy-intermediate quantum era, and fidelities above two or three nines become crucial for the implementation of quantum technologies.

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Phys. Rev. A 112, 022418– Published 12 August, 2025
  • Received 19 March 2025
  • Accepted 23 July 2025
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