none 10.1103/7q6l-d4qh American Physical Society (APS) American Physical Society 16 179787664 5203 20250812140540 10.1103 2025-08-12T15:26:15Z 2025-07-24T14:30:21Z 1 Physical Review A Phys. Rev. A 2469-9926 2469-9934 PLRAAN 8 2025 112 2 Sumin Lim University of Oxford https://ror.org/052gg0110 https://orcid.org/0000-0001-8954-8862 Arzhang Ardavan University of Oxford https://ror.org/052gg0110 https://orcid.org/0000-0001-5521-2658 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. 8 12 2025 7 23 2025 022418 2.0 10.1103/crossmark-policy journals.aps.org true 2025-03-19 Published by the American Physical Society 2025 Horizon 2020 Framework Programme http://0-dx-doi-org.oasis.unisa.ac.za/10.13039/100010661 862893 863098 https://creativecommons.org/licenses/by/4.0/ 10.48550/arXiv.2503.12142 10.1103/7q6l-d4qh 20250812140540 https://link.aps.org/doi/10.1103/7q6l-d4qh http://0-harvest-aps-org.oasis.unisa.ac.za/v2/journals/articles/10.1103/7q6l-d4qh/fulltext https://0-link-aps-org.oasis.unisa.ac.za/article/10.1103/7q6l-d4qh 10.1103/PhysRevA.64.012310 10.1103/PhysRevA.77.032309 10.1103/PhysRevLett.125.080503 10.1103/PhysRevX.10.031050 10.1103/PhysRevLett.125.260509 10.1103/PhysRevLett.133.260601 10.1038/s41567-018-0414-3 10.1103/PhysRevLett.125.043602 10.1038/nature18949 10.1038/s41586-020-2603-3 Stabilizer Codes and Quantum Error Correction D. Gottesman 1997 10.1103/PhysRevA.55.900 10.1103/PhysRevLett.84.2525 10.1038/s41586-022-05434-1 10.1103/RevModPhys.87.307 10.1103/PhysRevLett.77.3260 10.1103/PhysRevLett.77.198 10.1021/acs.jpclett.0c02213 10.1103/PhysRevLett.127.010504 10.1103/PhysRevA.108.062403 10.1038/s41534-024-00829-6 10.1039/D1SC01506K 10.1063/5.0053378 10.1103/PhysRevA.108.022424 10.1103/PRXQuantum.5.020355 10.1103/PhysRevA.108.022428 10.1103/PRXQuantum.4.040333 10.1103/PhysRevLett.134.070603 10.1038/s41567-024-02745-0 10.22331/q-2018-08-06-79 10.1038/s41586-021-04182-y 10.1038/s41586-021-04273-w 10.1038/s41565-017-0014-x 10.1038/s41586-019-1666-5 10.1103/PhysRevLett.127.180501 10.1038/s41586-021-03588-y 10.1038/s41586-023-06927-3 10.1038/s41467-021-22274-1 10.1103/PhysRevLett.124.130501 10.1103/PhysRevX.9.041031 10.1103/PhysRevResearch.5.013035 10.1038/s41534-021-00466-3 10.1038/s41467-024-45368-y 10.1038/s41586-020-2057-7 10.1103/PhysRevLett.115.087602 10.1103/PhysRevB.93.024305 10.1002/qute.202000005 10.1103/PhysRevLett.110.027601 10.1103/PhysRevLett.112.097603 10.1038/nphys1969 10.1103/PhysRevLett.122.037202 10.1126/sciadv.abf8103 10.1038/s41567-021-01355-4 10.1038/nature10314 10.1103/PhysRevA.54.1862 10.1016/j.ccr.2021.213984 10.1021/ic801142p 10.1103/PhysRevLett.102.087603 10.1103/PhysRevLett.131.063001 10.1103/PhysRevA.105.L061101 10.1038/s41467-018-04079-x 10.1038/s41467-017-00378-x 10.1016/j.mssp.2016.10.039 10.1103/PhysRevLett.123.106802 10.1002/mrc.1665 10.1039/C7SC03749J 10.1109/18.681315