Effcient classical error correction for parity encoded spin systems

• URL: http://arxiv.org/abs/2502.07170v2
• Date: Fri, 14 Feb 2025 14:34:55 GMT
• Title: Effcient classical error correction for parity encoded spin systems
• Authors: Yoshihiro Nambu,
• Abstract summary: This paper addresses how to correct errors in a spin readout of PE architecture. We have shown that independent and identically distributed errors in a spin readout can be corrected by a very simple decoding algorithm.
• Score: 0.0
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• Abstract: Fast solvers for combinatorial optimization problems (COPs) have attracted engineering interest in various industrial and social applications. Quantum annealing (QA) has emerged as a promising candidate and significant efforts have been dedicated to its development. Since COP is encoded in the Ising interaction between logical spins, its realization requires a spin system with all-to-all connectivity, which poses technical difficulties in the physical implementation of large-scale QA devices. W. Lechner, P. Hauke, and P. Zoller proposed parity-encoding (PE) architecture, consisting of a larger system of physical spins with only local connectivities between them, to avoid this diffculty in the near future QA device development. They suggested that this architecture not only reduces implementation diffculties and improves scalability, but also has intrinsic fault tolerance because logical spins are redundantly and nonlocally encoded into the physical spins. Nevertheless, it remains unclear how these advantageous features can be exploited. This paper addresses how to correct errors in a spin readout of PE architecture. Our work is based on the close connection between PE architecture and classical low-density parity-check (LDPC) codes. We have shown that independent and identically distributed errors in a spin readout can be corrected by a very simple decoding algorithm that can be regarded as a bit flipping (BF) algorithm for the LDPC codes. The BF algorithm was shown to have comparable performance to the belief propagation (BP) decoding algorithm. Furthermore, it is suggested that the introduction of post-readout BF decoding reduces the total computational cost and improves the performance of the global optimal solution search using the PE architecture. We believe that our results indicate that the PE architecture is a promising platform for near-term QA devices.

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