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  • Open Access

Practical hybrid decoding scheme for parity-encoded spin systems

Yoshihiro Nambu*

  • *Contact author: y-nambu@aist.go.jp
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Phys. Rev. Applied 25, 014046 – Published 20 January, 2026

DOI: https://doi.org/10.1103/drry-blqs

Abstract

We propose a practical hybrid decoding scheme for the parity-encoding architecture. This architecture was first introduced by N. Sourlas [Phys. Rev. Lett. 94, 070601 (2005)] as a computational technique for tackling hard optimization problems, especially those modeled by spin systems such as the Ising model and spin glasses, and reinvented by W. Lechner, P. Hauke, and P. Zoller [Sci. Adv. 1, e1500838 (2015)] to develop quantum annealing devices. We study the specific model, called the SLHZ model, aiming to achieve a near-term quantum annealing device implemented solely through geometrically local spin interactions. Taking account of the close connection between the SLHZ model and a classical low-density parity-check (LDPC) code, two approaches can be chosen for the decoding: (1) finding the ground state of a spin Hamiltonian derived from the SLHZ model, which can be achieved via stochastic decoders such as a quantum annealer or a classical Monte Carlo sampler; or (2) using deterministic decoding techniques for the classical LDPC code, such as belief propagation and a bit-flip decoder. The proposed hybrid approach combines the two approaches by applying bit-flip decoding to the readout of the stochastic decoder based on the SLHZ model. We present simulations demonstrating that this approach can reveal the latent potential of the SLHZ model, realizing the soft-annealing concept proposed by Sourlas.

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Phys. Rev. Applied 25, 014046– Published 20 January, 2026
  • Received 23 July 2024
  • Revised 14 May 2025
  • Accepted 17 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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