Practical hybrid decoding scheme for parity-encoded spin systems

Abstract

We propose a practical hybrid decoding scheme for the parity-encoding architecture. This architecture was first introduced by N. Sourlas 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 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 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; (2) using deterministic decoding techniques for the classical LDPC code, such as belief propagation and 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 soft-annealing concept proposed by Sourlas.

21 pages, 12 figures, 1 Supplemental material. Published in Physical Review Applied. arXiv admin note: substantial text overlap with arXiv:2502.07170

References in corpus (12)

• Adiabatic Quantum Computing
• Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design
• Quantum annealing with a network of all-to-all connected, two-photon driven Kerr nonlinear oscillators
• Noisy Gradient Descent Bit-Flip Decoding for LDPC Codes
• Robust quantum optimizer with full connectivity
• A quantum annealer with fully programmable all-to-all coupling via Floquet engineering
• Stabilisers as a design tool for new forms of Lechner-Hauke-Zoller Annealer
• Two-photon driven Kerr resonator for quantum annealing with three-dimensional circuit QED
• Error correction for encoded quantum annealing
• Simulated Quantum Annealing with Two All-to-All Connectivity Schemes
• Correlated oscillations in Kerr parametric oscillators with tunable effective coupling
• Statistical Mechanics and Capacity-Approaching Error-Correcting Codes