Practical hybrid decoding scheme for parity-encoded spin systems

TL;DR

This paper introduces a hybrid decoding scheme for parity-encoded spin systems, combining stochastic and deterministic methods to improve decoding efficiency and effectiveness in quantum annealing architectures.

Contribution

It presents a novel hybrid decoding approach that integrates stochastic and classical decoding techniques for the SLHZ model in quantum annealing.

Findings

Hybrid decoding improves error correction performance.

Simulations show potential for near-term quantum devices.

Combines belief propagation with stochastic decoding.

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.