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 quantum annealing or classical Monte Carlo samplers; (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.

翻译：我们提出了一种针对奇偶编码架构的实用混合解码方案。该架构最初由N. Sourlas提出，作为解决复杂优化问题（特别是以自旋系统建模的问题，如伊辛模型和自旋玻璃）的计算技术，后由W. Lechner、P. Hauke和P. Zoller重新设计以开发量子退火设备。我们研究了一种称为SLHZ模型的具体模型，旨在实现仅通过几何局域自旋相互作用构建的近期量子退火设备。考虑到SLHZ模型与经典低密度奇偶校验码的紧密关联，解码可采用两种途径：（1）寻找从SLHZ模型导出的自旋哈密顿量的基态，这可通过随机解码器（如量子退火或经典蒙特卡洛采样器）实现；（2）使用经典LDPC码的确定性解码技术，如置信传播和比特翻转解码器。所提出的混合方法通过将比特翻转解码应用于基于SLHZ模型的随机解码器输出，将两种途径相结合。我们通过仿真证明，该方法能够揭示SLHZ模型的潜在优势，实现Sourlas提出的软退火概念。