AI 中文总结
该研究对线性码ML解码的QUBO/伊辛公式进行系统比较，表明两种公式在神经元数量等方面权衡不同，首选公式与求解器选择有关，还指出仅基态正确性不足，信号处理任务应与神经形态硬件模型共同公式化。
AI 中文摘要
神经形态计算目前主要由机器学习工作负载驱动，但其潜在特性使其特别适合以伊辛或QUBO形式表示的组合优化问题。虽然神经形态伊辛求解器已得到证明，但如何将给定问题进行公式化以最适合神经形态动力学却很少受到关注。最大似然（ML）信道解码可表示为伊辛/QUBO问题，量子退火文献中已有两种不同公式：平方惩罚公式使用较少自旋但产生密集的内部校验耦合，链积公式以额外辅助自旋为代价提高局部性。两者在足够的约束执行下都将ML码字置于基态，但尚未在神经形态硬件施加的约束下进行比较。本文首次对线性码的ML解码的QUBO/伊辛公式进行了系统的并列比较。我们表明，这两种公式在神经元数量、突触密度、局部性和收敛行为方面存在根本不同的权衡。首选公式与求解器的选择密不可分，两者必须共同考虑。最后，我们表明仅基态正确性是一个不足的设计标准，如果神经形态计算要扩展到接收器流水线中，信号处理任务理想情况下应与其神经形态硬件模型共同公式化。
英文摘要
Neuromorphic computing has so far been driven predominantly by machine-learning workloads, yet its underlying properties also make it particularly well suited to combinatorial optimization problems expressed in Ising or QUBO form. While neuromorphic Ising solvers have been demonstrated, how a given problem should be formulated to best suit neuromorphic dynamics has received far less attention. Maximum-likelihood (ML) channel decoding can be expressed as an Ising/QUBO problem, and two distinct formulations already exist in the quantum-annealing literature: a squared-penalty formulation that uses few spins but produces dense intra-check couplings, and a chain-product formulation that improves locality at the cost of additional auxiliary spins. Both place the ML codeword at the ground state under sufficient constraint enforcement, but they have not been compared under the constraints that neuromorphic hardware imposes. This work provides the first systematic side-by-side comparison of QUBO/Ising formulations of ML decoding for linear codes. We show that the two formulations impose fundamentally different tradeoffs in neuron count, synaptic density, locality, and convergence behavior. The preferred formulation is inseparable from the choice of solver, and the two must be considered jointly. Finally, we show that ground-state correctness alone is an insufficient design criterion, and that signal processing tasks should ideally be co-formulated with their neuromorphic hardware models if neuromorphic computing is to extend into the receiver pipeline.
CommentsAccepted for Publication IEEE CAMAD 2026
