Combinatorial optimization problems are central to science and engineering and specialized hardware from quantum annealers to classical Ising machines are being actively developed to address them. These systems typically sample from a fixed energy landscape defined by the problem Hamiltonian encoding the discrete optimization problem. The recently introduced Probabilistic Approximate Optimization Algorithm (PAOA) takes a different approach: it treats the optimization landscape itself as variational, iteratively learning circuit parameters from samples. Here, we demonstrate PAOA on a 64$\times$64 perimeter-gated single-photon avalanche diode (pgSPAD) array fabricated in 0.35 $μ$m CMOS, the first realization of the algorithm using intrinsically stochastic nanodevices. Each p-bit exhibits a device-specific, asymmetric (Gompertz-type) activation function due to dark-count variability. Rather than calibrating devices to enforce a uniform symmetric (logistic/tanh) activation, PAOA learns around device variations, absorbing residual activation and other mismatches into the variational parameters. On canonical 26-spin Sherrington-Kirkpatrick instances, PAOA achieves high approximation ratios with $2p$ parameters ($p$ up to 17 layers), and pgSPAD-based inference closely tracks CPU simulations. These results show that variational learning can accommodate the non-idealities inherent to nanoscale devices, suggesting a practical path toward larger-scale, CMOS-compatible probabilistic computers.

翻译：组合优化问题是科学与工程领域的核心问题，从量子退火器到经典伊辛机等专用硬件正被积极开发以解决此类问题。这些系统通常从由编码离散优化问题的问题哈密顿量所定义的固定能量景观中进行采样。近期提出的概率近似优化算法（PAOA）采用了一种不同的思路：它将优化景观本身视为可变的，通过迭代地从样本中学习电路参数。本文中，我们在采用0.35微米CMOS工艺制造的64×64周界门控单光子雪崩二极管（pgSPAD）阵列上实现了PAOA，这是该算法首次利用本征随机纳米器件实现。由于暗计数变异性的影响，每个p比特呈现出器件特定的非对称（冈珀茨型）激活函数。PAOA无需通过校准器件来强制实现均匀对称（逻辑/双曲正切）激活，而是通过学习适应器件变异，将残余激活及其他失配吸收到变分参数中。在经典的26自旋谢林顿-柯克帕特里克实例上，PAOA以2p个参数（p最多达17层）实现了较高的近似比，且基于pgSPAD的推理结果与CPU仿真高度吻合。这些结果表明变分学习能够适应纳米尺度器件固有的非理想特性，为构建更大规模、CMOS兼容的概率计算机提供了一条实用路径。