Generalized Probabilistic Approximate Optimization Algorithm
This is an incremental advancement for researchers in quantum-inspired optimization and probabilistic computing, offering a new classical variational method for Ising machines.
The paper tackles the problem of solving optimization problems like spin-glass models by introducing a generalized Probabilistic Approximate Optimization Algorithm (PAOA), which extends prior work and shows superior performance over QAOA on a 26-spin Sherrington-Kirkpatrick model and improves upon simulated annealing on heavy-tailed problems such as SK-Lévy.
We introduce a generalized \textit{Probabilistic Approximate Optimization Algorithm (PAOA)}, a classical variational Monte Carlo framework that extends and formalizes prior work by Weitz \textit{et al.}~\cite{Combes_2023}, enabling parameterized and fast sampling on present-day Ising machines and probabilistic computers. PAOA operates by iteratively modifying the couplings of a network of binary stochastic units, guided by cost evaluations from independent samples. We establish a direct correspondence between derivative-free updates and the gradient of the full Markov flow over the exponentially large state space, showing that PAOA admits a principled variational formulation. Simulated annealing emerges as a limiting case under constrained parameterizations, and we implement this regime on an FPGA-based probabilistic computer with on-chip annealing to solve large 3D spin-glass problems. Benchmarking PAOA against QAOA on the canonical 26-spin Sherrington-Kirkpatrick model with matched parameters reveals superior performance for PAOA. We show that PAOA naturally extends simulated annealing by optimizing multiple temperature profiles, leading to improved performance over SA on heavy-tailed problems such as SK-Lévy.