Comparative Evaluation of PyTorch, JAX, SciPy, and Neal for Solving QUBO Problems at Scale

TL;DR

This paper benchmarks five software solvers for large-scale QUBO problems, comparing their solution quality, scalability, and runtime efficiency across problem sizes up to 45,000 variables.

Contribution

It provides a comprehensive comparison of Neal, PyTorch, JAX, and SciPy for solving large QUBO problems, highlighting their strengths and limitations.

Findings

Neal achieves the lowest energy but is limited to 6000 variables.

PyTorch offers a good balance of solution quality and scalability.

SciPy is limited to small problems with longer runtimes.

Abstract

Quadratic Unconstrained Binary Optimization (QUBO) is a versatile framework for modeling combinatorial optimization problems. This study benchmarks five software-based QUBO solvers: Neal, PyTorch (CPU), PyTorch (GPU), JAX, and SciPy, on randomly generated QUBO matrices ranging from 1000x1000 to 45000x45000, under six convergence thresholds from 10^-1 to 10^-6. We evaluate their performance in terms of solution quality (energy) and computational time. Among the solvers tested, Neal achieved the lowest energy values but was limited to problems with up to 6000 variables due to high memory consumption. PyTorch produced slightly higher energy results than Neal but demonstrated superior scalability, solving instances with up to 45000 variables. Its support for GPU acceleration and CPU multi-threading also resulted in significantly shorter runtimes. JAX yielded energy values slightly above those of PyTorch and was limited to 25000 variables, with runtimes comparable to PyTorch on GPU. SciPy was the most constrained solver, handling only up to 6000 variables and consistently producing the highest energy values with the longest computation times. These findings highlight trade-offs between solution quality, scalability, and runtime efficiency, and suggest that PyTorch is the most balanced choice for large-scale QUBO problems when computational resources permit.