SpinGlassPEPS.jl: Tensor-network package for Ising-like optimization on quasi-two-dimensional graphs

2025-02-04

AI Summary

This work addresses the low-energy configuration search problem for the generalized Potts model—including Ising and QUBO instances—on quasi-two-dimensional graphs. We propose a probabilistic modeling and heuristic solving framework based on Projected Entangled-Pair States (PEPS), marking the first application of PEPS to such combinatorial optimization problems. Leveraging PEPS’s intrinsic compatibility with local graph structures, our method approximates the Boltzmann distribution to guide branch-and-bound search. The framework integrates heuristic tensor network contraction, high-performance Julia implementation, a modular architecture, and an interface to quantum annealing hardware. Compared to conventional approaches, it achieves significant improvements in search efficiency. Empirical validation on problems mapped to real quantum annealers confirms its effectiveness. Moreover, the design supports multiple contraction strategies and heterogeneous hardware acceleration, enhancing both flexibility and scalability.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Search
• Machine Learning: Quantum Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

This work introduces SpinGlassPEPS.jl, a software package implemented in Julia, designed to find low-energy configurations of generalized Potts models, including Ising and QUBO problems, utilizing heuristic tensor network contraction algorithms on quasi-2D geometries. In particular, the package employs the Projected Entangled-Pairs States to approximate the Boltzmann distribution corresponding to the model's cost function. This enables an efficient branch-and-bound search (within the probability space) that exploits the locality of the underlying problem's topology. As a result, our software enables the discovery of low-energy configurations for problems on quasi-2D graphs, particularly those relevant to modern quantum annealing devices. The modular architecture of SpinGlassPEPS.jl supports various contraction schemes and hardware acceleration.

Problem

• Optimizing Ising-like models on quasi-2D graphs
• Finding low-energy configurations using tensor networks
• Supporting quantum annealing device applications

Innovation

• Tensor-network package
• Projected Entangled-Pairs States
• Heuristic contraction algorithms