HOBOTAN: Efficient Higher Order Binary Optimization Solver with Tensor Networks and PyTorch
Shoya Yasuda, Shunsuke Sotobayashi, Yuichiro Minato
TL;DR
This paper tackles high-order binary optimization (HOBO) by introducing HOBOTAN, a tensor-network-based solver with a PyTorch GPU backend. By mapping HOBO problems to HOBO tensors and using tensor contractions, along with integer encoding to reduce qubits, the approach enables scalable optimization on CPUs and GPUs. The authors demonstrate the framework on three problems— seating optimization, Pythagorean triples, and the traveling salesman problem— and show substantial improvements through contraction-path optimization and decompositions such as SVD and tensor trains. The work highlights practical impacts for large-scale combinatorial optimization and sets the stage for future multi-GPU and quantum-computing applications.
Abstract
In this study, we introduce HOBOTAN, a new solver designed for Higher Order Binary Optimization (HOBO). HOBOTAN supports both CPU and GPU, with the GPU version developed based on PyTorch, offering a fast and scalable system. This solver utilizes tensor networks to solve combinatorial optimization problems, employing a HOBO tensor that maps the problem and performs tensor contractions as needed. Additionally, by combining techniques such as batch processing for tensor optimization and binary-based integer encoding, we significantly enhance the efficiency of combinatorial optimization. In the future, the utilization of increased GPU numbers is expected to harness greater computational power, enabling efficient collaboration between multiple GPUs for high scalability. Moreover, HOBOTAN is designed within the framework of quantum computing, thus providing insights for future quantum computer applications. This paper details the design, implementation, performance evaluation, and scalability of HOBOTAN, demonstrating its effectiveness.