[HYBRID] Quantum Computing Seminar: Limitations of Tensor Network Approaches for Optimisation and Sampling

Annotation

Finding the ground state of the Ising model is a well-known NP-hard problem. It is connected to Quadratic Unconstrained Binary Optimization (QUBO), a mathematical framework that can express optimization problems relevant to various fields. There are many heuristic algorithms and hardware solutions for tackling QUBOs. In recent years, quantum annealing devices have emerged as a possible avenue for addressing this task. They encode optimization problems as physical systems, which, when evolved, settle into the ground state of the relevant Ising model.

In this talk, I will present the results of our research group's work. First, I will briefly introduce quantum annealers and classical Ising machines to provide context to our work. Next, I will describe SpinGlassPEPS, a novel tensor-network-based heuristic algorithm that uncovers the low-energy spectrum of Ising-like problems. In particular, those with a connectivity structure relevant to present-day quantum annealers. Our deterministic approach combines a branch-and-bound search strategy with an approximate calculation of marginals via tensor-network contractions. I will show extensive benchmarks of our method, focusing on ground state search and the diversity of found low-energy solutions. This will be followed by a discussion on how and why the tensor network approach is breaking. Finally, a short hands-on tutorial on SpinGlassPEPS.jl, the Julia implementation of our algorithm, will be provided.

This talk will be based on research published in the following papers:
1.  Dziubyna, A.M., Śmierzchalski, T., Gardas, B., Rams, M.M. and Mohseni, M., 2024. Limitations of tensor network approaches for optimization and sampling: A comparison against quantum and classical Ising machines. arXiv preprint arXiv:2411.16431.

2. Śmierzchalski, T., Dziubyna, A.M., Jałowiecki, K., Mzaouali, Z., Pawela, Ł., Gardas, B. and Rams, M.M., 2025. SpinGlassPEPS. jl: Tensor-network package for Ising-like optimization on quasi-two-dimensional graphs. arXiv preprint arXiv:2502.02317.

Benefits for the attendees, what they will learn:

Attendees will learn basic information about quantum annealing, what problems it tackles, and the devices that use it. They will gain an understanding of the SpinGlassPEPS algorithm, together with a hands-on tutorial for a package that implements it. Furthermore, participants will gain an insight into how and why the tensor network approach breaks down in the context of sampling and optimization.

Level

intermediate - advanced

Language

English

Prerequisites

Basic knowledge of Julia programming

Basic understanding of linear algebra

Basic familiarity with combinatorial optimization problems and algorithms

Tutor

Tomasz Śmierzchalski is a PhD student employed in the research grant: “Simulations of physical systems with near-term annealing technology” realized at the Institute of Theoretical and Applied Informatics, Polish Academy of Sciences. He was also involved in the EuroHPC-PL project. He participated in many conferences, workshops, and summer schools, including the prestigious summer school at the Los Alamos National Laboratory. His research contributions lie in the fields of Quantum Annealing and Combinatorial Optimisation. Currently, his research interest is employing machine learning to aid quantum computation. He is one of the developers of the SpinGlassPEPS.jl package.

Acknowledgements

This project has received funding from the European High-Performance Computing Joint Undertaking (JU) under grant agreement No 101101903. The JU receives support from the Digital Europe Programme and Germany, Bulgaria, Austria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Greece, Hungary, Ireland, Italy, Lithuania, Latvia, Poland, Portugal, Romania, Slovenia, Spain, Sweden, France, Netherlands, Belgium, Luxembourg, Slovakia, Norway, Türkiye, Republic of North Macedonia, Iceland, Montenegro, Serbia. This project has received funding from the Ministry of Education, Youth and Sports of the Czech Republic.

This course was supported by the Ministry of Education, Youth and Sports of the Czech Republic through the e-INFRA CZ (ID:90254).