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

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.

References in corpus (18)

• Ising formulations of many NP problems
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Criticality, the area law, and the computational power of PEPS
• The computational complexity of PEPS
• Quantum critical dynamics in a 5000-qubit programmable spin glass
• Two-Dimensional Tensor Product Variational Formulation
• Pegasus: The second connectivity graph for large-scale quantum annealing hardware
• Scaling Advantage in Approximate Optimization with Quantum Annealing
• Approximate optimization, sampling and spin-glass droplets discovery with tensor networks
• Corner transfer matrix renormalization group approach in the zoo of Archimedean lattices
• 4-clique Network Minor Embedding for Quantum Annealers
• Instability of the ferromagnetic phase under random fields in an Ising spin glass with correlated disorder
• Limitations of tensor network approaches for optimization and sampling: A comparison to quantum and classical Ising machines
• Corner Transfer Matrix Approach to the Yang-Lee Singularity in the 2D Ising Model in a magnetic field
• VeloxQ: A Fast and Efficient QUBO Solver
• Critical Droplets and Replica Symmetry Breaking
• Tensor Network Efficiently Representing Schmidt Decomposition of Quantum Many-Body States