GitHub

TenSolver.jl

Tensor Network-based solver for discrete polynomial optimization.

Overview

TenSolver.jl provides an efficient solver for QUBO problems using tensor network methods, leveraging the Density Matrix Renormalization Group (DMRG) algorithm. The package is particularly useful for:

  • Solving large-scale discrete optimization problems
  • Finding approximate solutions to NP-hard problems
  • Exploring the solution space of combinatorial optimization problems
  • Enforcing hard constraints exactly through projection, without penalty terms
  • GPU-accelerated optimization

Installation

using Pkg
Pkg.add("TenSolver")

Quick Start

The simplest way to use this package is passing a matrix to the solver:

using TenSolver

assets = ["Wind", "Solar", "Battery"]

# Wind and solar overlap, while storage pairs well with either source.
Q = [0.0 1.0 -1.5;
     1.0 0.0 -0.5;
     -1.5 -0.5 0.0]
E, psi = TenSolver.minimize(Q; verbosity=0)

# Verify we found the minimum
E ≈ -3.0

# output

true

The returned argument E is the calculated estimate for the minimum value, while psi is a probability distribution over all possible solutions to the problem. You can sample from it:

x = TenSolver.sample(psi)

# Verify the sampled solution achieves the minimum and inspect the chosen assets
(x' * Q * x ≈ E, join(assets[findall(==(1), x)], ", "))

# output

(true, "Wind, Battery")

Features

  • Tensor Network Optimization: Uses advanced tensor network methods (DMRG) for efficient optimization
  • Probability Distribution: Returns a probability distribution over optimal solutions
  • Hard Constraints: Enforces constraints exactly via CoTenN-style projection MPOs, so sampled solutions are always feasible (see Constrained Optimization)
  • JuMP Integration: Works seamlessly with the JuMP modeling language
  • GPU Support: Supports GPU acceleration via CUDA.jl, Metal.jl, and other accelerators
  • Flexible Configuration: Numerous parameters to control accuracy vs. performance trade-off

Citing TenSolver

If you use TenSolver in your research, please cite our NeurIPS 2025 Workshop paper:

@inproceedings{tensolver2025,
  title     = {Quantum-Inspired Tensor Network Methods for Quadratic Unconstrained Binary Optimization},
  author    = {Iago {Leal de Freitas} and Jo{\~a}o Victor {Paim de Cerqueira Melo Souza} and David E. {Bernal Neira}},
  booktitle = {NeurIPS Workshop on GPU-Accelerated and Scalable Optimization},
  year      = {2025},
  url       = {https://openreview.net/forum?id=EL002DTBRA}
}

Contents