Gaussian boson sampling for binary optimization

TL;DR

This paper introduces a novel approach using Gaussian Boson Sampling with threshold detectors to solve binary optimization problems, demonstrating promising results on complex instances like 3-SAT and graph partitioning.

Contribution

It proposes a new quantum-inspired method for binary optimization by mapping problems onto a GBS framework and optimizing the energy's CVaR, with efficient classical computation of the cost function and gradients.

Findings

Significant performance improvements over random guessing.

First proof of concept for GBS-based binary optimization.

Efficient classical computation of cost and gradient for low-degree polynomials.

Abstract

Binary optimization is a fundamental area in computational science, with wide-ranging applications from logistics to cryptography, where the tasks are often formulated as Quadratic or Polynomial Unconstrained Binary Optimization problems (QUBO/PUBO). In this work, we propose to use a parametrized Gaussian Boson Sampler (GBS) with threshold detectors to address such problems. We map general PUBO instance onto a quantum Hamiltonian and optimize the Conditional Value-at-Risk of its energy with respect to the GBS ansatz. In particular, we observe that, when the algorithm reduces to standard Variational Quantum Eigensolver, the cost function is analytical. Therefore, it can be computed efficiently, along with its gradient, for low-degree polynomials using only classical computing resources. Numerical experiments on 3-SAT and Graph Partitioning problems show significant performance gains over random guessing, providing a first proof of concept for our proposed approach.