Posiform Planting: Generating QUBO Instances for Benchmarking

TL;DR

This paper introduces posiform planting, a novel method for generating large, hard QUBO instances with known solutions, enabling effective benchmarking of quantum and classical optimization algorithms on various hardware architectures.

Contribution

It presents a new technique for creating QUBO problems with guaranteed unique solutions, tailored to hardware connectivity, and demonstrates its application in benchmarking quantum annealers.

Findings

Quantum annealers sampled solutions with high accuracy

Posiform planting generates instances with known optimal solutions

Benchmarking shows D-Wave devices handle large QUBOs effectively

Abstract

We are interested in benchmarking both quantum annealing and classical algorithms for minimizing Quadratic Unconstrained Binary Optimization (QUBO) problems. Such problems are NP-hard in general, implying that the exact minima of randomly generated instances are hard to find and thus typically unknown. While brute forcing smaller instances is possible, such instances are typically not interesting due to being too easy for both quantum and classical algorithms. In this contribution, we propose a novel method, called posiform planting, for generating random QUBO instances of arbitrary size with known optimal solutions, and use those instances to benchmark the sampling quality of four D-Wave quantum annealers utilizing different interconnection structures (Chimera, Pegasus, and Zephyr hardware graphs) as well as the simulated annealing algorithm. Posiform planting differs from many existing methods in two key ways. It ensures the uniqueness of the planted optimal solution, thus avoiding groundstate degeneracy, and it enables the generation of QUBOs that are tailored to a given hardware connectivity structure, provided that the connectivity is not too sparse. Posiform planted QUBOs are a type of 2-SAT boolean satisfiability combinatorial optimization problems. Our experiments demonstrate the capability of the D-Wave quantum annealers to sample the optimal planted solution of combinatorial optimization problems with up to $5627$ qubits.