📝 SummarXiv

Abstract

For various optimization problems, the classical time to solution is super-polynomial and intractable to solve with classical bit-based computing hardware to date. Digital and quantum annealers have the potential to identify near-optimal solutions for such optimization problems using a quadratic unconstrained binary optimization (QUBO) problem formulation. This work benchmarks two use cases to evaluate the utility of QUBO solvers for combinatorial optimization problems, in order to determine if a QUBO formulation and annealing-based algorithms have an advantage over classical mixed-integer programming (MIP) and constraint programming (CP) solvers. Various QUBO and solver metrics such as problem mapping, quantitative interconnectivity, penalty structure, solver minimum cost (obtained optimal value) and solver time to solution have been applied to evaluate different QUBO problems. Constrained and unconstrained QUBO solvers are compared including the Fujitsu digital annealer (DA), various D-Wave hybrid quantum annealing solvers (QA, HQA), and the classical MIP/CP solvers HiGHS, Gurobi, SCIP, and CP-SAT. The two industrially relevant use cases are reaction network pathway analysis and mRNA codon selection. For reaction pathway analysis, classical MIP/CP solvers are observed to solve the problem to optimality in reasonable time frames while the DA is not able to do so. For mRNA codon selection, CP-SAT displayed the best performance for standard and large protein datasets (under 1500 amino acids). For the extra-large protein dataset (11000 to 14000 amino acids), the D-Wave Nonlinear HQA solver performed comparably to CP-SAT, outperforming it in minimum cost in 2 out of the 4 problems.