Comparative Studies of Quantum Annealing, Digital Annealing, and Classical Solvers for Reaction Network Pathway Analysis and mRNA Codon Selection
Milind Upadhyay, Mark Nicholas Jones
TL;DR
This work benchmarks quantum annealing, digital annealing, and classical solvers on QUBO-formulated optimization problems across two industrially relevant use cases: reaction network pathway analysis and mRNA codon selection. It analyzes problem-mapping overhead, QUBO structure (connectivity and penalties), and solver performance to determine where quantum-inspired methods offer advantages. The results show classical MILP/CP solvers (notably Gurobi) solving CRN pathways to optimality, while mRNA codon selection benefits from linearization and constraint-aware solvers; D-Wave NL HQA provides near-optimal or competitive performance for some sizes, whereas unconstrained D-Wave HQA and some CQM/HQA variants exhibit exponential scaling. Overall, solver performance is highly problem-structure dependent, underscoring the need to match QUBO formulation and solver type to the specific problem class for practical quantum utility.
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 (especially Gurobi and CP-SAT) are observed to solve the problem to optimality in reasonable time frames. For mRNA codon selection, Gurobi outperformed all other solvers in time to solution for all problem sizes, followed by CP-SAT and the D-Wave Nonlinear (NL) HQA solver.