QUBO formulation of process superstructures via extended process network theory: Opportunities and current limitations

Abstract

Superstructure synthesis enables comprehensive process optimization but requires efficient methods to solve large-scale combinatorial problems. This study develops an extended process network theory that formulates process superstructures as quadratic unconstrained binary optimization (QUBO) problems, enabling the use of emerging combinatorial optimization solvers, including quantum annealers. By introducing binary variables into the adjacency matrix and developing polynomial approximations for recycling stream inverse matrices and fractional concentration terms, the proposed methodology extends process network theory from fixed-structure analysis to superstructure optimization. The approach is demonstrated through a two-stage separation case study with a recycling configuration. Computational experiments compare three solver types: a commercial optimizer (Gurobi), a graphics processing unit (GPU)-based QUBO solver, and quantum annealing hardware (D-Wave Advantage2). The GPU solver maintains stable performance across all problem scales, with solution times of 3–4 s, whereas the commercial optimizer exhibits exponential time growth at higher discretization levels. Current quantum annealing hardware successfully solves minimal instances but fails at larger scales owing to physical topology connectivity constraints rather than qubit count limitations. The variable growth resulting from quadratization remains a significant challenge. These results establish a theoretical framework for QUBO-based process optimization. Practical implementation will depend on advances in quantum hardware connectivity and hybrid decomposition strategies.