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Many applications in automated auditing and the analysis and consistencycheck of financial documents can be formulated in part as the subset sumproblem: Given a set of numbers and a target sum, find the subset of numbersthat sums up to the target. The problem is NP-hard and classical solvingalgorithms are therefore not practical to use in many real applications. Wetackle the problem as a QUBO (quadratic unconstrained binary optimization)problem and show how gradient descent on Hopfield Networks reliably findssolutions for both artificial and real data. We outline how this algorithm canbe applied by adiabatic quantum computers (quantum annealers) and specializedhardware (field programmable gate arrays) for digital annealing and runexperiments on quantum annealing hardware.

Solving Subset Sum Problems using Quantum Inspired Optimization Algorithms with Applications in Auditing and Financial Data Analysis