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

TL;DR

This paper presents a quantum-inspired optimization approach using Hopfield Networks to efficiently solve subset sum problems, with applications in auditing and financial data analysis, leveraging quantum annealing hardware.

Contribution

It introduces a novel method of formulating subset sum as a QUBO problem and demonstrates its effectiveness on artificial and real data using Hopfield Networks and quantum hardware.

Findings

Gradient descent on Hopfield Networks reliably finds solutions.

The approach is applicable to adiabatic quantum computers and specialized hardware.

Experiments show promising results on quantum annealing hardware.

Abstract

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