A Quantum Approach to Subset-Sum and Similar Problems

TL;DR

This paper explores a quantum heuristic method for solving the subset-sum problem, suggesting potential polynomial-time solutions and exponential speed-ups over classical algorithms under certain assumptions.

Contribution

It introduces a quantum heuristic approach inspired by quantum Arthur-Merlin games for subset-sum, proposing possible polynomial-time solutions and applications to knapsack problems.

Findings

Potential polynomial-time solution for subset-sum under certain assumptions

Exponential speed-up over classical algorithms suggested

Numerical example provided to illustrate approach

Abstract

In this paper, we study the subset-sum problem by using a quantum heuristic approach similar to the verification circuit of quantum Arthur-Merlin games. Under described certain assumptions, we show that the exact solution of the subset sum problem my be obtained in polynomial time and the exponential speed-up over the classical algorithms may be possible. We give a numerical example and discuss the complexity of the approach and its further application to the knapsack problem.