Towards An Implementation of the Subset-sum Problem on the IBM Quantum Experience

TL;DR

This paper introduces a new quantum algorithm for the subset-sum problem that aims to achieve polynomial-time complexity for many cases, advancing quantum computing capabilities for combinatorial problems.

Contribution

The paper presents a novel quantum algorithm for subset-sum that potentially offers polynomial-time solutions, improving upon previous exponential-time algorithms.

Findings

Proposes a quantum algorithm with potential polynomial-time complexity for subset-sum

Builds on quantum binary search techniques used in quantum Arthur-Merlin games

Provides a theoretical framework for efficient quantum solutions to subset-sum

Abstract

In seeking out an algorithm to test out the capability of the IBM Quantum Experience quantum computer, we were given a review paper covering various algorithms for solving the subset-sum problem, including both classical and quantum algorithms. The paper went on to present a novel algorithm that beat the previous best algorithm known at the time. The complex nature of the algorithm made it difficult to see a path for implementation on the Quantum Experience machine and the exponential cost - only slightly better than the best classical algorithm - left us looking for a different approach for solving this problem. We present here a new quantum algorithm for solving the subset-sum problem that for many cases should lead to O(poly(n))-time to solution. The work is reminiscent of the verification procedure used in a polynomial-time algorithm for the quantum Arthur-Merlin games presented elsewhere, where the use of a quantum binary search to find a maximum eigenvalue in the final output stage has been adapted to the subset-sum problem as in another paper.