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In seeking out an algorithm to test out the capability of the IBM QuantumExperience quantum computer, we were given a review paper covering variousalgorithms for solving the subset-sum problem, including both classical andquantum algorithms. The paper went on to present a novel algorithm that beatthe previous best algorithm known at the time. The complex nature of thealgorithm made it difficult to see a path for implementation on the QuantumExperience machine and the exponential cost - only slightly better than thebest classical algorithm - left us looking for a different approach for solvingthis problem. We present here a new quantum algorithm for solving thesubset-sum problem that for many cases should lead to O(poly(n))-time tosolution. The work is reminiscent of the verification procedure used in apolynomial-time algorithm for the quantum Arthur-Merlin games presentedelsewhere, where the use of a quantum binary search to find a maximumeigenvalue in the final output stage has been adapted to the subset-sum problemas in another paper.

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