Document Type

Technical Report

Publication Date

2024

Embargo Period

10-1-2024

Abstract

We investigate the implementation of an oracle for the Subset Sum problem for quantum search using Grover’s algorithm. Our work concerns reducing the number of qubits, gates, and multi-controlled gates required by the oracle.

We describe the compilation of a Subset Sum instance into a quantum oracle, using a Python library we developed for Qiskit and have published in GitHub. We then present techniques to conserve qubits and gates along with experiments showing their effectiveness on random instances of Subset Sum. These techniques include moving from fixed to varying-width arithmetic, using partial sums of a set’s integers to determine specific integer widths, and sorting the set to obtain provably the most efficient partial sums.

We present a new method for computing bit-string comparisons that avoids arbitrarily large multiple-control gates, and we introduce a simple modification to the oracle that allows for approximate solutions to the Subset Sum problem via Grover search.

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

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