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
This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
Benoit, Angelo G.; Schwartz, Sam; and Cytron, Ron K., "Optimization of a Quantum Subset Sum Oracle" Report Number: (2024). All Computer Science and Engineering Research.
https://openscholarship.wustl.edu/cse_research/1188