We develop a new benchmarking scheme for the Decoded Quantum Interferometry (DQI) algorithm quantifying the number of quantum gates required to obtain an optimal solution to a problem amenable to DQI. We apply the benchmarking scheme to the Binary Paint Shop Problem (BPSP) in order to benchmark the performance of DQI against a state of the art classical solver. To do so, we provide an explicit construction of a quantum circuit implementation of a greedy decoder for low-density parity check codes arising from max-2-XORSAT problems.
@article{arxiv.2603.24441,
title = {Benchmarking Techniques for Decoded Quantum Interferometry},
author = {Leon Bollmann and Maximilian Hess},
journal= {arXiv preprint arXiv:2603.24441},
year = {2026}
}