The parity mapping provides a geometrically local encoding of the Quantum Approximate Optimization Algorithm (QAOA), at the expense of having a quadratic qubit overhead for all-to-all connected problems. In this work, we benchmark the parity-encoded QAOA on spin-glass models. We address open questions in the scaling of this algorithm. In particular, we show that for fixed number of parity-encoded QAOA layers, the performance or the output energy, vanishes towards zero (the value achieved by random guessing) with problem size N as N−1/2. Our results suggest that the parity-encoded QAOA does not have a promising scaling compared to the standard version of QAOA. We perform tensor-network calculations to confirm our results, and comment on the concentration of optimal QAOA parameters over problem instances.
@article{arxiv.2311.02151,
title = {Vanishing performance of the parity-encoded quantum approximate optimization algorithm applied to spin-glass models},
author = {Elisabeth Wybo and Martin Leib},
journal= {arXiv preprint arXiv:2311.02151},
year = {2024}
}