Imaginarity as a necessary resource for trainability in QAOA
Quantum Physics
2026-08-05 v1
Abstract
The quantum approximate optimization algorithm (QAOA) tackles combinatorial problems by tuning a quantum circuit in a classical loop, often guided by gradients. We show that the gradient used to tune the circuit's final parameter is bounded by imaginarity, which weights phase relationships between candidate solutions by how strongly the circuit connects them and how differently the problem scores them. Imaginarity is necessary but not sufficient for a nonzero gradient. We extend the bound to three common noise models and compare it numerically with the gradient in Max-Cut simulations.
Cite
@article{arxiv.2608.05093,
title = {Imaginarity as a necessary resource for trainability in QAOA},
author = {Syed Muhammad Ali Hassan and Kostas Blekos and Stefan Kühn and Nikos Kollas and Karl Jansen},
journal= {arXiv preprint arXiv:2608.05093},
year = {2026}
}