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arXiv · 2608.05093

Imaginarity as a necessary resource for trainability in QAOA

Syed Muhammad Ali Hassan·Kostas Blekos·Stefan Kühn·Nikos Kollas·Karl Jansen
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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.

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Syed Muhammad Ali Hassan, Kostas Blekos, Stefan Kühn, Nikos Kollas, Karl Jansen. 2026-08-05. Imaginarity as a necessary resource for trainability in QAOA. https://arxiv.org/abs/2608.05093

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