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End-to-end protocol for high-quality quantum approximate optimization algorithm parameters with few shots

Tianyi Hao1,*, Zichang He1,*,†, Ruslan Shaydulin1,‡, Jeffrey Larson2, and Marco Pistoia1

  • *These authors contributed equally to this work.
  • †Contact author: zichang.he@jpmchase.com
  • ‡Contact author: ruslan.shaydulin@jpmchase.com
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Phys. Rev. Research 7, 033179 – Published 21 August, 2025

DOI: https://doi.org/10.1103/24gg-7p8z

Abstract

The quantum approximate optimization algorithm (QAOA) is a quantum heuristic for combinatorial optimization that has been demonstrated to scale better than state-of-the-art classical solvers for some problems. For a given problem instance, QAOA performance depends crucially on the choice of the parameters. While average-case optimal parameters are available in many cases, meaningful performance gains can be obtained by fine-tuning these parameters for a given instance. This task is especially challenging, however, when the number of circuit executions (shots) is limited. In this work, we develop an end-to-end protocol that combines multiple parameter settings and fine-tuning techniques. We use large-scale numerical experiments to optimize the protocol for the shot-limited setting and observe that optimizers with the simplest internal model (linear) perform best. We implement the optimized pipeline on a trapped-ion processor using up to 32 qubits and 5 QAOA layers, and we demonstrate that the pipeline is robust to small amounts of hardware noise. To the best of our knowledge, these are the largest demonstrations of QAOA parameter fine-tuning on a trapped-ion processor in terms of two-qubit gate count.

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Phys. Rev. Research 7, 033179– Published 21 August, 2025
  • Received 13 December 2024
  • Accepted 1 August 2025
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