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Quantum-classical auxiliary field quantum Monte Carlo with matchgate shadows on trapped ion quantum computers

Luning Zhao*, Joshua J. Goings, Willie Aboumrad, Andrew Arrasmith, Lazaro Calderin, Spencer Churchill, Dor Gabay, Thea Harvey-Brown, Melanie Hiles et al.

Arseny Kovyrshin, Lars Tornberg, and Anders Broo

Jeff R. Hammond

Zohim Chandani, Pradnya Khalate, and Elica Kyoseva

Yi-Ting Chen, Eric M. Kessler, Cedric Yen-Yu Lin, Gandhi Ramu, and Ryan Shaffer

Michael Brett, Benchen Huang, Maxime R. Hugues, and Tyler Y. Takeshita

Magda Kaja, Matthew Keesan, Karolina Kulesz, Andrii Maksymov, Mei Maruo, Mauricio Muñoz, Bas Nijholt, Rebekah Schiller, Yvette de Sereville, Amy Smidutz, Felix Tripier, Grace Yao, Trishal Zaveri, Coleman Collins, Martin Roetteler, and Evgeny Epifanovsky

  • IonQ Inc, College Park, Maryland 20740, USA

  • NVIDIA Helsinki Oy, Porkkalankatu 1, Helsinki 00180, Finland

  • AWS Quantum Technologies, Seattle, Washington 98121, USA

  • AWS Worldwide Specialist Organization, Seattle, Washington 98170, USA

  • *Contact author: zhao@ionq.co
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Phys. Rev. Research 8, 033061 – Published 15 July, 2026

DOI: https://doi.org/10.1103/n1tf-8kr7

Abstract

We demonstrate an end-to-end workflow to model chemical reaction barriers with the quantum-classical auxiliary field quantum Monte Carlo (QC-AFQMC) algorithm with quantum tomography using matchgate shadows. The workflow operates within an accelerated quantum supercomputing environment with the IonQ Forte quantum computer and NVIDIA graphic processing units (GPUs) on Amazon Web Services. We present several algorithmic innovations and an efficient GPU-accelerated execution that achieves a several orders of magnitude speedup over the state-of-the-art implementation of QC-AFQMC. We apply the algorithm to simulate the oxidative addition step of the nickel-catalyzed Suzuki-Miyaura reaction using 24 qubits of IonQ Forte with 16 qubits used to represent the trial state, plus 8 additional ancilla qubits for error mitigation, resulting in the largest QC-AFQMC with matchgate shadow experiments ever performed on quantum hardware. We achieve a 9× speedup in collecting matchgate circuit measurements, and our distributed-parallel postprocessing implementation attains a 656× time-to-solution improvement over the prior state of the art. Chemical reaction barriers for the model reaction evaluated with active-space QC-AFQMC are within the uncertainty interval of ±4 kcal/mol from the reference CCSD(T) (coupled cluster singles and doubles with perturbative triples) result when matchgates are sampled on the ideal simulator and within 10 kcal/mol from reference when measured on quantum processing unit. This work marks a step toward practical quantum chemistry simulations on quantum devices while identifying several opportunities for further development.

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Phys. Rev. Research 8, 033061– Published 15 July, 2026
  • Received 15 August 2025
  • Accepted 17 June 2026
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