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  • Open Access

Enhancing quantum computations with the synergy of auxiliary field quantum Monte Carlo and computational basis tomography

Viktor Khinevich* and Wataru Mizukami†

  • Graduate School of Engineering Science, The University of Osaka, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan and Center for Quantum Information and Quantum Biology, The University of Osaka, 1-2 Machikaneyama, Toyonaka 560-8531, Japan

  • *Contact author: victorkh711@gmail.com
  • †Contact author: mizukami.wataru.qiqb@osaka-u.ac.jp
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Phys. Rev. Research 7, 043344 – Published 29 December, 2025

DOI: https://doi.org/10.1103/rbhc-dkh1

Abstract

We introduce QC-CBT-AFQMC, a hybrid algorithm that incorporates computational basis tomography (CBT) into the quantum-classical auxiliary field quantum Monte Carlo (QC-AFQMC) method proposed by Huggins et al. [Nature (London) 603, 416 (2022)], replacing the use of classical shadows. While the original QC-AFQMC showed high accuracy for quantum chemistry calculations, it required exponentially costly postprocessing. Subsequent work using Matchgate shadows [Wan et al., Commun. Math. Phys. 404, 629 (2023)] improved scalability, but still suffers from prohibitive computational requirements that limit practical applications. Our QC-CBT-AFQMC approach uses shallow Clifford circuits with a quadratic reduction of two-qubit gates over the original algorithm, significantly reducing computational requirements and enabling accurate calculations under limited measurement budgets. We demonstrate its effectiveness on the hydroxyl radical, ethylene, and nitrogen molecule, producing potential energy curves that closely match established benchmarks. We also examine the influence of CBT measurement counts on accuracy, showing that subtracting the active space AFQMC energy mitigates measurement-induced errors. Furthermore, we apply QC-CBT-AFQMC to estimate reaction barriers in [3+2] cycloaddition reactions, achieving agreement with high-level references and successfully incorporating complete basis set extrapolation techniques. These results highlight QC-CBT-AFQMC as a practical quantum-classical hybrid method that bridges the capabilities of quantum devices and accurate chemical simulations.

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References (60)

  1. B. Bauer, S. Bravyi, M. Motta, and G. K.-L. Chan, Quantum algorithms for quantum chemistry and quantum materials science, Chem. Rev. 120, 12685 (2020).
  2. M. Motta and J. E. Rice, Emerging quantum computing algorithms for quantum chemistry, WIREs Comput. Mol. Sci. 12, e1580 (2022).
  3. A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O’Brien, A variational eigenvalue solver on a photonic quantum processor, Nat. Commun. 5, 4213 (2014).
  4. S. Lloyd, Universal quantum simulators, Science 273, 1073 (1996).
  5. A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, and M. Head-Gordon, Simulated quantum computation of molecular energies, Science 309, 1704 (2005).
  6. M. Krompiec and D. M. Ramo, Strongly contracted N-electron valence state perturbation theory using reduced density matrices from a quantum computer, arXiv:2210.05702.
  7. A. Tammaro, D. E. Galli, J. E. Rice, and M. Motta, N-electron valence perturbation theory with reference wave functions from quantum computing: Application to the relative stability of hydroxide anion and hydroxyl radical, J. Phys. Chem. A 127, 817 (2023).
  8. K. Mitarai, K. Toyoizumi, and W. Mizukami, Perturbation theory with quantum signal processing, Quantum 7, 1000 (2023).
  9. C. L. Cortes, M. Loipersberger, R. M. Parrish, S. Morley-Short, W. Pol, S. Sim, M. Steudtner, C. S. Tautermann, M. Degroote, N. Moll, R. Santagati, and M. Streif, Fault-tolerant quantum algorithm for symmetry-adapted perturbation theory, PRX Quantum 5, 010336 (2024).
  10. S. Nishio, Y. Oba, and Y. Kurashige, Statistical errors in reduced density matrices sampled from quantum circuit simulation and the impact on multireference perturbation theory, Phys. Chem. Chem. Phys. 25, 30525 (2023).
  11. P. Schleich, J. S. Kottmann, and A. Aspuru-Guzik, Improving the accuracy of the variational quantum eigensolver for molecular systems by the explicitly-correlated perturbative [2]R12-correction, Phys. Chem. Chem. Phys. 24, 13550 (2022).
  12. S. McArdle and D. P. Tew, Improving the accuracy of quantum computational chemistry using the transcorrelated method, arXiv:2006.11181.
  13. A. Kumar, A. Asthana, C. Masteran, E. F. Valeev, Y. Zhang, L. Cincio, S. Tretiak, and P. A. Dub, Quantum simulation of molecular electronic states with a transcorrelated Hamiltonian: Higher accuracy with fewer qubits, J. Chem. Theory Comput. 18, 5312 (2022).
  14. I. O. Sokolov, W. Dobrautz, H. Luo, A. Alavi, and I. Tavernelli, Orders of magnitude increased accuracy for quantum many-body problems on quantum computers via an exact transcorrelated method, Phys. Rev. Res. 5, 023174 (2023).
  15. W. J. Huggins, B. A. O’Gorman, N. C. Rubin, D. R. Reichman, R. Babbush, and J. Lee, Unbiasing fermionic quantum Monte Carlo with a quantum computer, Nature (London) 603, 416 (2022).
  16. S. Zhang and H. Krakauer, Quantum Monte Carlo method using phase-free random walks with Slater determinants, Phys. Rev. Lett. 90, 136401 (2003).
  17. L. Zhao, J. J. Goings, W. Aboumrad, A. Arrasmith, L. Calderin, S. Churchill, D. Gabay, T. Harvey-Brown, M. Hiles, M. Kaja, et al., Quantum-classical auxiliary field quantum Monte Carlo with matchgate shadows on trapped ion quantum computers, arXiv:2506.22408.
  18. J. J. Goings, K. Shin, S. Noh, W. Kyoung, D. Kim, J. Baek, M. Roetteler, E. Epifanovsky, and L. Zhao, Molecular properties in quantum-classical auxiliary-field quantum Monte Carlo: Correlated sampling with application to accurate nuclear forces, J. Chem. Theory Comput. 21, 12573 (2025).
  19. M. Motta and S. Zhang, Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method, WIREs Comput. Mol. Sci. 8, e1364 (2018).
  20. J. Lee, H. Q. Pham, and D. R. Reichman, Twenty years of auxiliary-field quantum Monte Carlo in quantum chemistry: An overview and assessment on main group chemistry and bond-breaking, J. Chem. Theory Comput. 18, 7024 (2022).
  21. Y. Chen, L. Zhang, W. E, and R. Car, Hybrid auxiliary field quantum Monte Carlo for molecular systems, J. Chem. Theory Comput. 19, 4484 (2023).
  22. Y. Yoshida, L. Erhart, T. Murokoshi, R. Nakagawa, C. Mori, H. Tagami, and W. Mizukami, The auxiliary-field quantum Monte Carlo method with seniority-zero trial wave function, J. Chem. Theory Comput. 21, 9404 (2025).
  23. M. Kiser, M. Beuerle, and F. Simkovic, Contextual subspace auxiliary-field quantum Monte Carlo: Improved bias with reduced quantum resources, J. Chem. Theory Comput. 21, 2256 (2025).
  24. H.-Y. Huang, R. Kueng, and J. Preskill, Predicting many properties of a quantum system from very few measurements, Nat. Phys. 16, 1050 (2020).
  25. K. Wan, W. J. Huggins, J. Lee, and R. Babbush, Matchgate shadows for fermionic quantum simulation, Commun. Math. Phys. 404, 629 (2023).
  26. B. Huang, Y.-T. Chen, B. Gupt, M. Suchara, A. Tran, S. McArdle, and G. Galli, Evaluating a quantum-classical quantum Monte Carlo algorithm with Matchgate shadows, Phys. Rev. Res. 6, 043063 (2024).
  27. N. Takemori, Y. Teranishi, W. Mizukami, and N. Yoshioka, Balancing error budget for fermionic k-RDM estimation, arXiv:2312.17452.
  28. G. Mazzola and G. Carleo, Exponential challenges in unbiasing quantum Monte Carlo algorithms with quantum computers, arXiv:2205.09203.
  29. J. Lee, D. R. Reichman, R. Babbush, N. C. Rubin, F. D. Malone, B. O’Gorman, and W. J. Huggins, Response to “Exponential challenges in unbiasing quantum Monte Carlo algorithms with quantum computers”, arXiv:2207.13776.
  30. M. Kohda, R. Imai, K. Kanno, K. Mitarai, W. Mizukami, and Y. O. Nakagawa, Quantum expectation-value estimation by computational basis sampling, Phys. Rev. Res. 4, 033173 (2022).
  31. E. Bäumer and S. Woerner, Measurement-based long-range entangling gates in constant depth, Phys. Rev. Res. 7, 023120 (2025).
  32. L. Erhart, Y. Yoshida, V. Khinevich, and W. Mizukami, Coupled cluster method tailored with quantum computing, Phys. Rev. Res. 6, 023230 (2024).
  33. G. Sugiyama and S. Koonin, Auxiliary field Monte-Carlo for quantum many-body ground states, Ann. Phys. 168, 1 (1986).
  34. F. D. Malone, A. Mahajan, J. S. Spencer, and J. Lee, Ipie: A Python-based auxiliary-field quantum Monte Carlo program with flexibility and efficiency on CPUs and GPUs, J. Chem. Theory Comput. 19, 109 (2023).
  35. Chemqulacs, software package, https://github.com/wmizukami/chemqulacs/ (2025).
  36. Y. Suzuki, Y. Kawase, Y. Masumura, Y. Hiraga, M. Nakadai, J. Chen, K. M. Nakanishi, K. Mitarai, R. Imai, S. Tamiya, T. Yamamoto, T. Yan, T. Kawakubo, Y. O. Nakagawa, Y. Ibe, Y. Zhang, H. Yamashita, H. Yoshimura, A. Hayashi, and K. Fujii, Qulacs: A fast and versatile quantum circuit simulator for research purpose, Quantum 5, 559 (2021).
  37. Q. Sun, T. C. Berkelbach, N. S. Blunt, G. H. Booth, S. Guo, Z. Li, J. Liu, J. D. McClain, E. R. Sayfutyarova, S. Sharma, S. Wouters, and G. K.-L. Chan, PySCF: The Python-based simulations of chemistry framework, WIREs Comput. Mol. Sci. 8, e1340 (2018).
  38. S. R. Langhoff and E. R. Davidson, Configuration interaction calculations on the nitrogen molecule, Int. J. Quantum Chem. 8, 61 (1974).
  39. F. Neese, The ORCA program system, WIREs Comput. Mol. Sci. 2, 73 (2012).
  40. J. C. Jewett and C. R. Bertozzi, Cu-free click cycloaddition reactions in chemical biology, Chem. Soc. Rev. 39, 1272 (2010).
  41. N. K. Devaraj, The future of bioorthogonal chemistry, ACS Cent. Sci. 4, 952 (2018).
  42. D. H. Ess and K. N. Houk, Activation energies of pericyclic reactions: Performance of DFT, MP2, and CBS-QB3 methods for the prediction of activation barriers and reaction energetics of 1,3-dipolar cycloadditions, and revised activation enthalpies for a standard set of hydrocarbon pericyclic reactions, J. Phys. Chem. A 109, 9542 (2005).
  43. A. Karton and L. Goerigk, Accurate reaction barrier heights of pericyclic reactions: Surprisingly large deviations for the CBS-QB3 composite method and their consequences in DFT benchmark studies, J. Comput. Chem. 36, 622 (2015).
  44. T. Stuyver, K. Jorner, and C. W. Coley, Reaction profiles for quantum chemistry-computed [3+2] cycloaddition reactions, Sci. Data 10, 66 (2023).
  45. P. Vermeeren, M. Dalla Tiezza, M. E. Wolf, M. E. Lahm, W. D. Allen, H. F. Schaefer, T. A. Hamlin, and F. M. Bickelhaupt, Pericyclic reaction benchmarks: Hierarchical computations targeting CCSDT(Q)/CBS and analysis of DFT performance, Phys. Chem. Chem. Phys. 24, 18028 (2022).
  46. K. Kanno, M. Kohda, R. Imai, S. Koh, K. Mitarai, W. Mizukami, and Y. O. Nakagawa, Quantum-selected configuration interaction: classical diagonalization of Hamiltonians in subspaces selected by quantum computers, arXiv:2302.11320.
  47. Y. O. Nakagawa, M. Kamoshita, W. Mizukami, S. Sudo, and Y.-Y. Ohnishi, ADAPT-QSCI: Adaptive construction of an input state for quantum-selected configuration interaction, J. Chem. Theory Comput. 20, 10817 (2024).
  48. J. Robledo-Moreno, M. Motta, H. Haas, A. Javadi-Abhari, P. Jurcevic, W. Kirby, S. Martiel, K. Sharma, S. Sharma, T. Shirakawa, et al., Chemistry beyond exact solutions on a quantum-centric supercomputer, Sci. Adv. 11, eadu9991 (2025).
  49. S. Barison, J. Robledo Moreno, and M. Motta, Quantum-centric computation of molecular excited states with extended sample-based quantum diagonalization, Quantum Sci. Technol. 10, 025034 (2025).
  50. D. Kaliakin, A. Shajan, F. Liang, J. R. Moreno, Z. Li, A. Mitra, M. Motta, C. Johnson, A. A. Saki, S. Das, I. Sitdikov, A. Mezzacapo, and K. M. Merz Jr., Accurate quantum-centric simulations of supramolecular interactions, Commun. Phys. 8, 396 (2025).
  51. K. Sugisaki, S. Kanno, T. Itoko, R. Sakuma, and N. Yamamoto, Hamiltonian simulation-based quantum-selected configuration interaction for large-scale electronic structure calculations with a quantum computer, Phys. Chem. Chem. Phys. 27, 20869 (2025).
  52. M. Mikkelsen and Y. O. Nakagawa, Quantum-selected configuration interaction with time-evolved state, Phys. Rev. Res. 7, 043043 (2025).
  53. J. Yu, J. R. Moreno, J. T. Iosue, L. Bertels, D. Claudino, B. Fuller, P. Groszkowski, T. S. Humble, P. Jurcevic, W. Kirby, et al., Quantum-centric algorithm for sample-based Krylov diagonalization, arXiv:2501.09702.
  54. S. Kanno, H. Nakamura, T. Kobayashi, S. Gocho, M. Hatanaka, N. Yamamoto, and Q. Gao, Quantum computing quantum Monte Carlo with hybrid tensor network for electronic structure calculations, npj Quantum Inf. 10, 56 (2024).
  55. N. S. Blunt, L. Caune, and J. Quiroz-Fernandez, A quantum computing approach to fixed-node Monte Carlo using classical shadows, J. Chem. Theory Comput. 21, 1652 (2025).
  56. A. Halkier, T. Helgaker, P. Jørgensen, W. Klopper, and J. Olsen, Basis-set convergence of the energy in molecular Hartree–Fock calculations, Chem. Phys. Lett. 302, 437 (1999).
  57. F. N. N. Pansini, A. C. Neto, and A. J. C. Varandas, Extrapolation of Hartree–Fock and multiconfiguration self-consistent-field energies to the complete basis set limit, Theor. Chem. Acc. 135, 261 (2016).
  58. M. Lesiuk and B. Jeziorski, Complete basis set extrapolation of electronic correlation energies using the Riemann zeta function, J. Chem. Theory Comput. 15, 5398 (2019).
  59. T. Helgaker, W. Klopper, H. Koch, and J. Noga, Basis-set convergence of correlated calculations on water, J. Chem. Phys. 106, 9639 (1997).
  60. M. Amsler, P. Deglmann, M. Degroote, M. P. Kaicher, M. Kiser, M. Kühn, C. Kumar, A. Maier, G. Samsonidze, A. Schroeder, M. Streif, D. Vodola, C. Wever, and QUTAC Material Science Working Group, Classical and quantum trial wave functions in auxiliary-field quantum Monte Carlo applied to oxygen allotropes and a CuBr2 model system, J. Chem. Phys. 159, 044119 (2023).

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Phys. Rev. Research 7, 043344– Published 29 December, 2025
  • Received 28 April 2025
  • Accepted 7 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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