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Boson Sampling Enhanced Quantum Chemistry

Zhong-Xia Shang1,2,3,*,†, Yukun Zhang4,5,†, Han-Sen Zhong6, Cheng-Cheng Yu1,2,3, Xiao Yuan4,5, Chao-Yang Lu1,2,3,‡, Jian-Wei Pan1,2,3, and Ming-Cheng Chen1,2,3,§

  • *Contact author: ustcszx@mail.ustc.edu.cn
  • †Z.-X.S. and Y.Z. contributed equally to this work.
  • ‡Contact author: cylu@ustc.edu.cn
  • §Contact author: cmc@ustc.edu.cn
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PRX Quantum 6, 040357 – Published 5 December, 2025

DOI: https://doi.org/10.1103/gw1c-5b58

Abstract

In this work, we give a hybrid quantum-classical algorithm for solving electronic structure problems of molecules using only linear quantum optical systems. The variational ansatz we proposed is a hybrid of noninteracting boson dynamics and classical computational chemistry methods, specifically, the Hartree-Fock method and the configuration interaction method. The boson part is built by a linear optical interferometer, which is easier to realize compared with the well-known unitary coupled cluster (UCC) ansatz composed of quantum gates in conventional variational quantum eigensolver, and the classical part is merely classical processing acting on the Hamiltonian. The appearance of permanents in the boson part has its physical intuition to provide different kinds of resources from commonly used single, double, and higher excitations in classical methods and the UCC ansatz to explore chemical quantum states. Such resources can help enhance the accuracy of methods used in the classical parts. We give a scalable hybrid homodyne and photon-number measurement procedure for evaluating the energy value, which has intrinsic abilities to mitigate photon loss errors, and discuss the extra measurement cost induced by the no Pauli exclusion principle for bosons with its solutions. To demonstrate our proposal, we run numerical experiments on several molecules and obtain their potential energy curves reaching chemical accuracy.

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Physics Subject Headings (PhySH)

Popular Summary

Quantum chemistry aims to predict molecular behavior at the atomic level, essential for innovations in drugs, materials, and energy. Yet, classical computers struggle with the exponential complexity of electron interactions. Quantum computers promise efficiency, but noisy intermediate-scale quantum (NISQ) devices face error and circuit depth challenges. Crucially, how can we harness quantum advantages for chemistry simulations using feasible hardware? And how do we bridge quantum optics with chemical computations to overcome these limits? Addressing these is significant, as it could speed up discoveries by enabling accurate predictions of chemical reactions and molecular properties beyond the reach of classical computing.

We present a hybrid quantum-classical algorithm using passive linear quantum optical systems—known for robust, low-noise photons—to solve electronic potential energy surface problems. Our approach harnesses boson sampling: noninteracting photons traverse a simple linear optical interferometer, generating “permanents,” mathematical objects that offer a unique quantum resource for exploring molecular states. This complements classical methods like Hartree-Fock and configuration interaction, creating a variational ansatz that is experimentally simpler than gate-based circuits.

We devise a scalable hybrid measurement scheme with homodyne and photon-number detectors, inherently mitigating photon losses and handling bosons’ lack of electron-like exclusion rules. Numerical simulations on molecules like lithium hydride and beryllium dihydride yield potential energy curves at chemical accuracy.

This work paves the way for optical quantum advantages in NISQ-era chemistry, inspiring scalable hardware implementations and broader applications in quantum simulation. This method can help experimentalists prioritize the impactful improvements and clarify when photonics should be combined with classical computation to tackle increasingly challenging chemistry.

Article Text

References (54)

  1. P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Linear optical quantum computing with photonic qubits, Rev. Mod. Phys. 79, 135 (2007).
  2. J. I. Cirac and P. Zoller, Quantum computations with cold trapped ions, Phys. Rev. Lett. 74, 4091 (1995).
  3. A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation, Phys. Rev. A 69, 062320 (2004).
  4. L. Henriet, L. Beguin, A. Signoles, T. Lahaye, A. Browaeys, G.-O. Reymond, and C. Jurczak, Quantum computing with neutral atoms, Quantum 4, 327 (2020).
  5. E. Knill, R. Laflamme, and G. J. Milburn, A scheme for efficient quantum computation with linear optics, Nature 409, 46 (2001).
  6. R. Raussendorf, D. E. Browne, and H. J. Briegel, Measurement-based quantum computation on cluster states, Phys. Rev. A 68, 022312 (2003).
  7. S. Aaronson and A. Arkhipov, The computational complexity of linear optics, in Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing (Association for Computing Machinery, New York, NY, USA, 2011), pp. 333–342.
  8. H.-S. Zhong, H. Wang, Y.-H. Deng, M.-C. Chen, L.-C. Peng, Y.-H. Luo, J. Qin, D. Wu, X. Ding, Y. Hu et al., Quantum computational advantage using photons, Science 370, 1460 (2020).
  9. H.-S. Zhong, Y.-H. Deng, J. Qin, H. Wang, M.-C. Chen, L.-C. Peng, Y.-H. Luo, D. Wu, S.-Q. Gong, H. Su et al., Phase-programmable Gaussian boson sampling using stimulated squeezed light, Phys. Rev. Lett. 127, 180502 (2021).
  10. L. S. Madsen, F. Laudenbach, M. F. Askarani, F. Rortais, T. Vincent, J. F. Bulmer, F. M. Miatto, L. Neuhaus, L. G. Helt, M. J. Collins et al., Quantum computational advantage with a programmable photonic processor, Nature 606, 75 (2022).
  11. Y.-H. Deng, Y.-C. Gu, H.-L. Liu, S.-Q. Gong, H. Su, Z.-J. Zhang, H.-Y. Tang, M.-H. Jia, J.-M. Xu, M.-C. Chen et al., Gaussian boson sampling with pseudo-photon-number-resolving detectors and quantum computational advantage, Phys. Rev. Lett. 131, 150601 (2023).
  12. L. Banchi, M. Fingerhuth, T. Babej, C. Ing, and J. M. Arrazola, Molecular docking with Gaussian boson sampling, Sci. Adv. 6, eaax1950 (2020).
  13. J. Huh, G. G. Guerreschi, B. Peropadre, J. R. McClean, and A. Aspuru-Guzik, Boson sampling for molecular vibronic spectra, Nat. Photonics 9, 615 (2015).
  14. J. M. Arrazola and T. R. Bromley, Using Gaussian boson sampling to find dense subgraphs, Phys. Rev. Lett. 121, 030503 (2018).
  15. J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2, 79 (2018).
  16. S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, and X. Yuan, Quantum computational chemistry, Rev. Mod. Phys. 92, 015003 (2020).
  17. J. R. McClean, J. Romero, R. Babbush, and A. Aspuru-Guzik, The theory of variational hybrid quantum-classical algorithms, New J. Phys. 18, 023023 (2016).
  18. M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio et al., Variational quantum algorithms, Nat. Rev. Phys. 3, 625 (2021).
  19. R. Jozsa and A. Miyake, Matchgates and classical simulation of quantum circuits, Proc. R. Soc. A: Math. Phys. Eng. Sci. 464, 3089 (2008).
  20. J. R. Sabin and E. J. Brändas, Advances in Quantum Chemistry (Academic Press, 2011), Vol. 62.
  21. J. Romero, R. Babbush, J. R. McClean, C. Hempel, P. J. Love, and A. Aspuru-Guzik, Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz, Quantum Sci. Technol. 4, 014008 (2018).
  22. A. Anand, P. Schleich, S. Alperin-Lea, P. W. Jensen, S. Sim, M. Díaz-Tinoco, J. S. Kottmann, M. Degroote, A. F. Izmaylov, and A. Aspuru-Guzik, A quantum computing view on unitary coupled cluster theory, Chem. Soc. Rev. 51, 1659 (2022).
  23. D. J. Brod, Bosons vs. fermions—A computational complexity perspective, Rev. Bras. Ensino Fís. 43, e20200403 (2021).
  24. M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Experimental realization of any discrete unitary operator, Phys. Rev. Lett. 73, 58 (1994).
  25. Z.-X. Shang, M.-C. Chen, X. Yuan, C.-Y. Lu, and J.-W. Pan, Schrödinger-Heisenberg variational quantum algorithms, Phys. Rev. Lett. 131, 060406 (2023).
  26. W. Mizukami, K. Mitarai, Y. O. Nakagawa, T. Yamamoto, T. Yan, and Y. Y. Ohnishi, Orbital optimized unitary coupled cluster theory for quantum computer, Phys. Rev. Res. 2, 033421 (2020).
  27. N. J. Cerf, G. Leuchs, and E. S. Polzik, in Quantum Information With Continuous Variables of Atoms and Light (World Scientific, 2007), p. 141.
  28. C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Gaussian quantum information, Rev. Mod. Phys. 84, 621 (2012).
  29. L. Chakhmakhchyan and N. J. Cerf, Boson sampling with Gaussian measurements, Phys. Rev. A 96, 032326 (2017).
  30. P. Lolur, M. Skogh, W. Dobrautz, C. Warren, J. Biznarova, A. Osman, G. Tancredi, G. Wendin, J. Bylander, and M. Rahm, Reference-state error mitigation: A strategy for high accuracy quantum computation of chemistry, J. Chem. Theory Comput. 19, 783 (2023).
  31. A. Cross, The IBM Q experience and Qiskit open-source quantum computing software, in APS March Meeting Abstracts (2018), Vol. 2018, pp. L58–003.
  32. U. Baek, D. Hait, J. Shee, O. Leimkuhler, W. J. Huggins, T. F. Stetina, M. Head-Gordon, and K. B. Whaley, Say no to optimization: A nonorthogonal quantum eigensolver, PRX Quantum 4, 030307 (2023).
  33. H.-J. Werner and P. J. Knowles, An efficient internally contracted multiconfiguration–Reference configuration interaction method, J. Chem. Phys. 89, 5803 (1988).
  34. Y. Lim and C. Oh, Efficient classical algorithms for linear optical circuits, ArXiv:2502.12882.
  35. J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven, Barren plateaus in quantum neural network training landscapes, Nat. Commun. 9, 4812 (2018).
  36. Z. Holmes, K. Sharma, M. Cerezo, and P. J. Coles, Connecting ansatz expressibility to gradient magnitudes and barren plateaus, PRX Quantum 3, 010313 (2022).
  37. F. Arute et al., Google AI Quantum and Collaborators, Hartree-Fock on a superconducting qubit quantum computer, Science 369, 1084 (2020).
  38. H. Wang, J. Qin, X. Ding, M.-C. Chen, S. Chen, X. You, Y.-M. He, X. Jiang, L. You, Z. Wang et al., Boson sampling with 20 input photons and a 60-mode interferometer in a 1 0 14-dimensional Hilbert space, Phys. Rev. Lett. 123, 250503 (2019).
  39. Y. Wu, W.-S. Bao, S. Cao, F. Chen, M.-C. Chen, X. Chen, T.-H. Chung, H. Deng, Y. Du, D. Fan et al., Strong quantum computational advantage using a superconducting quantum processor, Phys. Rev. Lett. 127, 180501 (2021).
  40. J. M. Pino, J. M. Dreiling, C. Figgatt, J. P. Gaebler, S. A. Moses, M. Allman, C. Baldwin, M. Foss-Feig, D. Hayes, K. Mayer et al., Demonstration of the trapped-ion quantum CCD computer architecture, Nature 592, 209 (2021).
  41. D. Bluvstein, H. Levine, G. Semeghini, T. T. Wang, S. Ebadi, M. Kalinowski, A. Keesling, N. Maskara, H. Pichler, M. Greiner et al., A quantum processor based on coherent transport of entangled atom arrays, Nature 604, 451 (2022).
  42. E. Y. Loh, Jr., J. E. Gubernatis, R. T. Scalettar, S. R. White, D. J. Scalapino, and R. L. Sugar, Sign problem in the numerical simulation of many-electron systems, Phys. Rev. B 41, 9301 (1990).
  43. A. P. Lund, M. J. Bremner, and T. C. Ralph, Quantum sampling problems, bosonsampling and quantum supremacy, Npj Quantum Inf. 3, 15 (2017).
  44. S. Olivares, A. Allevi, G. Caiazzo, M. G. Paris, and M. Bondani, Quantum tomography of light states by photon-number-resolving detectors, New J. Phys. 21, 103045 (2019).
  45. H.-Y. Huang, R. Kueng, and J. Preskill, Predicting many properties of a quantum system from very few measurements, Nat. Phys. 16, 1050 (2020).
  46. X. Ding, Y. He, Z.-C. Duan, N. Gregersen, M.-C. Chen, S. Unsleber, S. Maier, C. Schneider, M. Kamp, S. Höfling et al., On-demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar, Phys. Rev. Lett. 116, 020401 (2016).
  47. P. Senellart, G. Solomon, and A. White, High-performance semiconductor quantum-dot single-photon sources, Nat. Nanotechnol. 12, 1026 (2017).
  48. A. Zavatta, J. Fiurášek, and M. Bellini, A high-fidelity noiseless amplifier for quantum light states, Nat. Photonics 5, 52 (2011).
  49. F. Raffaelli, G. Ferranti, D. H. Mahler, P. Sibson, J. E. Kennard, A. Santamato, G. Sinclair, D. Bonneau, M. G. Thompson, and J. C. Matthews, A homodyne detector integrated onto a photonic chip for measuring quantum states and generating random numbers, Quantum Sci. Technol. 3, 025003 (2018).
  50. J. R. McClean, N. C. Rubin, K. J. Sung, I. D. Kivlichan, X. Bonet-Monroig, Y. Cao, C. Dai, E. S. Fried, C. Gidney, B. Gimby et al., Openfermion: The electronic structure package for quantum computers, Quantum Sci. Technol. 5, 034014 (2020).
  51. 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 et al., PySCF: The Python-based simulations of chemistry framework, Wiley Interdiscip. Rev.: Comput. Mol. Sci. 8, e1340 (2018).
  52. B. Gupt, J. Izaac, and N. Quesada, The Walrus: A library for the calculation of hafnians, Hermite polynomials and Gaussian boson sampling, J. Open Source Softw. 4, 1705 (2019).
  53. Z.-X. Shang, Data and example codes, GitHub repository (2023), https://github.com/ustcszx/BS-C-VQE.
  54. G. Van Kempen and L. Van Vliet, Mean and variance of ratio estimators used in fluorescence ratio imaging, Cytometry: J. Int. Soc. Anal. Cytol. 39, 300 (2000).

Outline

Information

PRX Quantum 6, 040357– Published 5 December, 2025
  • Received 11 November 2024
  • Revised 19 September 2025
  • Accepted 6 November 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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