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Faster Quantum Chemistry Simulations on a Quantum Computer with Improved Tensor Factorization and Active Volume Compilation

Athena Caesura1, Cristian L. Cortes1, William Pol1, Sukin Sim1, Mark Steudtner1,*, Gian-Luca R. Anselmetti2, Matthias Degroote2,†, Nikolaj Moll2, Raffaele Santagati2 et al.

Michael Streif2 and Christofer S. Tautermann3

  • 1PsiQuantum, 700 Hansen Way, Palo Alto, California 94304, USA
  • 2Quantum Lab, Boehringer Ingelheim, 55218 Ingelheim am Rhein, Germany
  • 3Medicinal Chemistry, Boehringer Ingelheim Pharma GmbH & Co. KG, 88397 Biberach, Germany

  • *Contact author: msteudtner@psiquantum.com
  • †Contact author: matthias.degroote@boehringer-ingelheim.com
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PRX Quantum 6, 030337 – Published 28 August, 2025

DOI: https://doi.org/10.1103/yngp-5fpm

Abstract

Electronic structure calculations of molecular systems are among the most promising applications for fault-tolerant quantum computing (FTQC) in quantum chemistry and drug design. However, while recent algorithmic advancements such as qubitization and tensor hypercontraction (THC) have significantly reduced the complexity of such calculations, they do not yet achieve computational runtimes short enough to be practical for industrially relevant use cases. In this work, we combine several advances to electronic structure calculation for molecular systems, resulting in a 2-orders-of-magnitude speedup of estimated runtimes over prior-art algorithms run on comparable quantum devices. One of these advances is a novel framework for block-invariant symmetry-shifted tensor hypercontraction, with which we achieve the tightest Hamiltonian factorizations reported to date. We compile our algorithm for an active volume (AV) architecture, a technical layout that has recently been proposed for fusion-based photonic quantum hardware. AV compilation contributes towards a lower runtime of our computation by eliminating overheads stemming from connectivity issues in the underlying surface code. We present a detailed benchmark of our approach, focusing primarily on the computationally challenging benchmark molecule P450. Leveraging a number of hardware trade-offs in interleaving-based photonic FTQC, we estimate runtimes for the electronic structure calculation of P450 as a function of the device footprint.

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Popular Summary

Quantum computers are a promising technology platform to calculate properties of interesting molecules. However, the resource requirements for a single calculation and the projected sizes of the first error-corrected devices are still far apart. This paper fits in a large body of work trying to obtain ground-state energies with less resources. We demonstrate the performance of our techniques on the active site of cytochrome P450, an import enzyme in the human body, and on the iron-molybdenum cofactor in nitrogenase, a key component in natural fertilizer production.

We achieve a factor of 8 improvement by compressing the data that need to be loaded into the quantum computer. This is achieved by exploiting the symmetries of the system through the block-invariant symmetry shift combined with the most performant Hamiltonian factorization method. An additional factor of 25 comes from dividing the circuit in active volume blocks and counting only the resources that are needed to compute these blocks. An active volume architecture executes only active operations in a logical circuit without wasting resources on idling operations. Together, we achieve an overall factor of 233 improvement that is independent of the type of hardware that is executing the circuit. Finally, we go one level deeper and find the physical resources in terms of interleaving modules and wall-clock calculation time for fusion-based photonic quantum computers.

This result is not the final step in speeding up calculations; further improvements can be made in the loading of Hamiltonians or the structure of Hamiltonian simulation algorithms. Moreover, the active volume resources could be optimized more globally instead of on a routine-to-routine basis, meaning a tighter analysis of costs with an immediate impact on the speedup without requiring changes to the algorithm itself.

Article Text

References (68)

  1. R. M. Langer, The quantum mechanics of chemical reaction, Phys. Rev. 34, 92 (1929).
  2. D. G. Truhlar, B. C. Garrett, and S. J. Klippenstein, Current status of transition-state theory, J. Phys. Chem. 100, 12771 (1996).
  3. U. Ryde and P. Söderhjelm, Ligand-binding affinity estimates supported by quantum-mechanical methods, Chem. Rev. 116, 5520 (2016).
  4. Y.-H. Lam, Y. Abramov, R. S. Ananthula, J. M. Elward, L. R. Hilden, S. O. Nilsson Lill, P.-O. Norrby, A. Ramirez, E. C. Sherer, J. Mustakis, and G. J. Tanoury, Applications of quantum chemistry in pharmaceutical process development: Current state and opportunities, Org. Process Res. Dev. 24, 1496 (2020).
  5. R. Santagati, A. Aspuru-Guzik, R. Babbush, M. Degroote, L. González, E. Kyoseva, N. Moll, M. Oppel, R. M. Parrish, N. C. Rubin, M. Streif, C. S. Tautermann, H. Weiss, N. Wiebe, and C. Utschig-Utschig, Drug design on quantum computers, Nat. Phys. 20, 549 (2024).
  6. A. Baiardi, M. Christandl, and M. Reiher, Quantum computing for molecular biology, ChemBioChem 24, e202300120 (2023).
  7. E. W. C. Spotte-Smith, S. M. Blau, X. Xie, H. D. Patel, M. Wen, B. Wood, S. Dwaraknath, and K. A. Persson, Quantum chemical calculations of lithium-ion battery electrolyte and interphase species, Sci. Data 8, 203 (2021).
  8. I. H. Kim, Y.-H. Liu, S. Pallister, W. Pol, S. Roberts, and E. Lee, Fault-tolerant resource estimate for quantum chemical simulations: Case study on Li-ion battery electrolyte molecules, Phys. Rev. Res. 4, 023019 (2022).
  9. A. Delgado, P. A. M. Casares, R. dos Reis, M. S. Zini, R. Campos, N. Cruz-Hernández, A.-C. Voigt, A. Lowe, S. Jahangiri, M. A. Martin-Delgado, J. E. Mueller, and J. M. Arrazola, Simulating key properties of lithium-ion batteries with a fault-tolerant quantum computer, Phys. Rev. A 106, 032428 (2022).
  10. C. J. Jacobsen, S. Dahl, A. Boisen, B. S. Clausen, H. Topsøe, A. Logadottir, and J. K. Nørskov, Optimal catalyst curves: Connecting density functional theory calculations with industrial reactor design and catalyst selection, J. Catal. 205, 382 (2002).
  11. N. Mardirossian and M. Head-Gordon, Thirty years of density functional theory in computational chemistry: An overview and extensive assessment of 200 density functionals, Mol. Phys. 115, 2315 (2017).
  12. Y. Cao, J. Romero, J. P. Olson, M. Degroote, P. D. Johnson, M. Kieferová, I. D. Kivlichan, T. Menke, B. Peropadre, N. P. D. Sawaya, S. Sim, L. Veis, and A. Aspuru-Guzik, Quantum chemistry in the age of quantum computing, Chem. Rev. 119, 10856 (2019).
  13. S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, and X. Yuan, Quantum computational chemistry, Rev. Mod. Phys. 92, 015003 (2020).
  14. A. Aspuru-Guzik, Simulated quantum computation of molecular energies, Science 309, 1704 (2005).
  15. M. Reiher, N. Wiebe, K. M. Svore, D. Wecker, and M. Troyer, Elucidating reaction mechanisms on quantum computers, Proc. Natl. Acad. Sci. 114, 7555 (2017).
  16. 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).
  17. M. Steudtner, S. Morley-Short, W. Pol, S. Sim, C. L. Cortes, M. Loipersberger, R. M. Parrish, M. Degroote, N. Moll, R. Santagati, and M. Streif, Fault-tolerant quantum computation of molecular observables, Quantum 7, 1164 (2023).
  18. J. J. Goings, A. White, J. Lee, C. S. Tautermann, M. Degroote, C. Gidney, T. Shiozaki, R. Babbush, and N. C. Rubin, Reliably assessing the electronic structure of cytochrome P450 on today’s classical computers and tomorrow’s quantum computers, Proc. Natl. Acad. Sci. 119, e2203533119 (2022).
  19. F. P. Guengerich, A history of the roles of cytochrome P450 enzymes in the toxicity of drugs, Toxicol. Res. 37, 1 (2021).
  20. G. H. Low and I. L. Chuang, Optimal Hamiltonian simulation by quantum signal processing, Phys. Rev. Lett. 118, 010501 (2017).
  21. A. M. Childs and N. Wiebe, Hamiltonian simulation using linear combinations of unitary operations, Quantum Info. Comput. 12, 901 (2012).
  22. G. H. Low and I. L. Chuang, Hamiltonian simulation by qubitization, Quantum 3, 163 (2019).
  23. D. W. Berry, C. Gidney, M. Motta, J. R. McClean, and R. Babbush, Qubitization of arbitrary basis quantum chemistry leveraging sparsity and low rank factorization, Quantum 3, 208 (2019).
  24. A. Gilyén, Y. Su, G. H. Low, and N. Wiebe, in Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 (Association for Computing Machinery, New York, NY, USA, 2019), p. 193–204.
  25. R. Babbush, C. Gidney, D. W. Berry, N. Wiebe, J. McClean, A. Paler, A. Fowler, and H. Neven, Encoding electronic spectra in quantum circuits with linear T complexity, Phys. Rev. X 8, 041015 (2018).
  26. J. Lee, D. W. Berry, C. Gidney, W. J. Huggins, J. R. McClean, N. Wiebe, and R. Babbush, Even more efficient quantum computations of chemistry through tensor hypercontraction, PRX Quantum 2, 030305 (2021).
  27. V. V. Burg, G. H. Low, T. Häner, D. S. Steiger, M. Reiher, M. Roetteler, and M. Troyer, Quantum computing enhanced computational catalysis, Phys. Rev. Res. 3, 033055 (2021).
  28. D. Rocca, C. L. Cortes, J. F. Gonthier, P. J. Ollitrault, R. M. Parrish, G.-L. Anselmetti, M. Degroote, N. Moll, R. Santagati, and M. Streif, Reducing the runtime of fault-tolerant quantum simulations in chemistry through symmetry-compressed double factorization, J. Chem. Theory Comput. 20, 4639 (2024).
  29. A. Y. Kitaev, Quantum measurements and the Abelian stabilizer problem, arXiv:quant-ph/9511026.
  30. S. Lloyd, Universal quantum simulators, Science 273, 1073 (1996).
  31. I. Loaiza and A. F. Izmaylov, Block-invariant symmetry shift: Preprocessing technique for second-quantized Hamiltonians to improve their decompositions to linear combination of unitaries, J. Chem. Theory Comput. 19, 8201 (2023).
  32. S. Patel, A. Sankar Brahmachari, J. T. Cantin, L. Wang, and A. F. Izmaylov, Global minimization of electronic Hamiltonian 1-norm via linear programming in the block invariant symmetry shift (BLISS) method, arXiv:2409.18277.
  33. D. W. Berry, Y. Tong, T. Khattar, A. White, T. In Kim, G. H. Low, S. Boixo, Z. Ding, L. Lin, S. Lee, G. Kin-Lic Chan, R. Babbush, and N. C. Rubin, Rapid initial-state preparation for the quantum simulation of strongly correlated molecules, PRX Quantum 6, 020327 (2025).
  34. O. Oumarou, M. Scheurer, R. M. Parrish, E. G. Hohenstein, and C. Gogolin, Accelerating quantum computations of chemistry through regularized compressed double factorization, Quantum 8, 1371 (2024).
  35. K. Deka and E. Zak, Simultaneously optimizing symmetry shifts and tensor factorizations for cost-efficient fault-tolerant quantum simulations of electronic Hamiltonians, J. Chem. Theory Comput. 21, 4458 (2025).
  36. S. A. Adcock and J. A. McCammon, Molecular dynamics: Survey of methods for simulating the activity of proteins, Chem. Rev. 106, 1589 (2006).
  37. M. C. Zwier and L. T. Chong, Reaching biological timescales with all-atom molecular dynamics simulations, Curr. Opin. Pharmacol. 10, 745 (2010).
  38. T. Ginex, J. Vázquez, C. Estarellas, and F. Luque, Quantum mechanical-based strategies in drug discovery: Finding the pace to new challenges in drug design, Curr. Opin. Struct. Biol. 87, 102870 (2024).
  39. D. Litinski and N. Nickerson, Active volume: An architecture for efficient fault-tolerant quantum computers with limited non-local connections, arXiv:2211.15465.
  40. D. Litinski, How to compute a 256-bit elliptic curve private key with only 50 million Toffoli gates, arXiv:2306.08585.
  41. H. Bombin, I. H. Kim, D. Litinski, N. Nickerson, M. Pant, F. Pastawski, S. Roberts, and T. Rudolph, Interleaving: Modular architectures for fault-tolerant photonic quantum computing, arXiv:2103.08612.
  42. C. L. Cortes, D. Rocca, J. F. Gonthier, P. J. Ollitrault, R. M. Parrish, G.-L. R. Anselmetti, M. Degroote, N. Moll, R. Santagati, and M. Streif, Assessing the query complexity limits of quantum phase estimation using symmetry-aware spectral bounds, Phys. Rev. A 110, 022420 (2024).
  43. R. M. Parrish, E. G. Hohenstein, T. J. Martínez, and C. D. Sherrill, Tensor hypercontraction. II. Least-squares renormalization, J. Chem. Phys. 137, 224106 (2012).
  44. E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory, J. Chem. Phys. 137, 044103 (2012).
  45. I. Loaiza, A. M. Khah, N. Wiebe, and A. F. Izmaylov, Reducing molecular electronic Hamiltonian simulation cost for linear combination of unitaries approaches, Quantum Sci. Technol. 8, 035019 (2023).
  46. G. H. Low, V. Kliuchnikov, and L. Schaeffer, Trading T gates for dirty qubits in state preparation and unitary synthesis, Quantum 8, 1375 (2024).
  47. C. Gidney, Halving the cost of quantum addition, Quantum 2, 74 (2018).
  48. D. Horsman, A. G. Fowler, S. Devitt, and R. V. Meter, Surface code quantum computing by lattice surgery, New J. Phys. 14, 123011 (2012).
  49. D. Litinski, A game of surface codes: Large-scale quantum computing with lattice surgery, Quantum 3, 128 (2019).
  50. We also assume that each individual workspace qubit is used infrequently enough that we can rotate rough and smooth edges to face the workspace qubits when each one is needed.
  51. In the architecture presented in the original AV paper the authors assumed that m=w. This was largely for simplicity.
  52. We occasionally refer to the total number of interleaving modules as the footprint, as it determines the physical size of the quantum computer and due to the term “size” being inaccurate. If the number of IMs is to increase, do we need to build a larger machine or do we need to make the quantum computer smaller? We say that devices with more (less) interleaving modules have a bigger (smaller) footprint.
  53. A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Phys. Rev. A 86, 032324 (2012).
  54. C. Gidney and M. Ekerå, How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits, Quantum 5, 433 (2021).
  55. R. Acharya et al., Quantum error correction below the surface code threshold, Nature 638, 920 (2024).
  56. S. Bartolucci, P. Birchall, H. Bombín, H. Cable, C. Dawson, M. Gimeno-Segovia, E. Johnston, K. Kieling, N. Nickerson, M. Pant, F. Pastawski, T. Rudolph, and C. Sparrow, Fusion-based quantum computation, Nat. Commun. 14, 912 (2023).
  57. J. J. Goings, A. White, C. S. Tautermann, M. Degroote, C. Gidney, T. Shiozaki, R. Babbush, and N. C. Rubin, Data for “Reliably assessing the electronic structure of cytochrome P450 on today’s classical computers and tomorrow’s quantum computers” (2022),
  58. A. Caesura, C. Cortes, W. Pol, S. Sim, M. Steudtner, G.-L. Anselmetti, M. Degroote, N. Moll, M. Streif, and C. Tautermann, Data for “Faster quantum chemistry simulations on a quantum computer with improved tensor factorization and active volume compilation” (2025),.
  59. Q. Sun et al., Recent developments in the PySCF program package, J. Chem. Phys. 153, 024109 (2020).
  60. We occasionally refer to the number of memory qubits as highwater, due to its nonadditivity: the highwater is determined by the largest number of qubits used in all the subroutines of the algorithm. The term is mostly used when resources are estimated, i.e., when we are trying to determine the size of the memory register.
  61. This is indeed the value of prior art after our redefinition of ℶ.
  62. C. Gidney, N. Shutty, and C. Jones, Magic state cultivation: Growing T states as cheap as CNOT gates, arXiv:2409.17595.
  63. S. Bravyi, A. W. Cross, J. M. Gambetta, D. Maslov, P. Rall, and T. J. Yoder, High-threshold and low-overhead fault-tolerant quantum memory, Nature 627, 778 (2024).
  64. K. Sahay, J. Jin, J. Claes, J. D. Thompson, and S. Puri, High-threshold codes for neutral-atom qubits with biased erasure errors, Phys. Rev. X 13, 041013 (2023).
  65. C. T. Hann, K. Noh, H. Putterman, M. H. Matheny, J. K. Iverson, M. T. Fang, C. Chamberland, O. Painter, and F. G. S. L. Brandão, Hybrid cat-transmon architecture for scalable, hardware-efficient quantum error correction, PRX Quantum 6, 030305 (2025).
  66. J. M. Montgomery and D. A. Mazziotti, Strong electron correlation in nitrogenase cofactor, FeMoco, J. Phys. Chem. A 122, 4988 (2018).
  67. Z. Li, J. Li, N. S. Dattani, C. J. Umrigar, and G. K.-L. Chan, The electronic complexity of the ground-state of the FeMo cofactor of nitrogenase as relevant to quantum simulations, J. Chem. Phys. 150, 024302 (2019).
  68. H. Zhai, H. R. Larsson, S. Lee, Z.-H. Cui, T. Zhu, C. Sun, L. Peng, R. Peng, K. Liao, J. Tölle, J. Yang, S. Li, and G. K.-L. Chan, Block2: A comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond, J. Chem. Phys. 159, 234801 (2023).

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PRX Quantum 6, 030337– Published 28 August, 2025
  • Received 21 January 2025
  • Revised 21 May 2025
  • Accepted 22 July 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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