IDEAS home Printed from https://ideas.repec.org/a/nat/natcom/v16y2025i1d10.1038_s41467-025-57580-5.html
   My bibliography  Save this article

Efficient and practical Hamiltonian simulation from time-dependent product formulas

Author

Listed:
  • Jan Lukas Bosse

    (Phasecraft Ltd. 77 Charlotte Street
    University of Bristol)

  • Andrew M. Childs

    (Phasecraft Ltd. 77 Charlotte Street
    Institute for Advanced Computer Studies, Joint Center for Quantum Information and Computer Science, University of Maryland)

  • Charles Derby

    (Phasecraft Ltd. 77 Charlotte Street)

  • Filippo Maria Gambetta

    (Phasecraft Ltd. 77 Charlotte Street)

  • Ashley Montanaro

    (Phasecraft Ltd. 77 Charlotte Street
    University of Bristol)

  • Raul A. Santos

    (Phasecraft Ltd. 77 Charlotte Street)

Abstract

In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive application of well-known Trotter formulas, for systems where the evolution is determined by a Hamiltonian with different energy scales (i.e., one part is “large” and another part is “small”). Our algorithms generate a decomposition of the evolution operator into a product of simple unitaries that are directly implementable on a quantum computer. Although the theoretical scaling is suboptimal compared with state-of-the-art algorithms (e.g., quantum signal processing), the performance of the algorithms we propose is highly competitive in practice. We illustrate this via extensive numerical simulations for several models. For instance, in the strong-field regime of the 1D transverse-field Ising model, our algorithms achieve an improvement of one order of magnitude in both the system size and evolution time that can be simulated with a fixed budget of 1000 arbitrary 2-qubit gates, compared with standard Trotter formulas.

Suggested Citation

  • Jan Lukas Bosse & Andrew M. Childs & Charles Derby & Filippo Maria Gambetta & Ashley Montanaro & Raul A. Santos, 2025. "Efficient and practical Hamiltonian simulation from time-dependent product formulas," Nature Communications, Nature, vol. 16(1), pages 1-11, December.
  • Handle: RePEc:nat:natcom:v:16:y:2025:i:1:d:10.1038_s41467-025-57580-5
    DOI: 10.1038/s41467-025-57580-5
    as

    Download full text from publisher

    File URL: https://www.nature.com/articles/s41467-025-57580-5
    File Function: Abstract
    Download Restriction: no

    File URL: https://libkey.io/10.1038/s41467-025-57580-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Youngseok Kim & Andrew Eddins & Sajant Anand & Ken Xuan Wei & Ewout Berg & Sami Rosenblatt & Hasan Nayfeh & Yantao Wu & Michael Zaletel & Kristan Temme & Abhinav Kandala, 2023. "Evidence for the utility of quantum computing before fault tolerance," Nature, Nature, vol. 618(7965), pages 500-505, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chang-Kang Hu & Guixu Xie & Kasper Poulsen & Yuxuan Zhou & Ji Chu & Chilong Liu & Ruiyang Zhou & Haolan Yuan & Yuecheng Shen & Song Liu & Nikolaj T. Zinner & Dian Tan & Alan C. Santos & Dapeng Yu, 2025. "Digital simulation of zero-temperature spontaneous symmetry breaking in a superconducting lattice processor," Nature Communications, Nature, vol. 16(1), pages 1-10, December.
    2. Zenghui Bao & Yan Li & Zhiling Wang & Jiahui Wang & Jize Yang & Haonan Xiong & Yipu Song & Yukai Wu & Hongyi Zhang & Luming Duan, 2024. "A cryogenic on-chip microwave pulse generator for large-scale superconducting quantum computing," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
    3. Ryan Snodgrass & Vincent Kotsubo & Scott Backhaus & Joel Ullom, 2024. "Dynamic acoustic optimization of pulse tube refrigerators for rapid cooldown," Nature Communications, Nature, vol. 15(1), pages 1-8, December.
    4. Diego Ruiz & Jérémie Guillaud & Anthony Leverrier & Mazyar Mirrahimi & Christophe Vuillot, 2025. "LDPC-cat codes for low-overhead quantum computing in 2D," Nature Communications, Nature, vol. 16(1), pages 1-10, December.
    5. Yuxuan Du & Min-Hsiu Hsieh & Dacheng Tao, 2025. "Efficient learning for linear properties of bounded-gate quantum circuits," Nature Communications, Nature, vol. 16(1), pages 1-8, December.
    6. Spencer D. Fallek & Vikram S. Sandhu & Ryan A. McGill & John M. Gray & Holly N. Tinkey & Craig R. Clark & Kenton R. Brown, 2024. "Rapid exchange cooling with trapped ions," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
    7. F. A. Roy & J. H. Romeiro & L. Koch & I. Tsitsilin & J. Schirk & N. J. Glaser & N. Bruckmoser & M. Singh & F. X. Haslbeck & G. B. P. Huber & G. Krylov & A. Marx & F. Pfeiffer & C. M. F. Schneider & C., 2025. "Parity-dependent state transfer for direct entanglement generation," Nature Communications, Nature, vol. 16(1), pages 1-9, December.
    8. Michael Oliveira & Sathyawageeswar Subramanian & Leandro Mendes & Min-Hsiu Hsieh, 2025. "Unconditional advantage of noisy qudit quantum circuits over biased threshold circuits in constant depth," Nature Communications, Nature, vol. 16(1), pages 1-13, December.
    9. Isaiah Hull & Or Sattath & Eleni Diamanti & Göran Wendin, 2024. "Quantum Algorithms," Contributions to Economics, in: Quantum Technology for Economists, chapter 0, pages 37-103, Springer.
    10. Suhas Ganjam & Yanhao Wang & Yao Lu & Archan Banerjee & Chan U Lei & Lev Krayzman & Kim Kisslinger & Chenyu Zhou & Ruoshui Li & Yichen Jia & Mingzhao Liu & Luigi Frunzio & Robert J. Schoelkopf, 2024. "Surpassing millisecond coherence in on chip superconducting quantum memories by optimizing materials and circuit design," Nature Communications, Nature, vol. 15(1), pages 1-13, December.
    11. Oles Shtanko & Derek S. Wang & Haimeng Zhang & Nikhil Harle & Alireza Seif & Ramis Movassagh & Zlatko Minev, 2025. "Uncovering local integrability in quantum many-body dynamics," Nature Communications, Nature, vol. 16(1), pages 1-8, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nat:natcom:v:16:y:2025:i:1:d:10.1038_s41467-025-57580-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.nature.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.