IDEAS home Printed from https://ideas.repec.org/a/nat/natcom/v13y2022i1d10.1038_s41467-022-29887-0.html
   My bibliography  Save this article

Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian

Author

Listed:
  • Bin Yan

    (Los Alamos National Laboratory
    Los Alamos National Laboratory)

  • Nikolai A. Sinitsyn

    (Los Alamos National Laboratory)

Abstract

Ising spin Hamiltonians are often used to encode a computational problem in their ground states. Quantum Annealing (QA) computing searches for such a state by implementing a slow time-dependent evolution from an easy-to-prepare initial state to a low energy state of a target Ising Hamiltonian of quantum spins, HI. Here, we point to the existence of an analytical solution for such a problem for an arbitrary HI beyond the adiabatic limit for QA. This solution provides insights into the accuracy of nonadiabatic computations. Our QA protocol in the pseudo-adiabatic regime leads to a monotonic power-law suppression of nonadiabatic excitations with time T of QA, without any signature of a transition to a glass phase, which is usually characterized by a logarithmic energy relaxation. This behavior suggests that the energy relaxation can differ in classical and quantum spin glasses strongly, when it is assisted by external time-dependent fields. In specific cases of HI, the solution also shows a considerable quantum speedup in computations.

Suggested Citation

  • Bin Yan & Nikolai A. Sinitsyn, 2022. "Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian," Nature Communications, Nature, vol. 13(1), pages 1-12, December.
    • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-29887-0
    DOI: 10.1038/s41467-022-29887-0
    as

    Download full text from publisher

    File URL: https://www.nature.com/articles/s41467-022-29887-0
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1038/s41467-022-29887-0?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. M. W. Johnson & M. H. S. Amin & S. Gildert & T. Lanting & F. Hamze & N. Dickson & R. Harris & A. J. Berkley & J. Johansson & P. Bunyk & E. M. Chapple & C. Enderud & J. P. Hilton & K. Karimi & E. Ladiz, 2011. "Quantum annealing with manufactured spins," Nature, Nature, vol. 473(7346), pages 194-198, May.
    2. Toby S. Cubitt & David Perez-Garcia & Michael M. Wolf, 2015. "Undecidability of the spectral gap," Nature, Nature, vol. 528(7581), pages 207-211, December.
    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. Byron Tasseff & Tameem Albash & Zachary Morrell & Marc Vuffray & Andrey Y. Lokhov & Sidhant Misra & Carleton Coffrin, 2024. "On the emerging potential of quantum annealing hardware for combinatorial optimization," Journal of Heuristics, Springer, vol. 30(5), pages 325-358, December.
    2. Andreas Wichert, 2022. "Quantum Tree Search with Qiskit," Mathematics, MDPI, vol. 10(17), pages 1-28, August.
    3. Jia Si & Shuhan Yang & Yunuo Cen & Jiaer Chen & Yingna Huang & Zhaoyang Yao & Dong-Jun Kim & Kaiming Cai & Jerald Yoo & Xuanyao Fong & Hyunsoo Yang, 2024. "Energy-efficient superparamagnetic Ising machine and its application to traveling salesman problems," Nature Communications, Nature, vol. 15(1), pages 1-12, December.
    4. James D. Watson & Emilio Onorati & Toby S. Cubitt, 2022. "Uncomputably complex renormalisation group flows," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
    5. Marcello Calvanese Strinati & Claudio Conti, 2022. "Multidimensional hyperspin machine," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    6. Hamza Fawzi & Omar Fawzi & Samuel O. Scalet, 2024. "Certified algorithms for equilibrium states of local quantum Hamiltonians," Nature Communications, Nature, vol. 15(1), pages 1-6, December.
    7. Heinz Langhals, 2017. "Interaction of Components in Molecular Optoelectronics for the Next Generation of IT Devices," Scientific Review, Academic Research Publishing Group, vol. 3(3), pages 17-28, 03-2017.
    8. Kevin Wils & Boyang Chen, 2023. "A Symbolic Approach to Discrete Structural Optimization Using Quantum Annealing," Mathematics, MDPI, vol. 11(16), pages 1-29, August.
    9. Schmidhuber, Christof, 2022. "Chaitin’s Omega and an algorithmic phase transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 586(C).
    10. Fabian Böhm & Diego Alonso-Urquijo & Guy Verschaffelt & Guy Van der Sande, 2022. "Noise-injected analog Ising machines enable ultrafast statistical sampling and machine learning," Nature Communications, Nature, vol. 13(1), pages 1-13, December.
    11. Yuqian Zhao & Zhaohua Ma & Zhangzhen He & Haijun Liao & Yan-Cheng Wang & Junfeng Wang & Yuesheng Li, 2024. "Quantum annealing of a frustrated magnet," Nature Communications, Nature, vol. 15(1), pages 1-9, 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:13:y:2022:i:1:d:10.1038_s41467-022-29887-0. 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.