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Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian

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  • 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
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    References listed on IDEAS

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    1. Toby S. Cubitt & David Perez-Garcia & Michael M. Wolf, 2015. "Undecidability of the spectral gap," Nature, Nature, vol. 528(7581), pages 207-211, December.
    2. 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.
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