Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian

Bin Yan and Nikolai A. Sinitsyn ()
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Bin Yan: Los Alamos National Laboratory
Nikolai A. Sinitsyn: Los Alamos National Laboratory

Nature Communications, 2022, vol. 13, issue 1, 1-12

Abstract: 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.

Date: 2022
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DOI: 10.1038/s41467-022-29887-0

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