Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian.

Yan, Bin; Sinitsyn, Nikolai A · Nat Commun · 2022

basic_science · Level V

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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, H<sub>I</sub>. Here, we point to the existence of an analytical solution for such a problem for an arbitrary H<sub>I</sub> 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 H<sub>I</sub>, the solution also shows a considerable quantum speedup in computations.