Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian

• Published in: Nature communications Vol. 13; no. 1; pp. 2212 - 12
• Main Authors: Yan, Bin, Sinitsyn, Nikolai A.
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 25.04.2022; Nature Publishing Group; Nature Portfolio
• Subjects: 639/766/259; 639/766/483; 639/766/483/640; Adiabatic; Adiabatic flow; Annealing; Computer applications; Energy; Exact solutions; Humanities and Social Sciences; Ising model; Mathematical analysis; multidisciplinary; Science; Science (multidisciplinary); Spin glasses; Time dependence
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/s41467-022-29887-0

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 I . Here, we point to the existence of an analytical solution for such a problem for an arbitrary H I 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 I , the solution also shows a considerable quantum speedup in computations. The computational capabilities of quantum annealing in the accessible regimes of operation are still subject to debate. Here, the authors study a model admitting an analytical solution far from the adiabatic regime, and show evidences of better convergence and energy relaxation rates over classical annealing.