Quantum Annealing and Thermalization: Insights from Integrability

Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian

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.