Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian

TL;DR

This paper presents an analytical solution for nonadiabatic quantum annealing on arbitrary Ising Hamiltonians, revealing power-law suppression of excitations and potential quantum speedup, challenging traditional views on energy relaxation in spin glasses.

Contribution

It provides the first analytical solution for nonadiabatic quantum annealing on arbitrary Ising Hamiltonians, offering new insights into its accuracy and dynamics.

Findings

Power-law suppression of nonadiabatic excitations with annealing time T

No transition to glass phase observed in the pseudo-adiabatic regime

Potential quantum speedup in specific Ising Hamiltonian cases

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, $H_I$. 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.