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Ising spin Hamiltonians are often used to encode a computational problem intheir ground states. Quantum Annealing (QA) computing searches for such a stateby implementing a slow time-dependent evolution from an easy-to-prepare initialstate 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 aproblem for an arbitrary $H_I$ beyond the adiabatic limit for QA. This solutionprovides insights into the accuracy of nonadiabatic computations. Our QAprotocol in the pseudo-adiabatic regime leads to a monotonic power-lawsuppression of nonadiabatic excitations with time $T$ of QA, without anysignature of a transition to a glass phase, which is usually characterized by alogarithmic energy relaxation. This behavior suggests that the energyrelaxation can differ in classical and quantum spin glasses strongly, when itis assisted by external time-dependent fields. In specific cases of $H_I$, thesolution also shows a considerable quantum speedup in computations.

Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian