Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian

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.

15 pages, 8 figures

References in corpus (5)

• Mathematical Foundation of Quantum Annealing
• Quantum versus classical annealing: insights from scaling theory and results for spin glasses on 3-regular graphs
• Convergence theorems for quantum annealing
• Convergence of Quantum Annealing with Real-Time Schrodinger Dynamics
• Exact results for models of multichannel quantum nonadiabatic transitions

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• Nonadiabatic transitions during a passage near a critical point
• Parallel Ising Annealer via Gradient-based Hamiltonian Monte Carlo
• Optimal Quantum Likelihood Estimation
• Testing Quantum and Simulated Annealers on the Drone Delivery Packing Problem