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.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE; USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
- Grant/Contract Number:
- 89233218CNA000001
- OSTI ID:
- 1864877
- Report Number(s):
- LA-UR-21-23292; 2212; PII: 29887
- Journal Information:
- Nature Communications, Journal Name: Nature Communications Journal Issue: 1 Vol. 13; ISSN 2041-1723
- Publisher:
- Nature Publishing GroupCopyright Statement
- Country of Publication:
- United Kingdom
- Language:
- English
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