Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 35468917.
- Also identified by DOI 10.1038/s41467-022-29887-0 and PMC identifier 9038765.
- Licence recorded as CC BY.
- The licence permits redistribution, so the abstract is shown in full and the full text is available from the publisher.
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<sub>I</sub>. Here, we point to the existence of an analytical solution for such a problem for an arbitrary H<sub>I</sub> 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<sub>I</sub>, the solution also shows a considerable quantum speedup in computations.