Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian
Abstract
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.
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
- OSTI Identifier:
- 1864877
- Alternate Identifier(s):
- OSTI ID: 1876803
- Report Number(s):
- LA-UR-21-23292
Journal ID: ISSN 2041-1723; 2212; PII: 29887
- Grant/Contract Number:
- 89233218CNA000001
- Resource Type:
- Published Article
- Journal Name:
- Nature Communications
- Additional Journal Information:
- Journal Name: Nature Communications Journal Volume: 13 Journal Issue: 1; Journal ID: ISSN 2041-1723
- Publisher:
- Nature Publishing Group
- Country of Publication:
- United Kingdom
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Yan, Bin, and Sinitsyn, Nikolai A. Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian. United Kingdom: N. p., 2022.
Web. doi:10.1038/s41467-022-29887-0.
Yan, Bin, & Sinitsyn, Nikolai A. Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian. United Kingdom. https://doi.org/10.1038/s41467-022-29887-0
Yan, Bin, and Sinitsyn, Nikolai A. Mon .
"Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian". United Kingdom. https://doi.org/10.1038/s41467-022-29887-0.
@article{osti_1864877,
title = {Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian},
author = {Yan, Bin and Sinitsyn, Nikolai A.},
abstractNote = {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.},
doi = {10.1038/s41467-022-29887-0},
journal = {Nature Communications},
number = 1,
volume = 13,
place = {United Kingdom},
year = {Mon Apr 25 00:00:00 EDT 2022},
month = {Mon Apr 25 00:00:00 EDT 2022}
}
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