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Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian
Bin Yan1,2, Nikolai A Sinitsyn3
1Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
Nature Communications
|April 26, 2022
Summary
Researchers found an analytical solution for quantum annealing (QA) beyond the adiabatic limit. This approach offers insights into nonadiabatic computations and reveals a power-law suppression of errors, suggesting potential quantum speedups.
Area of Science:
- Quantum Computing
- Computational Physics
- Condensed Matter Physics
Background:
- Ising spin Hamiltonians are frequently employed to encode computational problems within their ground states.
- Quantum Annealing (QA) seeks these ground states via a slow, time-dependent evolution from an initial state to a low-energy state of a target Ising Hamiltonian (HI).
Purpose of the Study:
- To identify an analytical solution for arbitrary Ising Hamiltonians (HI) in Quantum Annealing (QA) computations, extending beyond the standard adiabatic limit.
- To investigate the accuracy of nonadiabatic computations and explore potential quantum speedups.
Main Methods:
- Development of an analytical solution for Quantum Annealing (QA) applicable to arbitrary Ising Hamiltonians (HI) beyond the adiabatic approximation.
- Analysis of a QA protocol in the pseudo-adiabatic regime to study the suppression of nonadiabatic excitations.
Main Results:
- An analytical solution for QA beyond the adiabatic limit was identified, offering insights into nonadiabatic computation accuracy.
- The QA protocol demonstrated a monotonic power-law suppression of nonadiabatic excitations with annealing time (T), lacking signatures of a glass phase transition.
- Specific Ising Hamiltonians (HI) showed considerable quantum speedup potential through this analytical solution.
Conclusions:
- The findings provide a novel analytical framework for understanding Quantum Annealing (QA) beyond the adiabatic approximation.
- The observed power-law suppression of excitations suggests distinct energy relaxation dynamics in quantum versus classical spin glasses under time-dependent fields.
- The study highlights the potential for significant quantum speedups in specific computational problems addressed by QA.
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