Yan Bin, Sinitsyn Nikolai A
Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
Nat Commun. 2022 Apr 25;13(1):2212. doi: 10.1038/s41467-022-29887-0.
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. Here, we point to the existence of an analytical solution for such a problem for an arbitrary H 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, the solution also shows a considerable quantum speedup in computations.
伊辛自旋哈密顿量常用于在其基态中编码计算问题。量子退火（QA）计算通过实现从易于制备的初始状态到量子自旋目标伊辛哈密顿量(H)的低能态的缓慢时间相关演化来搜索这样的状态。在这里，我们指出对于超出QA绝热极限的任意(H)，此类问题存在解析解。该解为非绝热计算的精度提供了见解。我们在准绝热区域的QA协议导致非绝热激发随QA时间(T)呈单调幂律抑制，没有任何向玻璃相转变的迹象，玻璃相通常以对数能量弛豫为特征。这种行为表明，当受到外部时间相关场的辅助时，经典和量子自旋玻璃中的能量弛豫可能有很大差异。在(H)的特定情况下，该解还显示出计算中有相当大的量子加速。
