On the time-independent Hamiltonian in real-time and imaginary-time quantum annealing?

• 作者: Jie Sun Songfeng Lu
• 来源期刊: 中国物理B（英文版）
• 年，卷（期）: 2020,（10）
• 所属期刊栏目: GENERAL
• 页码范围: 198-203
• 页数: 6页
• 语种: 英文
• DOI: 10.1088/1674-1056/aba2db

摘要

We present the analog analogue of Grover's problem as an example of the time-independent Hamiltonian for apply-ing the speed limit of the imaginary-time Schr?dinger equation derived by Okuyama and Ohzeki and the new class of energy-time uncertainty relation proposed by Kieu. It is found that the computational time of the imaginary-time quantum annealing of this Grover search can be exponentially small, while the counterpart of the quantum evolution driven by the real-time Schr?dinger equation could only provide square root speedup, compared with classic search. The present results are consistent with the cases of the time-dependent quantum evolution of the natural Grover problem in previous works. We once again emphasize that the logarithm and square root algorithmic performances are generic in imaginary-time quantum annealing and quantum evolution driven by real-time Schr?dinger equation, respectively. Also, we provide evidences to search deep reasons why the imaginary-time quantum annealing can lead to exponential speedup and the real-time quantum annealing can make square root speedup.