Chinese Physics B, Volume. 29, Issue 10, (2020)
On the time-independent Hamiltonian in real-time and imaginary-time quantum annealing
We present the analog analogue of Grover’s problem as an example of the time-independent Hamiltonian for applying 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.
Get Citation
Copy Citation Text
Jie Sun, Songfeng Lu. On the time-independent Hamiltonian in real-time and imaginary-time quantum annealing[J]. Chinese Physics B, 2020, 29(10):
Received: Mar. 4, 2020
Accepted: --
Published Online: Apr. 21, 2021
The Author Email: Sun Jie (lusongfeng@hotmail.com)