A family of system Hamiltonian in quantum adiabatic search type problem

2019 ◽  
Vol 17 (02) ◽  
pp. 1950015
Author(s):  
Jie Sun ◽  
Songfeng Lu
Keyword(s):  
General Class ◽  
Type Problem ◽  
Adiabatic Evolution ◽  
General Family ◽  
Shed Light ◽  
Quantum Adiabatic Evolution

In this paper [J. Sun, S. Lu and F. Liu, Open Syst. Info. Dyn.23(3) (2016) 1650016], we have studied a general class of adiabatic evolutions in quantum adiabatic search type problem, and found another limitation on it, besides those reported in our early work. In this paper, we extend this study by considering adding an extra driving scheme to the system Hamiltonian of this type of quantum adiabatic evolution. It will be shown that, like the previous study in [J. Sun, S. Lu and F. Liu, Open Syst. Info. Dyn.23(3) (2016) 1650016], the limitation above can also possibly penetrate into the search type quantum-adiabatic computation even by this more general family of system Hamiltonian, which may shed light on what we should have in mind when solving practical problems by means of quantum adiabatic evolution.

On the General Class of Models of Adiabatic Evolution

2016 ◽  
Vol 23 (03) ◽  
pp. 1650016 ◽  
Author(s):  
Jie Sun ◽  
Songfeng Lu ◽  
Fang Liu
Keyword(s):  
Ground State ◽  
General Class ◽  
Time Complexity ◽  
State Energy ◽  
Search Problem ◽  
Quantum Search ◽  
Final States ◽  
Adiabatic Evolution ◽  
Speed Up ◽  
Effective Use

The general class of models of adiabatic evolution was proposed to speed up the usual adiabatic computation in the case of quantum search problem. It was shown [8] that, by temporarily increasing the ground state energy of a time-dependent Hamiltonian to a suitable quantity, the quantum computation can perform the calculation in time complexity O(1). But it is also known that if the overlap between the initial and final states of the system is zero, then the computation based on the generalized models of adiabatic evolution can break down completely. In this paper, we find another severe limitation for this class of adiabatic evolution-based algorithms, which should be taken into account in applications. That is, it is still possible that this kind of evolution designed to deal with the quantum search problem fails completely if the interpolating paths in the system Hamiltonian are chosen inappropriately, while the usual adiabatic evolutions can do the same job relatively effectively. This implies that it is not always recommendable to use nonlinear paths in adiabatic computation. On the contrary, the usual simple adiabatic evolution may be sufficient for effective use.

Generalized relation between fidelity and quantum adiabatic evolution

2015 ◽  
Vol 14 (6) ◽  
pp. 1757-1765 ◽  
Author(s):  
Jie Sun ◽  
Songfeng Lu ◽  
Fang Liu ◽  
Qing Zhou ◽  
Zhigang Zhang
Keyword(s):  
Adiabatic Evolution ◽  
Quantum Adiabatic Evolution

scholarly journals Finding cliques by quantum adiabatic evolution

2002 ◽  
Vol 2 (3) ◽  
pp. 181-191
Author(s):  
A.M. Childs ◽  
E. Farhi ◽  
J. Goldstone ◽  
S. Gutmann
Keyword(s):  
Random Graph ◽  
High Probability ◽  
Numerical Study ◽  
Quantum Algorithm ◽  
Quantum Computers ◽  
Connected Subgraph ◽  
Combinatorial Search ◽  
Adiabatic Evolution ◽  
General Technique ◽  
Quantum Adiabatic Evolution

Quantum adiabatic evolution provides a general technique for the solution of combinatorial search problems on quantum computers. We present the results of a numerical study of a particular application of quantum adiabatic evolution, the problem of finding the largest clique in a random graph. An n-vertex random graph has each edge included with probability 1/2, and a clique is a completely connected subgraph. There is no known classical algorithm that finds the largest clique in a random graph with high probability and runs in a time polynomial in n. For the small graphs we are able to investigate ($n \le 18$), the quantum algorithm appears to require only a quadratic run time.

scholarly journals Adiabatic Evolution: The Influence of Non-Markovian Characters on Quantum Adiabatic Evolution (Ann. Phys. 1/2019)

2019 ◽  
Vol 531 (1) ◽  
pp. 1970010 ◽  
Author(s):  
Ye-Xiong Zeng ◽  
Tesfay Gebremariam ◽  
Ming-Song Ding ◽  
Chong Li
Keyword(s):  
Adiabatic Evolution ◽  
Quantum Adiabatic Evolution
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