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

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 Solving constrained quadratic binary problems via quantum adiabatic evolution

2016 ◽  
Vol 16 (11&12) ◽  
pp. 1029-1047
Author(s):  
Pooya Ronagh ◽  
Brad Woods ◽  
Ehsan Iranmanesh
Keyword(s):  
Quadratic Programming ◽  
A Priori ◽  
Inequality Constraints ◽  
Adiabatic Evolution ◽  
Binary Quadratic Programming ◽  
Constrained Problems ◽  
Linear Equality Constraints ◽  
Adiabatic Approach ◽  
Quadratic Programming Problems ◽  
Quantum Adiabatic Evolution

Quantum adiabatic evolution is perceived as useful for binary quadratic programming problems that are a priori unconstrained. For constrained problems, it is a common practice to relax linear equality constraints as penalty terms in the objective function. However, there has not yet been proposed a method for efficiently dealing with inequality constraints using the quantum adiabatic approach. In this paper, we give a method for solving the Lagrangian dual of a binary quadratic programming (BQP) problem in the presence of inequality constraints and employ this procedure within a branch-and-bound framework for constrained BQP (CBQP) problems.

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