Lower bound on the time complexity of local adiabatic evolution
Zhenghao Chen, Pang Wei Koh, Yan Zhao · Physical Review A · 2006
The adiabatic theorem of quantum physics has been, in recent times, utilized in the design of local search quantum algorithms, and has been proven to be equivalent to standard quantum computation, that is, the use of unitary operators [D. Aharonov et al. in Proceedings of the 45th Annual Symposium on the Foundations of Computer Science, 2004, Rome, Italy (IEEE Computer Society Press, New York, 2004), pp. 42--51]. Hence, the study of the time complexity of adiabatic evolution algorithms gives insight into the computational power of quantum algorithms. In this paper, we present two different approaches of evaluating the time complexity for local adiabatic evolution using time-independent parameters, thus providing effective tests (not requiring the evaluation of the entire time-dependent gap function) for the time complexity of newly developed algorithms. We further illustrate our tests by displaying results from the numerical simulation of some problems, viz. specially modified instances of the Hamming weight problem.