Adiabatic quantum search algorithm for structured problems (7 pages)

Mingsheng Ying, Zhaohui Wei, Zhongqing Ji

Jérémie Roland, Nicolas J. Cerf

The study of quantum computation has been motivated by the hope of finding efficient quantum algorithms for solving classically hard problems. In this context, quantum algorithms by local adiabatic evolution have been shown to solve an unstructured search problem with a quadratic speedup over a classical search, just as Grover's algorithm. In this paper, we study how the structure of the search problem may be exploited to further improve the efficiency of these quantum adiabatic algorithms. We show that by nesting a partial search over a reduced set of variables into a global search, it is possible to devise quantum adiabatic algorithms with a complexity that, although still exponential, grows with a reduced order in the problem size.

Lov K. Grover

Nicolas J. Cerf, Jérémie Roland

Daria Ahrensmeier, Saurya Das, Randy Kobes +2 more

We examine the use of adiabatic quantum algorithms to solve structured, or nested, search problems. We construct suitable time dependent Hamiltonians and derive the computation times for a general class of nested searches involving n qubits. As expected, we find that as additional structure is included, the Hamiltonians become more local and the computation times decrease.

Lov K. Grover