Fast quantum search driven by environmental engineering

Abstract

Studies have demonstrated that a joined complete graph is a typical mathematical model that can support the fast quantum search. In this paper, we study the implementations of joined complete graphs in atomic systems and realize a quantum search of runtime O(√N) based on this implementation with a success probability of 50%. Even though the practical systems are inevitably interacted with the surrounding environment, we reveal that the successful quantum search can be realized through delicately engineering the environment itself. We believe that our study in this work will bring a feasible way to realize quantum information processing including quantum algorithms in reality.

Quantum search of many vertices on the joined complete graph

“…[12][13][14][15][16][17][18][19] Quantum algorithms based on continuous-time quantum walks have revealed an exponential acceleration that surpasses any classical algorithm in solving a certain black-box problem, and can provide a corresponding framework for designing new algorithms, modeling quantum transmission and state transition problems. [20][21][22][23][24][25][26][27][28][29][30][31][32][33] Considering that the graph structure can represent different connections between the vertices, the quantum search algorithms on the graph are also very important. The viewpoint about the success of searching the vertices in the graph depending on the connectivity in the graph lasted over one decade.…”