Distributed exact Grover’s algorithm

Abstract

Distributed quantum computation has gained extensive attention. In this paper, we consider a search problem that includes only one target item in the unordered database. After that, we propose a distributed exact Grover’s algorithm (DEGA), which decomposes the original search problem into ⌊n/2⌋ parts. Specifically, (i) our algorithm is as exact as the modified version of Grover’s algorithm by Long, which means the theoretical probability of finding the objective state is 100%; (ii) the actual depth of our circuit is 8(n mod 2) + 9, which is less than the circuit depths of the original and modified Grover’s algorithms, \(1 + 8\left\lfloor {{\pi \over 4}\sqrt {{2^n}} } \right\rfloor \) and \(9 + 8\left\lfloor {{\pi \over 4}\sqrt {{2^n}} - {1 \over 2}} \right\rfloor \), respectively. It only depends on the parity of n, and it is not deepened as n increases; (iii) we provide particular situations of the DEGA on MindQuantum (a quantum software) to demonstrate the practicality and validity of our method. Since our circuit is shallower, it will be more resistant to the depolarization channel noise.