Quantum random-walk search algorithm

A Quantum Random Walk Search Algorithm

Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. However, it is still unclear how to use these novel properties to gain an algorithmic speed-up over classical algorithms. In this paper, we present a quantum search algorithm based on the quantum random walk architectu...

Optimized quantum random-walk search algorithms

Shenvi, Kempe and Whaley’s quantum random-walk search (SKW) algorithm [2003 Phys. Rev. A 67 052307] is known to require O( √ N) number of oracle queries to find the marked element, where N is the size of the search space. This scaling is thought to be the best achievable on a quantum computer. We prove that the final state of the quantum walk in the SKW algorithm yields the nearest neighbours o...

Quantum random walk search on satisfiability problems

Using numerical simulation, we measured the performance of several potential quantum algorithms, based on quantum random walks, to solve Boolean satisfiability (SAT) problems. We develop the fundamentals of quantum computing and the theory of classical algorithms to indicate how these algorithms could be implemented. We also discuss the development of quantum random walks and the principles tha...

Search via Quantum Walk

A Novel Clustering Algorithm Based on Quantum Random Walk

The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum random walk (QRW) with the problem of data clustering, and develop two clustering algorithms based on the one dimensional QRW. Then, the probability distributions on the positions induced by QRW in these algorithms are investigated, which also indicates the possibility of ob...