International Journal of Quantum Information · 2006 · 117 citations · 18 references
Quantum ScienceQuantum WalksEngineeringQuantum ComputingGraph TheoryQuantum Optimization AlgorithmContinuous TimeStructural Graph TheoryTopological Graph TheoryAlgebraic Graph TheoryQuantum AlgorithmQuantum WalkQuantum NetworkComputer ScienceDiscrete MathematicsQuantum EntanglementQuantum Algorithms
Quantum walks, both discrete (coined) and continuous time, on a general graph of N vertices with undirected edges are reviewed in some detail. The resource requirements for implementing a quantum walk as a program on a quantum computer are compared and found to be very similar for both discrete and continuous time walks. The role of the oracle, and how it changes if more prior information about the graph is available, is also discussed.
18
Seth Lloyd · Science · 1996 · 2.9K citations
Yakir Aharonov, L. Davidovich, N. Zagury · Physical Review A · 1993 · 1.6K citations
Quantum computation and decision trees
Edward Farhi, Sam Gutmann · Physical Review A · 1998 · 1.2K citations · Full text
Quantum random-walk search algorithm
Neil Shenvi, Julia Kempe, K. Birgitta Whaley · Physical Review A · 2003 · 1.1K citations · Full text
Spatial search by quantum walk
Andrew M. Childs, Jeffrey Goldstone · Physical Review A · 2004 · 711 citations · Full text
Engineering, Computational Complexity, Quantum Computing +16