2009 Searching via walking: How to find a marked subgraph of a graph using quantum walks 2009 Quantum searches on highly symmetric graphs 2008 Quantum walk based search algorithms 2016 Spatial search by quantum walk is optimal for almost all graphs 2016 Quantum algorithms: an overview 三个关键点:...
Quantum walks have beenS BerryAmbainis A. Kempe J. Vazirani U Aharanov D. "Quantum walks on graphs." In: Annual ACM STOC 33 (2001), pp. 50-59.D. Aharonov, A. Ambainis, J. Kempe, U. Vazirani, Quantum walks on graphs, in: Proc. 33rd Annual ACM STOC. (ACM, NY, 2001), ...
We set the ground for a theory of quantum walks on graphs- the generalization of random walks on finite graphs to the quantum world. Such quantum walks do not converge to any stationary distribution, as they are unitary and reversible. However, by suitably relaxing the definition, we can obta...
Quantum walks on graphs have shown prioritized benefits and applications in wide areas. In some scenarios, however, it may be more natural and accurate to mandate high-order relationships for hypergraphs, due to the density of information stored inherently. Therefore, we can explore the potential ...
We consider both dynamical evolution and asymptotic limits for coins of dimensions from two to eight on regular graphs. For low coin dimensions, quantum walks which spread faster (as measured by the second moment of their distribution on the graph) also exhibit faster convergence towards the ...
We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has $l$ integer self-loops, can be generalized to a quantum walk where each vertex has a single self...
We study discrete-time quantum walks on generalized Birkhoff polytope graphs (GBPGs), which arise in the solution-set to certain transportation linear programming problems (TLPs). It is known that quantum walks mix at most quadratically faster than random walks on cycles, two-dimensional lattices...
algorithms based on quantum walks, which improve the dependence onδquadratically, from 1/δto1/δ.54–56This framework has been used to obtain quantum speedups for a variety of problems,4ranging from determining whether a list of integers are all distinct54to finding triangles in graphs.57 ...
There are presently two models for quantum walks on graphs. The "coined" walk uses discrete-time steps, and contains, besides the particle making the walk,... M Hillery,J Bergou,E Feldman - 《Physical Review A》 被引量: 100发表: 2003年 Coined quantum walks on percolation graphs Quantum...
Quantum walks on graphs. In Proceedings of the thirty-third annual ACM symposium on Theory of computing, 50 (ACM, 2001). Kendon, V. Quantum walks on general graphs. International Journal of Quantum Information 4, 791 (2006). Article Google Scholar Reitzner, D., Nagaj, D. & Buzek, V...