In this chapter, we define coined quantum walks on graphs . The concepts of graph theory reviewed in Appendix B are required here for a full understanding of the definition of the coined quantum walk. We split the presentation into class 1 and class 2 graphs. Class 1 comprises graphs whose...
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...
We successfully map such graphs on quantum photonic chips using femtosecond-laser direct writing techniques in a geometrically scalable fashion. We experimentally demonstrate quantum fast hitting by implementing two-dimensional quantum walks on graphs with up to 160 nodes and a depth of eight layers, ...
2009 Searching via walking: How to find a marked subgraph of a graph using quantum walks 2009 Quantum searches on highly symmetric graphs 对于K5, marked point 0 的U矩阵可以写出: \left(\begin{array}{ccc} 0&1&0\\-e^{iφ}/2&0& \sqrt{3} /2\\ \sqrt{3} e^{iφ}/2&0&1/2\end...
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 ...
(2006). Mixing and decoherence in continuous-time quantum walks on cycles, Quantum Information and Computation, 6, 263–276, quant-ph/0509163. MATH MathSciNet Google Scholar Feldman, E., and Hillery, M. (2004a). Quantum walks on graphs and quantum scattering theory, Proceedings of ...
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...
【幻灯:图的量子游走】《Quantum walks on graphs》by Andrew Childs http://t.cn/RL0Vulq
Our findings underscore the promising avenues for investigating the mixing time of quantum walks on regular and Cayley graphs of non-abelian groups, highlighting their relevance in quantum algorithm design and analysis. Biography...