Quantum Interference, Graphs, Walks, and Polynomials
نویسندگان
چکیده
منابع مشابه
Quantum Walks on Cayley Graphs
We address the problem of the construction of quantum walks on Cayley graphs. Our main motivation is the relationship between quantum algorithms and quantum walks. In particular, we discuss the choice of the dimension of the local Hilbert space and consider various classes of graphs on which the structure of quantum walks may differ. We completely characterise quantum walks on free groups and p...
متن کاملQuantum walks on directed graphs
We consider the definition of quantum walks on directed graphs. Call a directed graph reversible if, for each pair of vertices (vi, vj), if vi is connected to vj then there is a path from vj to vi. We show that reversibility is a necessary and sufficient condition for a directed graph to allow the notion of a discrete-time quantum walk, and discuss some implications of this condition. We presen...
متن کاملFrom quantum graphs to quantum random walks
We give a short overview over recent developments on quantum graphs and outline the connection between general quantum graphs and so-called quantum random walks.
متن کاملQuantum Walks on Regular Graphs and Eigenvalues
We study the transition matrix of a quantum walk on strongly regular graphs. It is proposed by Emms, Hancock, Severini and Wilson in 2006, that the spectrum of S+(U3), a matrix based on the amplitudes of walks in the quantum walk, distinguishes strongly regular graphs. We find the eigenvalues of S+(U) and S+(U2) for regular graphs and show that S+(U2) = S+(U)2 + I.
متن کاملQuantum walks on graphs and quantum scattering theory
A number of classical algorithms are based on random walks on graphs. It is hoped that recently defined quantum walks can serve as the basis for quantum algorithms that will faster than the corresponding classical ones. We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle maki...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Chemical Reviews
سال: 2018
ISSN: 0009-2665,1520-6890
DOI: 10.1021/acs.chemrev.7b00733