Quantum Walks on Regular Graphs and Eigenvalues
نویسندگان
چکیده
منابع مشابه
Quantum 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 کاملRandom Walks on Regular and Irregular Graphs
For an undirected graph and an optimal cyclic list of all its vertices, the cyclic cover time is the expected time it takes a simple random walk to travel from vertex to vertex along the list, until it completes a full cycle. The main result of this paper is a characterization of the cyclic cover time in terms of simple and easy to compute graph properties. Namely, for any connected graph, the ...
متن کاملOn the extreme eigenvalues of regular graphs
In this paper, we present an elementary proof of a theorem of Serre concerning the greatest eigenvalues of k-regular graphs. We also prove an analogue of Serre’s theorem regarding the least eigenvalues of k-regular graphs: given > 0, there exist a positive constant c = c( , k) and a nonnegative integer g = g( , k) such that for any k-regular graph X with no odd cycles of length less than g, the...
متن کاملRegular Factors of Regular Graphs from Eigenvalues
Let r and m be two integers such that r > m. Let H be a graph with order |H|, size e and maximum degree r such that 2e > |H|r−m. We find a best lower bound on spectral radius of graph H in terms of m and r. Let G be a connected r-regular graph of order |G| and k < r be an integer. Using the previous results, we find some best upper bounds (in terms of r and k) on the third largest eigenvalue th...
متن کاملQuantum 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 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: The Electronic Journal of Combinatorics
سال: 2011
ISSN: 1077-8926
DOI: 10.37236/652