Quantum walks on simplicial complexes
نویسندگان
چکیده
منابع مشابه
Random walks on simplicial complexes and harmonics†
In this paper, we introduce a class of random walks with absorbing states on simplicial complexes. Given a simplicial complex of dimension d, a random walk with an absorbing state is defined which relates to the spectrum of the k-dimensional Laplacian for 1 ≤ k ≤ d. We study an example of random walks on simplicial complexes in the context of a semi-supervised learning problem. Specifically, we...
متن کاملFlows on Simplicial Complexes
Given a graph G, the number of nowhere-zero Zq-flows φG(q) is known to be a polynomial in q. We extend the definition of nowhere-zero Zq-flows to simplicial complexes ∆ of dimension greater than one, and prove the polynomiality of the corresponding function φ∆(q) for certain q and certain subclasses of simplicial complexes. Résumé. Et́ant donné une graphe G, on est connu que le nombre de Zq-flot...
متن کاملA duality on simplicial complexes
The usual definition of finite simplicial complex is a set of non-empty subsets of a finite set, closed under non-empty subset formation. For our purposes here, we will omit the non-emptiness and define a finite simplicial complex to be a down-closed subset of the set of subsets of a finite set. We can, and will suppose that the finite set is the integers 0,. . . ,N . We will denote by K the se...
متن کاملSimplicial Moves on Balanced Complexes
We introduce a notion of cross-flips: local moves that transform a balanced (i.e., properly (d + 1)-colored) triangulation of a combinatorial d-manifold into another balanced triangulation. These moves form a natural analog of bistellar flips (also known as Pachner moves). Specifically, we establish the following theorem: any two balanced triangulations of a closed combinatorial d-manifold can ...
متن کاملOn Finite Arithmetic Simplicial Complexes
We compute the Euler-Poincaré characteristic of quotients of the Bruhat-Tits building of PGL(n) under the action of arithmetic groups arising from central division algebras over rational function fields of positive characteristic. We use this result to determine the structure of the quotient simplicial complex in certain cases.
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: Quantum Information Processing
سال: 2016
ISSN: 1570-0755,1573-1332
DOI: 10.1007/s11128-016-1247-6