Related papers: Synthesis of a quantum tree Weyl matrix
We consider a generic elementary gate sequence which is needed to implement a general quantum gate acting on n qubits -- a unitary transformation with 4^n degrees of freedom. For synthesizing the gate sequence, a method based on the…
We introduce ring theoretic constructions that are similar to the construction of wreath product of groups. In particular, for a given graph $\Gamma=(V,E)$ and an associate algebra $A,$ we construct an algebra $B=A\, wr\, L(\Gamma)$ with…
In this article we continue to develop the theory of generating symmetries for integrable equations. A technique for computation of generating symmetries using Maple is presented. The technique is based on the standard symmetry method. By…
A Weyl group multiple Dirichlet series is a Dirichlet series in several complex variables attached to a root system Phi. The number of variables equals the rank r of the root system, and the series satisfies a group of functional equations…
A new algebraic Cayley graph is constructed using finite fields. Its connectedness and diameter bound are studied via Weil's estimate for character sums. These graphs provide a new source of expander graphs, extending classical results of…
Quantum cellular automata and quantum walks provide a framework for the foundations of quantum field theory, since the equations of motion of free relativistic quantum fields can be derived as the small wave-vector limit of quantum automata…
Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. A key issue is how to address the inherent non-linearity of classical deep learning, a problem in the quantum domain due to…
We solve $\mathcal{N}=1$ supersymmetric $A_{2}$ type $U(N)\times U(N)$ matrix models obtained by deforming $\mathcal{N}=2$ with symmetric tree level superpotentials of any degree exactly in the planar limit. These theories can be…
A one-to-one correspondence is proved between the N-rooted ribbon graphs, or maps, with e edges and the (e-N+1)-loop Feynman diagrams of a certain quantum field theory. This result is used to obtain explicit expressions and relations for…
Given a set of quantum gates and a target unitary operation, the most elementary task of quantum compiling is the identification of a sequence of the gates that approximates the target unitary to a determined precision $\varepsilon$.…
We suggest a combinatorial method of encoding continuous symbolic dynamical systems. A~continuous phase space, the infinite-dimensional cube, turns into the path space of a tree, and the shift is mapped to a transformation which was called…
Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency list-like array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity,…
In this paper, we propose an incremental algorithm for computing cylindrical algebraic decompositions. The algorithm consists of two parts: computing a complex cylindrical tree and refining this complex tree into a cylindrical tree in real…
One of the most important characteristics of a quantum graph is the average density of resonances, $\rho = \frac{\mathcal{L}}{\pi}$, where $\mathcal{L}$ denotes the length of the graph. This is a very robust measure. It does not depend on…
For any Hecke symmetry $R$ there is a natural quantization $A_n(R)$ of the Weyl algebra $A_n$. The aim of this paper is to study some general ring-theoretic aspects of $A_n(R)$ and its relations to formal deformations of $A_n$. We also…
We present a family of methods, which can describe behaviour of quantum ensembles and demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoherent from basic localized modes in…
We compute the Weyl group (in the sense of Segal) of the group of holomorphic isometries of a K\"ahler toric manifold with real analytic K\"ahler metric.
We propose an alternative approach for the construction of the unitary matrix which performs generalized unitary rotations of the system consisting of independent identical subsystems (for example spin system). This matrix, when applied to…
A positive function (conductivity) on the edges of a graph induces the Dirichlet-to- Neumann map between boundary values of harmonic functions. The inverse conductivity problem is to find the conductivity from the Dirichlet-to-Neumann map.…
This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…