Related papers: Mapping finite state machines to zk-SNARKS Using C…
We characterize the set of planar locally finite Cayley graphs, and give a finite representation of these graphs by a special kind of finite state automata called labeling schemes. As a result, we are able to enumerate and describe all…
We consider quantum state transfer on finite graphs which are attached to infinite paths. The finite graph represents an operational quantum system for performing useful quantum information tasks. In contrast, the infinite paths represent…
Finite-depth quantum circuits preserve the long-range entanglement structure in quantum states and map between states within a gapped phase. To map between states of different gapped phases, we can use Sequential Quantum Circuits which…
In the paper we introduce graphical objects (called state diagrams) related to functional programs. It is shown that state diagrams of functional programs can be used to solve problems of verification of functional programs. The proposed…
Tensor networks and circuits are widely used data structures to represent pseudo-Boolean functions. These two formalisms have been studied primarily in separate communities, and this paper aims to establish equivalences between them. We…
Boolean circuit is a computational graph that consists of the dynamic directed graph structure and static functionality. The commonly used logic optimization and Boolean matching-based transformation can change the behavior of the Boolean…
Graph states are versatile resources for quantum computation and quantum-enhanced measurement. Their generation illustrates a high level of control over entanglement. We report on the generation of continuous-variable graph states of atomic…
This paper addresses the problem of finding cycles in the state transition graphs of synchronous Boolean networks. Synchronous Boolean networks are a class of deterministic finite state machines which are used for the modeling of gene…
The Stallings construction for finitely generated subgroups of free groups is generalized by introducing the concept of Stallings section, which allows an eficient computation of the core of a Schreier graph based on edge folding. It is…
Graphs and graph transformation systems are a frequently used modelling technique for a wide range of different domains, cover- ing areas as diverse as refactorings, network topologies or reconfigurable software. Being a formal method,…
Entanglement is a fundamental resource for many applications in quantum information processing. Here, we investigate how quantum transport in simple quantum graphs, modeled as controlled two-level quantum systems, can be utilized to…
We consider the class of the topologically locally finite (in short TLF) planar vertex-transitive graphs, a class containing in particular all the one-ended planar Cayley graphs and the normal transitive tilings. We characterize these…
Control theory uses `signal-flow diagrams' to describe processes where real-valued functions of time are added, multiplied by scalars, differentiated and integrated, duplicated and deleted. These diagrams can be seen as string diagrams for…
We present an algorithm for efficiently simulating a quantum circuit in the graph formalism. In the graph formalism, we represent states as a linear combination of graphs with Clifford operations on their vertices. We show how a…
A coarse-grained cellular automaton is proposed to simulate traffic systems. There, cells represent road sections. A cell can be in two states: jammed or passable. Numerical calculations are performed for a piece of square lattice with open…
We consider infinite connected quasi-transitive locally finite graphs and show that every such graph with more than one end is a tree amalgamation of two other such graphs. This can be seen as a graph-theoretical version of Stallings'…
Graph states are used to represent mathematical graphs as quantum states on quantum computers. They can be formulated through stabilizer codes or directly quantum gates and quantum states. In this paper we show that a quantum graph neural…
Given a finite directed graph, a coloring of its edges turns the graph into a finite-state automaton. A k-synchronizing word of a deterministic automaton is a word in the alphabet of colors at its edges that maps the state set of the…
In finite-dimensional systems, circuit knitting can be used to simulate non-classical quantum operations using a limited set of resources. In this work, we extend circuit knitting techniques to infinite-dimensional quantum systems. We…
We provide a simple linear time transformation from a directed or undirected graph with labeled edges to an unlabeled digraph, such that paths in the input graph in which no two consecutive edges have the same label correspond to paths in…