相关论文: Perfect state transfer is poly-time

A partial complement of the graph $G$ is a graph obtained from $G$ by complementing all the edges in one of its induced subgraphs. We study the following algorithmic question: for a given graph $G$ and graph class $\mathcal{G}$, is there a…

The maximum clique problem is a classical NP-complete problem in graph theory and has important applications in many domains. In this paper we show, in a partially non-constructive way, the existence of an exact polynomial-time algorithm…

We introduce the concept of group state transfer on graphs, summarize its relationship to other concepts in the theory of quantum walks, set up a basic theory, and discuss examples. Let $X$ be a graph with adjacency matrix $A$ and consider…

The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…

Let A be the adjacency matrix of a graph $X$ and suppose U(t)=exp(itA). We view A as acting on $\cx^{V(X)}$ and take the standard basis of this space to be the vectors $e_u$ for $u$ in $V(X)$. Physicists say that we have perfect state…

Efficiently finding the maximum a posteriori (MAP) configuration of a graphical model is an important problem which is often implemented using message passing algorithms. The optimality of such algorithms is only well established for…

Let $G$ be a graph with adjacency matrix $A$. The transition matrix of $G$ relative to $A$ is defined by $H_{A}(t):=\exp{(-itA)},\;t\in\Rl$. We say that the graph $G$ admits perfect state transfer between the verteices $u$ and $v$ at…

A continuous quantum walk on a graph $X$ with adjacency matrix $A$ is specified by the 1-parameter family of unitary matrices $U(t)=\exp(itA)$. These matrices act on the state space of a quantum system, the states of which we may represent…

P-time event graphs are discrete event systems able to model cyclic production systems where tasks need to be performed within given time windows. Consistency is the property of admitting an infinite execution of such tasks that does not…

We introduce an NP-complete graph decision problem, the "Multi-stage graph Simple Path" (abbr. MSP) problem, which focuses on determining the existence of specific "global paths" in a graph $G$. We show that the MSP problem can be solved in…

The partition of graphs into "nice" subgraphs is a central algorithmic problem with strong ties to matching theory. We study the partitioning of undirected graphs into same-size stars, a problem known to be NP-complete even for the case of…

Given a bipartite graph that has a perfect matching, a prefect proportional allocation is an assignment of positive weights to the nodes of the right partition so that every left node is fractionally assigned to its neighbors in proportion…

We exploit a ferromagnetic chain of interacting $d$-level ($d>2$) particles for arbitrary perfect transfer of quantum states with $(d-1)$ levels. The presence of one extra degree of freedom in the Hilbert space of particles, which is not…

In this paper we show that it can be decided in polynomial time whether or not the visibility graph of a given point set is 4-colourable, and such a 4-colouring, if it exists, can also be constructed in polynomial time. We show that the…

Let $L$ denote the Laplacian matrix of a graph $G$. We study continuous quantum walks on $G$ defined by the transition matrix $U(t)=\exp\left(itL\right)$. The initial state is of the pair state form, $e_a-e_b$ with $a,b$ being any two…

The quantum Perfect State Transfer (PST) is a fundamental tool of quantum communication in a network. It is not easy to achieve in practice. The original idea of PST depends on the fundamentals of the continuous-time quantum walk. A path…

The \textit{transition matrix} of a graph $\Gamma$ with adjacency matrix $A$ is defined by $H(\tau ) := \exp(-\mathbf{i}\tau A)$, where $\tau \in \mathbb{R}$ and $\mathbf{i} = \sqrt{-1}$. The graph $\Gamma$ exhibits \textit{perfect state…

We present a general formalism to the problem of perfect state-transfer (PST), where the state involves multiple excitations of the quantum network. A key feature of our formalism is that it allows for inclusion of nontrivial interactions…

A general formalism of the problem of perfect state transfer is presented. We show that there are infinitely many Hamiltonians which may provide solution to this problem. In a first attempt to give a classification of them we investigate…

In this paper, we first give a necessary and sufficient condition for a graph to have Laplacian pretty good pair state transfer. As an application of such result, we give a complete characterization of Laplacian pretty good edge state…