Related papers: On errors generated by unitary dynamics of biparti…
We prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations, as predicted by random--matrix theory. The stability of these correlations with regard to non--universal corrections is analyzed in…
We present singly-exponential quantum algorithms for the One-Sided Crossing Minimization (OSCM) problem. Given an $n$-vertex bipartite graph $G=(U,V,E\subseteq U \times V)$, a $2$-level drawing $(\pi_U,\pi_V)$ of $G$ is described by a…
We study the problem of generating graphs with prescribed degree sequences for bipartite, directed, and undirected networks. We first propose a sequential method for bipartite graph generation and establish a necessary and sufficient…
In 2019, Aterias et al. constructed pairs of quantum isomorphic, non-isomorphic graphs from linear constraint systems. This article deals with quantum automorphisms and quantum isomorphisms of colored versions of those graphs. We show that…
Oriented graph complexes, in which graphs are not allowed to have oriented cycles, govern for example the quantization of Lie bialgebras and infinite dimensional deformation quantization. It is shown that the oriented graph complex GC^or_n…
This paper investigates continuous-time quantum walks on directed bipartite graphs based on a graph's adjacency matrix. We prove that on bipartite graphs, probability transport between the two node partitions can be completely suppressed by…
The one-shot zero-error classical capacity of a quantum channel is the amount of classical information that can be transmitted with zero probability of error by a single use. Then the one-shot zero-error classical capacity equals to the…
Nonautonomous linear ordinary differential equations of the form $\dot{v}(t) = A(t)\, v(t)$, where $A(t)$ is non-skew-symmetric, are often used to describe nonunitary dynamics in a variety of fields that range from open quantum system…
We derive an exact quantum propagator for nonadiabatic dynamics in multi-state systems using the mapping variable representation, where classical-like Cartesian variables are used to represent both continuous nuclear degrees of freedom and…
Graph states are multi-particle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions. They are many-body spin states of…
The explicit solution to the spectral problem of quantum graphs found recently in \cite{Anima}, is used to produce the exact periodic orbit theory description for the probability distributions of spectral statistics, including the…
In the Graph Isomorphism problem two N-vertex graphs G and G' are given and the task is to determine whether there exists a permutation of the vertices of G that preserves adjacency and transforms G into G'. If yes, then G and G' are said…
A unital completely positive map governing the time evolution of a quantum system is usually called a quantum channel, and it can be represented by a tuple of operators which are then referred to as the Kraus operators of the channel. We…
In 1940 Naimark showed that if a set of quantum observables are positive semi-definite and sum to the identity then, on a larger space, they have a joint resolution as commuting projectors. In 1955 Sz.-Nagy showed that any set of…
We present a theoretical framework for the analysis of amplitude transfer in Quantum Variational Algorithms (QVAs) for combinatorial optimisation with mixing unitaries defined by vertex-transitive graphs, based on their continuous-time…
We discuss several aspects concerning the asymptotic dynamics of dicrete-time semigroups associated with a quantum channel. By using an explicit expression of the asymptotic map, which describes the action of the quantum channel on its…
The quantum mechanics is proved to admit no hidden-variable in 1960s, which means the quantum systems are contextual. Revealing the mathematical structure of quantum mechanics is a significant task. We develop the approach of partial…
The study of quantum evolution on graphs for diversified topologies is beneficial to modeling various realistic systems. A systematic method, the dimerized decomposition, is proposed to analyze the dynamics on an arbitrary network. By…
We initiate a general study of what we call orientation completion problems. For a fixed class C of oriented graphs, the orientation completion problem asks whether a given partially oriented graph P can be completed to an oriented graph in…
Maximally entangled bipartite unitary operators or gates find various applications from quantum information to being building blocks of minimal models of many-body quantum chaos, and have been referred to as "dual unitaries". Dual unitary…