Related papers: Quantum invariants for the graph isomorphism probl…
In recent years, quantum computing has emerged as a transformative force in the field of combinatorial optimization, offering novel approaches to tackling complex problems that have long challenged classical computational methods. Among…
A fundamental problem in Quantum Information Processing is the discrimination amongst a set of quantum states of a system. In this paper, we address this problem on an open quantum system described by a graph, whose evolution is defined by…
We study free scalar field theory on a graph, which gives rise to a modified version of discrete Green's function on a graph studied in \cite{CY}. We show that this gives rise to a graph invariant, which is closely related to the 2-dim…
We introduce the Hidden Polynomial Function Graph Problem as a natural generalization of an abelian Hidden Subgroup Problem (HSP) where the subgroups and their cosets correspond to graphs of linear functions over the finite field F_p. For…
Quantum Approximate Optimization Algorithm (QAOA) is a hybrid classical-quantum algorithm to approximately solve NP optimization problems such as MAX-CUT. We describe a new application area of QAOA circuits: graph structure discovery. We…
We review quantum chaos on graphs. We construct a unitary operator which represents the quantum evolution on the graph and study its spectral and wavefunction statistics. This operator is the analogue of the classical evolution operator on…
The quantum circuit model is the default for encoding an algorithm intended for a NISQ computer or a quantum computing simulator. A simple graph and through it, a graph state - quantum state physically manifesting an abstract graph…
We present a strong connection between quantum information and quantum permutation groups. Specifically, we define a notion of quantum isomorphisms of graphs based on quantum automorphisms from the theory of quantum groups, and then show…
Testing graph completeness is a critical problem in computer science and network theory. Leveraging quantum computation, we present an efficient algorithm using the Szegedy quantum walk and quantum phase estimation (QPE). Our algorithm,…
The graph isomorphism problem is of practical importance, as well as being a theoretical curiosity in computational complexity theory in that it is not known whether it is $NP$-complete or $P$. However, for many graphs, the problem is…
The problem of graph isomorphism is an important but challenging problem in the field of graph analysis, for example: analyzing the similarity of two chemical molecules, or studying the expressive ability of graph neural networks. WL test…
Graph Neural Networks (GNNs) are powerful machine learning models that excel at analyzing structured data represented as graphs, demonstrating remarkable performance in applications like social network analysis and recommendation systems.…
Quantum Graph Neural Networks (QGNNs) represent a novel fusion of quantum computing and Graph Neural Networks (GNNs), aimed at overcoming the computational and scalability challenges inherent in classical GNNs that are powerful tools for…
The isomorphism problem for planar graphs is known to be efficiently solvable. For planar 3-connected graphs, the isomorphism problem can be solved by efficient parallel algorithms, it is in the class $AC^1$. In this paper we improve the…
In this paper, we present two main results. First, by only one conjecture (Conjecture 2.9) for recognizing a vertex symmetric graph, which is the hardest task for our problem, we construct an algorithm for finding an isomorphism between two…
The criteria for determining graph isomorphism are crucial for solving graph isomorphism problems. The necessary condition is that two isomorphic graphs possess invariants, but their function can only be used to filtrate and subdivide…
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…
A T-graph (a special case of a chordal graph) is the intersection graph of connected subtrees of a suitable subdivision of a fixed tree T . We deal with the isomorphism problem for T-graphs which is GI-complete in general - when T is a part…
Graph sparsification underlies a large number of algorithms, ranging from approximation algorithms for cut problems to solvers for linear systems in the graph Laplacian. In its strongest form, "spectral sparsification" reduces the number of…
We consider the subgraph isomorphism problem where, given two graphs G (source graph) and F (pattern graph), one is to decide whether there is a (not necessarily induced) subgraph of G isomorphic to F. While many practical heuristic…