Related papers: Discriminating Non-Isomorphic Graphs with an Exper…

Quantum graphs are defined by having a Laplacian defined on the edges of a metric graph with boundary conditions on each vertex such that the resulting operator, $\mathbf{L}$, is self-adjoint. We use Neumann boundary conditions although we…

Quantum annealing was originally proposed as an approach for solving combinatorial optimisation problems using quantum effects. D-Wave Systems has released a production model of quantum annealing hardware. However, the inherent noise and…

Quantum annealing is a powerful tool for solving and approximating combinatorial optimization problems such as graph partitioning, community detection, centrality, routing problems, and more. In this paper we explore the use of quantum…

Quantum annealing provides a promising route for the development of quantum optimization devices, but the usefulness of such devices will be limited in part by the range of implementable problems as dictated by hardware constraints. To…

Relations of simulated annealing and quantum annealing are studied by a mapping from the transition matrix of classical Markovian dynamics of the Ising model to a quantum Hamiltonian and vice versa. It is shown that these two operators, the…

We propose a novel hybrid quantum-classical approach to calculate Graver bases, which have the potential to solve a variety of hard linear and non-linear integer programs, as they form a test set (optimality certificate) with very appealing…

Quantum devices are affected by intrinsic and environmental noises. An in-depth characterization of noise effects is essential for exploiting noisy quantum computing. To this end, we studied the energy dissipative behavior of a quantum…

Can neural networks learn to compare graphs without feature engineering? In this paper, we show that it is possible to learn representations for graph similarity with neither domain knowledge nor supervision (i.e.\ feature engineering or…

We investigate a quantum annealing approach based on real-time quantum dynamics for graph coloring. In this approach, a driving Hamiltonian is chosen so that constraints are naturally satisfied without penalty terms, and the dimension of…

By analyzing the characteristics of hardware-native Ising Models and their performance on current and next generation quantum annealers, we provide a framework for determining the prospect of advantage utilizing adiabatic evolution compared…

We investigate the graph isomorphism (GI) in some cospectral networks. Two graph are isomorphic when they are related to each other by a relabeling of the graph vertices. We want to investigate the GI in two scalable (n + 2)-regular graphs…

Graph Isomorphism is such an important problem in computer science, that it has been widely studied over the last decades. It is well known that it belongs to NP class, but is not NP-complete. It is thought to be of comparable difficulty to…

Recently, a Hamiltonian dynamics simulation was performed on a kicked ferromagnetic 2D transverse field Ising model with a connectivity graph native to the 127 qubit heavy-hex IBM Quantum architecture using ZNE quantum error mitigation. We…

We address the spatially nonlocal dielectric functions of graphene at any frequency derived starting fromthe first principles of thermal quantum field theory using the formalism of the polarization tensor. After a brief review of this…

The existence of non-isomorphic graphs which share the same Laplace spectrum (to be referred to as isospectral graphs) leads naturally to the following question: What additional information is required in order to resolve isospectral…

We show that non-abelian quantum statistics can be studied using certain topological invariants which are the homology groups of configuration spaces. In particular, we formulate a general framework for describing quantum statistics of…

Using a quantum processor to embed and process classical data enables the generation of correlations between variables that are inefficient to represent through classical computation. A fundamental question is whether these correlations…

Over 50 years ago, Lov\'{a}sz proved that two graphs are isomorphic if and only if they admit the same number of homomorphisms from any graph [Acta Math. Hungar. 18 (1967), pp. 321--328]. In this work we prove that two graphs are quantum…

Quantum computers use quantum resources to carry out computational tasks and may outperform classical computers in solving certain computational problems. Special-purpose quantum computers such as quantum annealers employ quantum adiabatic…

Boltzmann machine is a powerful machine learning model with many real-world applications, for example by constructing deep belief networks. Statistical inference on a Boltzmann machine can be carried out by sampling from its posterior…