Related papers: Linked Cluster Expansions via Hypergraph Decomposi…
The nonintegrable transverse-field Ising model is a common platform for studying ergodic quantum dynamics. In this work, we introduce a simple variant of the model in which this ergodic behaviour is suppressed by introducing a spatial…
Tensor network contraction on arbitrary graphs is a fundamental computational challenge with applications ranging from quantum simulation to error correction. While belief propagation (BP) provides a powerful approximation algorithm for…
Hypergraphs are powerful mathematical structures that can model complex, high-order relationships in various domains, including social networks, bioinformatics, and recommender systems. However, generating realistic and diverse hypergraphs…
Hypergraph states are multiqubit states whose combinatorial description and entanglement properties generalize the well-studied class of graph states. Graph states are important in applications such as measurement-based quantum computation…
Graphical models for finite-dimensional spin glasses and real-world combinatorial optimization and satisfaction problems usually have an abundant number of short loops. The cluster variation method and its extension, the region graph…
Hypergraphs offer a generalized framework for understanding complex systems, covering group interactions of different orders beyond traditional pairwise interactions. This modelling allows for the simplified description of simultaneous…
Graph clustering is a longstanding research topic, and has achieved remarkable success with the deep learning methods in recent years. Nevertheless, we observe that several important issues largely remain open. On the one hand, graph…
The scaling of entanglement entropy for the nearest neighbor antiferromagnetic Heisenberg spin model is studied computationally for clusters joined by a single bond. Bisecting the balanced three legged Bethe Cluster, gives a second Renyi…
Many complex systems involve direct interactions among more than two entities and can be represented by hypergraphs, in which hyperedges encode higher-order interactions among an arbitrary number of nodes. To analyze structures and dynamics…
We develop a systematic cluster expansion for dilute systems in the highly dilute phase. We first apply it to the calculation of the entropy of the K-satisfiability problem in the satisfiable phase. We derive a series expansion in the…
Percolation theory dictates an intuitive picture depicting correlated regions in complex systems as densely connected clusters. While this picture might be adequate at small scales and apart from criticality, we show that highly correlated…
A full coupled-cluster expansion suitable for sparse algebraic operations is developed by expanding the commutators of the Baker-Campbell-Hausdorff series explicitly for cluster operators in binary representations. A full coupled-cluster…
The success of a quantum annealing algorithm requires a polynomial scaling of the energy gap. Recently it was shown that a two-dimensional transverse-field Ising model on a square lattice with nearest-neighbor $\pm J$ random coupling has a…
A two-replica graphical representation and associated cluster algorithm is described that is applicable to ferromagnetic Ising systems with arbitrary fields. Critical points are associated with the percolation threshold of the graphical…
Many networked systems are governed by non-pairwise interactions between nodes. The resulting higher-order interaction structure can then be encoded by means of a hypernetwork. In this paper we consider dynamical systems on hypernetworks by…
Graphs are one of the most important data structures for representing pairwise relations between objects. Specifically, a graph embedded in a Euclidean space is essential to solving real problems, such as physical simulations. A crucial…
A new approximate scheme, DSUB$m$, is described for the coupled cluster method. We then apply it to two well-studied (spin-1/2 Heisenberg antiferromagnet) spin-lattice models, namely: the $XXZ$ and the $XY$ models on the square lattice in…
Spin network states are a powerful tool for constructing the $SU(2)$ gauge theories on a graph. In loop quantum gravity (LQG), they have yielded many promising predictions, although progress has been limited by the computational challenge…
We develop an algebraic and operational framework for quantum isomorphisms of hypergraphs, using tools from compact quantum group theory. We introduce a new synchronous version of the hypergraph isomorphism game whose game algebra uniformly…
Looped Transformers have shown exceptional neural algorithmic reasoning capability in simulating traditional graph algorithms, but their application to more complex structures like hypergraphs remains underexplored. Hypergraphs generalize…