Related papers: A BQP-complete problem related to the Ising model …
We propose a generic framework to describe classical Ising-like models defined on arbitrary graphs. The energy spectrum is shown to be the Hadamard transform of a suitably defined sparse "coding" vector associated with the graph. We expect…
The primary objective of this paper is to present an exact and general procedure for mapping any sequence of quantum gates onto a network of probabilistic p-bits which can take on one of two values 0 and 1. The first $n$ p-bits represent…
We give a recursion formula to generate all equivalence classes of biconnected graphs with coefficients given by the inverses of the orders of their groups of automorphisms. We give a linear map to produce a connected graph with say, u,…
We show that there exist efficient algorithms for the triangle packing problem in colored permutation graphs, complete multipartite graphs, distance-hereditary graphs, k-modular permutation graphs and complements of k-partite graphs (when k…
We give an FPTAS for approximating the partition function of the hard-core model for bipartite graphs when there is sufficient imbalance in the degrees or fugacities between the sides $(L,R)$ of the bipartition. This includes, among others,…
We consider weighted tiling systems to represent functions from graphs to a commutative semiring such as the Natural semiring or the Tropical semiring. The system labels the nodes of a graph by its states, and checks if the neighbourhood of…
Many promising applications of quantum computing with a provable speedup center around the HHL algorithm. Due to restrictions on the hardware and its significant demand on qubits and gates in known implementations, its execution is…
Multipartite entanglement, linking multiple nodes simultaneously, is a higher-order correlation that offers advantages over pairwise connections in quantum networks (QNs). Creating reliable, large-scale multipartite entanglement requires…
In $k$-hypergraph matching, we are given a collection of sets of size at most $k$, each with an associated weight, and we seek a maximum-weight subcollection whose sets are pairwise disjoint. More generally, in $k$-hypergraph $b$-matching,…
Quantum computing holds immense potential for solving classically intractable problems by leveraging the unique properties of quantum mechanics. The scalability of quantum architectures remains a significant challenge. Multi-core quantum…
We give algorithms for approximating the partition function of the ferromagnetic $q$-color Potts model on graphs of maximum degree $d$. Our primary contribution is a fully polynomial-time approximation scheme for $d$-regular graphs with an…
The zero-field partition function of two-dimensional nearest neighbor Ising models of square lattices is derived in terms of the generalized hypergeometric series by evaluating the integral in the exact solution of Onsager. An approximate…
Quantum computer architectures impose restrictions on qubit interactions. We propose efficient circuit transformations that modify a given quantum circuit to fit an architecture, allowing for any initial and final mapping of circuit qubits…
We evaluate using programmable superconducting flux qubit D-Wave quantum annealers to approximate the partition function of Ising models. We propose the use of two distinct quantum annealer sampling methods: chains of Monte Carlo-like…
We present the reduction of the correlation functions of the Ising model on the anisotropic square lattice to complete elliptic integrals of the first, second and third kind, the extension of Kramers-Wannier duality to anisotropic…
We introduce a method for solving the Max-Cut problem using a variational algorithm and a continuous-variables quantum computing approach. The quantum circuit consists of two parts: the first one embeds a graph into a circuit using the…
In a recent preprint by Deutsch et al. [1995] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on $n$ qubits by 2-qubit unitary operations. We address that comment by proving strong lower…
Answering complex logical queries on incomplete knowledge graphs (KGs) with missing edges is a fundamental and important task for knowledge graph reasoning. The query embedding method is proposed to answer these queries by jointly encoding…
Given a property (graph class) $\Pi$, a graph $G$, and an integer $k$, the \emph{$\Pi$-completion} problem consists in deciding whether we can turn $G$ into a graph with the property $\Pi$ by adding at most $k$ edges to $G$. The…
Given an undirected graph $G(V, E)$, it is well known that partitioning a graph $G$ into $q$ connected subgraphs of equal or specificed sizes is in general NP-hard problem. On the other hand, it has been shown that the q-partition problem…