Related papers: Partitioning technique for a discrete quantum syst…
We present multiscale graph-based reduction algorithms for upscaling heterogeneous and anisotropic diffusion problems. The proposed coarsening approaches begin by constructing a partitioning of the computational domain into a set of…
Building large-scale quantum computers, essential to demonstrating quantum advantage, is a key challenge. Quantum Networks (QNs) can help address this challenge by enabling the construction of large, robust, and more capable quantum…
The quantum approximate optimization algorithm (QAOA) holds promise for combinatorial optimization but is constrained by limited qubits. While divide-and-conquer frameworks like QAOA$^{2}$ address scalability by partitioning graphs into…
Given a connected undirected weighted graph, we are concerned with problems related to partitioning the graph. First of all we look for the closest disconnected graph (the minimum cut problem), here with respect to the Euclidean norm. We…
We present an alternative application of discrete Morse theory for two-particle graph configuration spaces. In contrast to previous constructions, which are based on discrete Morse vector fields, our approach is through Morse functions,…
We consider finite quantum systems defined by a mixed set of commutation and anti-commutation relations between components of the Hamiltonian operator. These relations are represented by an anti-commutativity graph which contains a…
In this paper we present a unifying geometric and compositional framework for modeling complex physical network dynamics as port-Hamiltonian systems on open graphs. Basic idea is to associate with the incidence matrix of the graph a Dirac…
On neutral atom platforms, preparing specific quantum states is usually achieved by pulse shaping, i.e., by optimizing the time-dependence of the Hamiltonian related to the system. This process can be extremely costly, as it requires…
The ability to reliably distribute entanglement among the nodes of a network is an essential requirement for the development of effective quantum communication protocols and the realization of useful quantum networks. It has been…
This is a continuation of the work initiated in a previous paper on so-called driven cofactor systems, which are partially decoupling second-order differential equations of a special kind. The main purpose in that paper was to obtain an…
The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum system and phenomenon. However, for interacting many-body quantum systems, its…
We present a unified and simple method for deriving work theorems for classical and quantum Hamiltonian systems, both under equilibrium conditions and in a steady state. Throughout the paper, we adopt the partitioning of the total…
A generic procedure is proposed to construct many-body quantum Hamiltonians with partial dynamical symmetry. It is based on a tensor decomposition of the Hamiltonian and allows the construction of a hierarchy of interactions that have…
We discuss encodings of fermionic many-body systems by qubits in the presence of symmetries. Such encodings eliminate redundant degrees of freedom in a way that preserves a simple structure of the system Hamiltonian enabling quantum…
Graph partitioning (GP) and vertex connectivity have traditionally been two distinct fields of study. This paper introduces the highly connected graph partitioning (HCGP) problem, which partitions a graph into compact, size balanced, and…
We develop a quantum model based on the correspondence between energy distribution between harmonic oscillators and the partition of an integer number. A proper choice of the interaction Hamiltonian acting within this manifold of states…
Partitioning is a fundamental challenge for non-centralized control of large-scale systems, such as hierarchical, decentralized, distributed, and coalitional strategies. The problem consists of finding a decomposition of a network of…
Hypergraph partitioning is a recurring NP-hard problem in engineering; its efficient solution at scale hinges on parallelism. This work proposes a GPU-centric algorithm for multi-level hypergraph partitioning aimed at a specific set of…
We provide an explicit recursive divide and conquer approach for simulating quantum dynamics and derive a discrete first quantized non-relativistic QED Hamiltonian based on the many-particle Pauli Fierz Hamiltonian. We apply this recursive…
In this paper, we develop an optimization-based systematic approach for the challenging, less studied, and important problem of optimal partitioning of multi-thermal zone buildings for the decentralized control. The proposed method consists…