Related papers: Clustering in Hilbert space of a quantum optimizat…
We study Hilbert space fragmentation and quantum scars in quantum spin systems with Ising interactions. The system consists of two sets of quantum spins, A and B. As the parent system, set A is an Ising model on arbitrary lattices with a…
We present a framework that formulates the quest for the most efficient quantum state tomography scheme as an optimization problem which can be solved numerically. This approach can be applied to a broad spectrum of relevant setups…
This PhD thesis explores the potential of quantum computing to address computational challenges in high-energy physics (HEP). As the Standard Model (SM) leaves key questions unanswered and no signs of new physics have emerged since the…
It is demonstrated that almost any S-matrix of quantum field theory in curved spaces posses an infinite set of complex poles (or branch cuts). These poles can be transformed into complex eigenvalues, the corresponding eigenvectors being…
The practical application of quantum technologies to chemical problems faces significant challenges, particularly in the treatment of realistic basis sets and the accurate inclusion of electron correlation effects. A direct approach to…
Given a set of vectors $\F=\{f_1,\dots,f_m\}$ in a Hilbert space $\HH$, and given a family $\CC$ of closed subspaces of $\HH$, the {\it subspace clustering problem} consists in finding a union of subspaces in $\CC$ that best approximates…
A quantum eigensolver is designed under a multi-layer cluster mean-field (CMF) algorithm by partitioning a quantum system into spatially-separated clusters. For each cluster, a reduced Hamiltonian is obtained after a partial average over…
Alongside the effort underway to build quantum computers, it is important to better understand which classes of problems they will find easy and which others even they will find intractable. We study random ensembles of the QMA$_1$-complete…
The open quantum system eigenstate in the vicinity of low-energy decay channel may mimic its features, in particular the characteristic clustering properties of the decay channel. This generic mechanism of clusterization, the so-called…
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
We study hierarchical clusterings of metric spaces that change over time. This is a natural geometric primitive for the analysis of dynamic data sets. Specifically, we introduce and study the problem of finding a temporally coherent…
Determining ground state energies of quantum systems by hybrid classical/quantum methods has emerged as a promising candidate application for near-term quantum computational resources. Short of large-scale fault-tolerant quantum computers,…
Clustering is one of the most fundamental tasks in machine learning, and the k-means clustering algorithm is perhaps one of the most widely used clustering algorithms. However, it suffers from several limitations, such as sensitivity to…
Structure in quantum entanglement entropy is often leveraged to focus on a small corner of the exponentially large Hilbert space and efficiently parameterize the problem of finding ground states. A typical example is the use of matrix…
Finding the ground state of Ising spin glasses is notoriously difficult due to disorder and frustration. Often, this challenge is framed as a combinatorial optimization problem, for which a common strategy employs simulated annealing, a…
The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced $k$-center, $k$-median, and $k$-means clustering problems where the size of each cluster is constrained by…
We study the question of how to decompose Hilbert space into a preferred tensor-product factorization without any pre-existing structure other than a Hamiltonian operator, in particular the case of a bipartite decomposition into "system"…
We consider a quantum system with a finite number of distinguishable quantum states, which may be partitioned freely by a number of quantum particles, assumed to be maximally entangled. We show that if we partition the system into a number…
Quantum cluster theories are a set of approaches for the theory of correlated and disordered lattice systems, which treat correlations within the cluster explicitly, and correlations at longer length scales either perturbatively or within a…
Decoherence and einselection have been effective in explaining several features of an emergent classical world from an underlying quantum theory. However, the theory assumes a particular factorization of the global Hilbert space into…