Related papers: Clustering in Hilbert space of a quantum optimizat…
Clustering is a fundamental task in data science that aims to group data based on their similarities. However, defining similarity is often ambiguous, making it challenging to determine the most appropriate objective function for a given…
Is the dynamical evolution of physical systems objectively a manifestation of information processing by the universe? We find that an affirmative answer has important consequences for the measurement problem. In particular, we calculate the…
We present a complete classification of the geometry of the mutually complementary sets of entangled and separable states in three-dimensional Hilbert subspaces of bipartite and multipartite quantum systems. Our analysis begins by finding…
In the NISQ-era of quantum computing, we should not expect to see quantum devices that provide an exponential improvement in runtime for practical problems, due to the lack of error correction and small number of qubits available.…
We study the low energy states of finite spin chains with isotropic (Heisenberg) and anisotropic (XY and Ising-like) exchange interaction with uniform and non-uniform coupling constants. We show that for an odd number of sites a spin…
We consider the problem of center-based clustering in low-dimensional Euclidean spaces under the perturbation stability assumption. An instance is $\alpha$-stable if the underlying optimal clustering continues to remain optimal even when…
We theoretically explore quantum correlation properties of a dissipative Bose-Hubbard dimer in presence of a coherent drive. In particular, we focus on the regime where the semiclassical theory predicts a bifurcation with a spontaneous…
We introduce a self-consistent mean-field quantum optimization algorithm that approximates the ground state of classical Ising Hamiltonians. The algorithm decomposes the problem into independent subproblems and treats the interactions…
Entanglement entropy is a fundamental diagnostic for quantum chaos, typically exhibiting volume-law scaling in highly excited eigenstates of chaotic many-body systems. In this work, we present a striking counterexample: a Floquet-driven…
This article reviews and extends recent results concerning entanglement and frustration in multipartite systems which have some symmetry with respect to the ordering of the particles. Starting point of the discussion are Bell inequalities:…
We present a technique to coarse-grain quantum states in a finite-dimensional Hilbert space. Our method is distinguished from other approaches by not relying on structures such as a preferred factorization of Hilbert space or a preferred…
We consider the problem of subspace clustering: given points that lie on or near the union of many low-dimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses…
Product states, unentangled tensor products of single qubits, are a ubiquitous ansatz in quantum computation, including for state-of-the-art Hamiltonian approximation algorithms. A natural question is whether we should expect to efficiently…
The hardness to solve an unstructured quantum search problem by a standard quantum search algorithm mainly originates from the low efficiency to amplify the amplitude of the marked state by the oracle unitary operation associated with other…
Medium-scale ensembles of coupled qubits offer a platform for near-term quantum technologies including computing, sensing, and the study of mesoscopic quantum systems. Atom-like emitters in solids have emerged as promising quantum memories,…
Clustering is one of the most fundamental problems in data analysis and it has been studied extensively in the literature. Though many clustering algorithms have been proposed, clustering theories that justify the use of these clustering…
Random instances of Constraint Satisfaction Problems (CSP's) appear to be hard for all known algorithms, when the number of constraints per variable lies in a certain interval. Contributing to the general understanding of the structure of…
We propose an improved variant of the third-quantization scheme, for the spatially homogeneous and isotropic cosmological models in Einstein gravity coupled with a neutral massless scalar field. Our strategy is to specify a semi-Riemannian…
Quantum computation is frequently mischaracterized as the simultaneous execution of exponentially many classical computations. This article offers a conceptual clarification of why this ``branchwise parallelism'' picture is misleading,…
It has been recently shown that small subsystems of finite quantum systems generically equilibrate. We extend these results to infinite-dimensional Hilbert spaces of field theories and matrix models. We consider a quench setup, where…