Related papers: Solving a Nonlinear Eigenvalue Equation in Quantum…
We study the entanglement properties of a higher-integer-spin Affleck-Kennedy-Lieb-Tasaki model with quantum group symmetry in the periodic boundary condition. We exactly calculate the finite size correction terms of the entanglement…
Quantum entanglement is a particularly useful characterization of topological orders which lack conventional order parameters. In this work, we study the entanglement in topologically ordered states between two arbitrary spatial regions,…
We consider eigenvalue condition numbers and backward errors for a class of symmetric nonlinear eigenvalue problems with eigenvector nonlinearities. For both of these quantities, we derive explicit and computable expressions that can be…
We develop a numerical methodology for the computation of entanglement measures for mixed quantum states. Using the well-known Schr\"odinger-HJW theorem, the computation of convex roof entanglement measures is reframed as a search for…
Solving a quadratic nonlinear system of equations (QNSE) is a fundamental, but important, task in nonlinear science. We propose an efficient quantum algorithm for solving $n$-dimensional QNSE. Our algorithm embeds QNSE into a…
Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…
A remarkable extension of Rayleigh-Schroedinger perturbation method is found. Its (N+q) x (N+1) - dimensional Hamiltonians (as emerging, e.g., during quasi-exact constructions of bound states) are non-square matrices at q > 1. The role of…
Entanglement is one of the key resources of quantum information science which makes identification of entangled states essential to a wide range of quantum technologies and phenomena. This problem is however both computationally and…
A number of authors have suggested that nonlinear interactions can enhance resolution of phase shifts beyond the usual Heisenberg scaling of 1/n, where n is a measure of resources such as the number of subsystems of the probe state or the…
Quantum visual computing is advancing rapidly. This paper presents a new formulation for stereo matching with nonlinear regularizers and spatial pyramids on quantum annealers as a maximum a posteriori inference problem that minimizes the…
In recent years, artificial neural networks (ANNs) have become an increasingly popular tool for studying problems in quantum theory, and in particular entanglement theory. In this work, we analyse to what extent ANNs can accurately predict…
Any pure three-qubit state is uniquely characterized by one phase and four positive parameters. The geometric measure of entanglement as a function of state parameters can have different expressions. Each of expressions has its own…
In this chapter we are examining several iterative methods for solving nonlinear eigenvalue problems. These arise in variational image-processing, graph partition and classification, nonlinear physics and more. The canonical eigenproblem we…
Accurately solving the Schr\"odinger equation remains a central challenge in computational physics, chemistry, and materials science. Here, we propose an alternative eigenvalue problem based on a system's autocorrelation function, avoiding…
Studies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared to product states. In this paper, we quantify the metrological advantage of entanglement in a setting…
Contour integral methods for nonlinear eigenvalue problems seek to compute a subset of the spectrum in a bounded region of the complex plane. We briefly survey this class of algorithms, establishing a relationship to system realization…
We solve the eigenvalue problem of the five-qubit anisotropic Heisenberg model, without use of Bethe's Ansatz, and give analytical results for entanglement and mixedness of two nearest-neighbor qubits. The entanglement takes its maximum at…
Electronic ground states are of central importance in chemical simulations, but have remained beyond the reach of efficient classical algorithms except in cases of weak electron correlation or one-dimensional spatial geometry. We introduce…
In the broad range of studies related to quantum graphs, quantum graph spectra appear as a topic of special interest. They are important in the context of diffusion type problems posed on metric graphs. Theoretical findings suggest that…
In this article, we introduce a framework for entanglement characterization by time-resolved single-photon counting with measurement operators defined in the time domain. For a quantum system with unitary dynamics, we generate…