Related papers: On estimates for the discrete eigenvalues of two-d…
For bound states of atoms and molecules of $N$ electrons we consider the corresponding $K$-particle reduced density matrices, $\Gamma^{(K)}$, for $1 \le K \le N-1$. Previously, eigenvalue bounds were obtained in the case of $K=1$ and…
In this article we initiate the study of 1+ 2 dimensional wave maps on a curved spacetime in the low regularity setting. Our main result asserts that in this context the wave maps equation is locally well-posed at almost critical…
Various benchmarking metrics have been developed to quantify the performance of quantum computing hardware and help evaluate development. However, it is not always necessary to know the metric values precisely. This is especially true for…
In the first part of these notes, we review some of the recent developments in the study of the spectral properties of Wigner matrices. In the second part, we present a new proof of a Wegner estimate for the eigenvalues of a large class of…
We study the spectrum of the linearization around standing wave profiles for two quantum hydrodynamics systems with linear and nonlinear viscosity. The essential spectrum for such profiles is stable; we investigate the point spectrum using…
On a $2m$-dimensional closed manifold we investigate the existence of prescribed $Q$-curvature metrics with conical singularities. We present here a general existence and multiplicity result in the supercritical regime. To this end, we…
We study essentially bounded quantum random variables and show that the Gelfand spectrum of such a quantum random variable coincides with the hypoconvex hull of its essential range. Moreover, a notion of operator-valued variance is…
Estimating the overlap between an approximate wavefunction and a target eigenstate of the system Hamiltonian is essential for the efficiency of quantum phase estimation. In this work, we derive upper and lower bounds on this overlap using…
In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum…
We derive an optimal eigenvalue ratio estimate for finite weighted graphs satisfying the curvature-dimension inequality $CD(0,\infty)$. This estimate is independent of the size of the graph and provides a general method to obtain higher…
Estimating the eigenvalues of non-normal matrices is a foundational problem with far-reaching implications, from modeling non-Hermitian quantum systems to analyzing complex fluid dynamics. Yet, this task remains beyond the reach of standard…
We investigate the problem of determining the parameters that describe a quantum channel. It is assumed that the users of the channel have at best only partial knowledge of it and make use of a finite amount of resources to estimate it. We…
The Dirichlet p-Laplacian in tubes of arbitrary cross-section along infinite curves in Euclidean spaces of arbitrary dimension is investigated. First, it is shown that the gap between the lowest point of the generalised spectrum and the…
We prove quadratic eigenvalue perturbation bounds for generalized Hermitian eigenvalue problems. The bounds are proportional to the square of the norm of the perturbation matrices divided by the gap between the spectrums. Using the results…
By means of a suitable rational approximation to the logarithmic derivative of the wavefunction we obtain tight upper and lower bounds to the eigenvalues and critical parameters of the quartic double-well potential.
In this Near Intermediate-Scale Quantum era, there are two types of near-term quantum devices available on cloud: superconducting quantum processing units (QPUs) based on the discrete variable model and linear optics (photonics) QPUs based…
In this paper, we investigate universal estimates for eigenvalues of a buckling problem. For a bounded domain in a Euclidean space, we give a positive contribution for obtaining a sharp universal inequality for eigenvalues of the buckling…
We present a new method for quantum state tomography within a single-excitation subspace of two-qubit states in an open waveguide. The system under investigation consists of three qubits in an open waveguide, separated by a distance…
This article is a brief introduction to quantum algorithms for the eigenvalue problem in quantum many-body systems. Rather than a broad survey of topics, we focus on providing a conceptual understanding of several quantum algorithms that…
We determine the ultimate potential of quantum imaging for boosting the resolution of a far-field, diffraction-limited, linear imaging device within the paraxial approximation. First we show that the problem of estimating the separation…