Related papers: Spectral Projections for Density Matrices in Quant…
We derive simple and unified closed-form expressions for projections with respect to fidelity (equivalently, the Bures and purified distances) onto several sets of interest. These include projections of bipartite positive semidefinite (PSD)…
We propose new quantum algorithms for estimating spectral sums of positive semi-definite (PSD) matrices. The spectral sum of an PSD matrix $A$, for a function $f$, is defined as $ \text{Tr}[f(A)] = \sum_j f(\lambda_j)$, where $\lambda_j$…
We propose a novel projection-based particle method for solving the McKean-Vlasov stochastic differential equations. Our approach is based on a projection-type estimation of the marginal density of the solution in each time step. The…
In quantum mechanics, predictions are made by way of calculating expectation values of observables, which take the form of Hermitian operators. It is far less common to exploit non-Hermitian operators to perform measurements. Here, we show…
We present a novel analytical method for calculating the spectral function and the density of states in speckle potentials, valid in the semiclassical regime. Our approach relies on stationary phase approximations, allowing us to describe…
There is an increasing body of work exploring the integration of random projection into algorithms for numerical linear algebra. The primary motivation is to reduce the overall computational cost of processing large datasets. A suitably…
This review elaborates on the foundation, the advantages, and the prospects of tensor network representations for quantum states in vibrational spectroscopy. The focus is on the recently introduced matrix product state decomposition of…
We present a subspace projection technique to conduct large-scale Kohn-Sham density functional theory calculations using spectral finite-element discretization. The proposed method treats both metallic and insulating materials in a single…
We compute the spectral statistics of the sum H of two independent complex Wishart matrices, each of which is correlated with a different covariance matrix. Random matrix theory enjoys many applications including sums and products of random…
We review the problem of how to compute the spectral density of sparse symmetric random matrices, i.e. weighted adjacency matrices of undirected graphs. Starting from the Edwards-Jones formula, we illustrate the milestones of this line of…
Quantum entanglement plays a crucial role in quantum information, quantum teleportation and quantum computation. The information about the entanglement content between subsystems of the composite system is encoded in the Schmidt…
Modeling joint probability distributions over sequences has been studied from many perspectives. The physics community developed matrix product states, a tensor-train decomposition for probabilistic modeling, motivated by the need to…
We present a spectral scheme for atomic structure calculations in pseudopotential Kohn-Sham density functional theory. In particular, after applying an exponential transformation of the radial coordinates, we employ global polynomial…
We provide a new approach to open quantum systems which is based on the Feshbach projection method in an appropriate Hilbert space. Instead of looking for a master equation for the dynamical map acting in the space of density operators we…
In this survey the possible approaches to the description of the evolution of states of quantum many-particle systems by means of the possible modifications of the density operator which kernel known as density matrix are considered. In…
This thesis studies matrix field theories, which are a special type of matrix models. First, the different types of applications are pointed out, from (noncommutative) quantum field theory over 2-dimensional quantum gravity up to algebraic…
By applying the projector to the filled lattice eigenstates on a specific position, or applying the local electron annihilation operator on the many-body ground state, one can construct a quantum state localized around a specific position…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…
Sketch-and-project is a framework which unifies many known iterative methods for solving linear systems and their variants, as well as further extensions to non-linear optimization problems. It includes popular methods such as randomized…