相关论文: Efficient Diagonalization of Kicked Quantum System…
An entirely quantum mechanical approach to diagonalize hermitean matrices has been presented recently. Here, the genuinely quantum mechanical approach is considered in detail for (2x2) matrices. The method is based on the measurement of…
In this paper, building on a previous analysis [1] of exact diagonalization of the space-discretized evolution operator for the study of properties of non-relativistic quantum systems, we present a substantial improvement to this method. We…
The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting…
The time-evolution operator for the kicked Harper model is reduced to block matrix form when the effective Planck's constant hbar = 2 pi M/N and M and N are integers. Each block matrix is spanned by an orthonormal set of N "kq"…
Numerical linked-cluster expansions allow one to calculate finite-temperature properties of quantum lattice models directly in the thermodynamic limit through exact solutions of small clusters. However, full diagonalization is often the…
An application of an effective numerical algorithm for solving eigenvalue problems which arise in modelling electronic properties of quantum disordered systems is considered. We study the electron states at the localization-delocalization…
A semi-infinite weighted Hankel matrix with entries defined in terms of basic hypergeometric series is explicitly diagonalized as an operator on $\ell^{2}(\mathbb{N}_{0})$. The approach uses the fact that the operator commutes with a…
In this paper we study the lattice quasi-periodic operators with power-law long-range hopping and meromorphic monotone potentials, and diagonalize the operators via a Nash-Moser iteration scheme. As applications, we obtain uniform power-law…
We show constructively that, under certain regularity assumptions, any system of coupled linear differential equations with variable coefficients can be tridiagonalized by a time-dependent Lanczos-like method. The proof we present formally…
Dimer decimation scheme is introduced in order to study the kicked quantum systems exhibiting localization transition. The tight-binding representation of the model is mapped to a vectorized dimer where an asymptotic dissociation of the…
A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…
We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are…
We present a method for the explicit diagonalization of some Hankel operators. This method allows us to recover classical results on the diagonalization of Hankel operators with the absolutely continuous spectrum. It leads also to new…
Many standard conversion matrices between coefficients in classical orthogonal polynomial expansions can be decomposed using diagonally-scaled Hadamard products involving Toeplitz and Hankel matrices. This allows us to derive…
We analyze the method for calculation of properties of non-relativistic quantum systems based on exact diagonalization of space-discretized short-time evolution operators. In this paper we present a detailed analysis of the errors…
In many problems in Computational Physics and Chemistry, one finds a special kind of sparse matrices, termed "banded matrices". These matrices, which are defined as having non-zero entries only within a given distance from the main…
We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements, {\em without restricting to variational ansatzes}. The lattice of size $N$ is partitioned into two subclusters. At…
We describe a series of algorithms that efficiently implement Gaussian model-X knockoffs to control the false discovery rate on large scale feature selection problems. Identifying the knockoff distribution requires solving a large scale…
We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…
Presented here is a matrix inversion method utilizing quantum searching algorithm. In this method, huge Hilbert space as a whole spanned by myriad of eigen states is searched and evaluated efficiently by sequential reduction in dimension…