Related papers: Bootstrapping Simple QM Systems
We report multipronged progress on the stochastic averaging approach to numerical analytic continuation of quantum Monte Carlo data. With the sampled spectrum parametrized with delta-functions in continuous frequency space, a calculation of…
We review a recent approach for the simulation of many-body interacting systems based on an efficient generalization of the Lanczos method for Quantum Monte Carlo simulations. This technique allows to perform systematic corrections to a…
We introduce a bootstrap procedure for high-frequency statistics of Brownian semistationary processes. More specifically, we focus on a hypothesis test on the roughness of sample paths of Brownian semistationary processes, which uses an…
We present a Kolmogorov-like algorithm for the computation of a normal form in the neighborhood of an invariant torus in `isochronous' Hamiltonian systems, i.e., systems with Hamiltonians of the form $\mathcal{H}=\mathcal{H}_0+\varepsilon…
We consider a quantum system consisting of a one-dimensional chain of M identical harmonic oscillators with natural frequency $\omega$, coupled by means of springs. Such systems have been studied before, and appear in various models. In…
We present an efficient numerical method for simulating the low-energy properties of disordered many-particle systems. The method which is based on the quantum-chemical configuration interaction approach consists in diagonalizing the…
There is an increasing amount of literature focused on Bayesian computational methods to address problems with intractable likelihood. One approach is a set of algorithms known as Approximate Bayesian Computational (ABC) methods. One of the…
The bootstrap is a foundational tool in statistical inference, but its classical implementation relies on Monte Carlo resampling, introducing approximation error and incurring high computational cost -- especially for large datasets and…
Characterizing noisy quantum devices requires methods for learning the underlying quantum Hamiltonian which governs their dynamics. Often, such methods compare measurements to simulations of candidate Hamiltonians, a task which requires…
We develop a computational method to learn a molecular Hamiltonian matrix from matrix-valued time series of the electron density. As we demonstrate for three small molecules, the resulting Hamiltonians can be used for electron density…
There are some papers which describe the use of bootstrap techniques in point process statistics. The aim of the present paper is to show that the form in which bootstrap is used there is dubious. In case of variance estimation of pair…
The paper intends to lay out the first steps towards constructing a unified framework to understand the symplectic and spectral theory of finite dimensional integrable Hamiltonian systems. While it is difficult to know what the best…
The Fourier series method is used to solve the homogeneous equation governing the motion of the harmonic oscillator. It is shown that the general solution to the problem can be found in a surprisingly simple way for the case of the simple…
Integrability is a cornerstone of classical mechanics, where it has a precise meaning. Extending this notion to quantum systems, however, remains subtle and unresolved. In particular, deciding whether a quantum Hamiltonian - viewed simply…
Quantum computing architectures require an accurate and efficient description in terms of many-electron states. Recent implementations include quantum dot arrays, where the ground state of a multi q-bit system can be altered by voltages…
Multiple systems estimation using a Poisson loglinear model is a standard approach to quantifying hidden populations where data sources are based on lists of known cases. Information criteria are often used for selecting between the large…
Much research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians with Hamming symmetric potentials, such as the well studied "spike" example. Due to the large amount of symmetry in these potentials such problems…
We develop a method to determine the eigenvalues and eigenfunctions of two-boson Hamiltonians include a wide class of quantum optical models. The quantum Hamiltonians have been transformed in the form of the one variable differential…
The tight-binding model of quantum particles on a honeycomb lattice is investigated in the presence of homogeneous magnetic field. Provided the magnetic flux per unit hexagon is rational of the elementary flux, the one-particle Hamiltonian…
High control in the preparation and manipulation of states is an experimental and theoretical important task in many quantum protocols. Shortcuts to adiabaticity methods allow to obtain desirable states of a adiabatic dynamics but in short…