Gaussian-process-regression-based method for the localization of
exceptional points in complex resonance spectra
- URL: http://arxiv.org/abs/2402.05972v1
- Date: Wed, 7 Feb 2024 09:03:26 GMT
- Title: Gaussian-process-regression-based method for the localization of
exceptional points in complex resonance spectra
- Authors: Patrick Egenlauf, Patric Rommel, J\"org Main
- Abstract summary: We introduce an efficient machine learning algorithm to find exceptional points based on Gaussian process regression (GPR)
The GPR-based method is developed and tested on a simple low-dimensional matrix model and then applied to a challenging real physical system.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: Resonances in open quantum systems depending on at least two controllable
parameters can show the phenomenon of exceptional points (EPs), where not only
the eigenvalues but also the eigenvectors of two or more resonances coalesce.
Their exact localization in the parameter space is challenging, in particular
in systems, where the computation of the quantum spectra and resonances is
numerically very expensive. We introduce an efficient machine learning
algorithm to find exceptional points based on Gaussian process regression
(GPR). The GPR-model is trained with an initial set of eigenvalue pairs
belonging to an EP and used for a first estimation of the EP position via a
numerically cheap root search. The estimate is then improved iteratively by
adding selected exact eigenvalue pairs as training points to the GPR-model. The
GPR-based method is developed and tested on a simple low-dimensional matrix
model and then applied to a challenging real physical system, viz., the
localization of EPs in the resonance spectra of excitons in cuprous oxide in
external electric and magnetic fields. The precise computation of EPs, by
taking into account the complete valence band structure and central-cell
corrections of the crystal, can be the basis for the experimental observation
of EPs in this system.
Related papers
- Regularized relativistic corrections for polyelectronic and polyatomic systems with explicitly correlated Gaussians [0.0]
Drachmann's regularization approach is implemented for floating explicitly correlated Gaussians (fECGs) and molecular systems.
The numerical approach is found to be precise and robust over a range of molecular systems and nuclear configurations.
arXiv Detail & Related papers (2024-04-09T06:29:17Z) - Dawn and fall of non-Gaussianity in the quantum parametric oscillator [0.0]
We study the emergence of non-Gaussianity in the single quantum OPO with an applied external field.
Our findings reveal a nontrivial interplay between parametric drive and applied field.
arXiv Detail & Related papers (2023-12-27T11:20:13Z) - Eigenvalue sensitivity from eigenstate geometry near and beyond
arbitrary-order exceptional points [0.0]
Systems with an effectively non-Hermitian Hamiltonian display an enhanced sensitivity to parametric and dynamic perturbations.
This sensitivity can be quantified by the phase rigidity, which mathematically corresponds to the eigenvalue condition number.
I derive an exact nonperturbative expression for this sensitivity measure that applies to arbitrary eigenvalue configurations.
arXiv Detail & Related papers (2023-07-12T16:36:39Z) - On optimization of coherent and incoherent controls for two-level
quantum systems [77.34726150561087]
This article considers some control problems for closed and open two-level quantum systems.
The closed system's dynamics is governed by the Schr"odinger equation with coherent control.
The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation.
arXiv Detail & Related papers (2022-05-05T09:08:03Z) - Numerical Simulations of Noisy Quantum Circuits for Computational
Chemistry [51.827942608832025]
Near-term quantum computers can calculate the ground-state properties of small molecules.
We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
arXiv Detail & Related papers (2021-12-31T16:33:10Z) - Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity.
For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles.
In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
arXiv Detail & Related papers (2021-12-22T15:27:30Z) - Gaussian Process Regression for Absorption Spectra Analysis of Molecular
Dimers [68.8204255655161]
We discuss an approach based on a machine learning technique, where the parameters for the numerical calculations are chosen from Gaussian Process Regression (GPR)
This approach does not only quickly converge to an optimal parameter set, but in addition provides information about the complete parameter space.
We find that indeed the GPR gives reliable results which are in agreement with direct calculations of these parameters using quantum chemical methods.
arXiv Detail & Related papers (2021-12-14T17:46:45Z) - Simulation of absorption spectra of molecular aggregates: a Hierarchy of
Stochastic Pure States approach [68.8204255655161]
hierarchy of pure states (HOPS) provides a formally exact solution based on local, trajectories.
Exploiting the localization of HOPS for the simulation of absorption spectra in large aggregares requires a formulation in terms of normalized trajectories.
arXiv Detail & Related papers (2021-11-01T16:59:54Z) - Digital quantum simulation of strong correlation effects with iterative
quantum phase estimation over the variational quantum eigensolver algorithm:
$\mathrm{H_4}$ on a circle as a case study [0.0]
We generate the initial state by using the classical-quantum hybrid variational quantum eigensolver algorithm with unitary coupled cluster ansatz.
We demonstrate that a carefully and appropriately prepared initial state can greatly reduce the effects of noise due to sampling in the estimation of the desired eigenphase.
arXiv Detail & Related papers (2021-10-06T15:48:53Z) - Machine Learning for Vibrational Spectroscopy via Divide-and-Conquer
Semiclassical Initial Value Representation Molecular Dynamics with
Application to N-Methylacetamide [56.515978031364064]
A machine learning algorithm for partitioning the nuclear vibrational space into subspaces is introduced.
The subdivision criterion is based on Liouville's theorem, i.e. best preservation of the unitary of the reduced dimensionality Jacobian determinant.
The algorithm is applied to the divide-and-conquer semiclassical calculation of the power spectrum of 12-atom trans-N-Methylacetamide.
arXiv Detail & Related papers (2021-01-11T14:47:33Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.