Modelování velmi chladných plynů ve vícedimenzionálních optických mřížkách

Title: Modelling of Ultracold Gases in Multidimensional Optical Lattices Author: Miroslav Urbanek Department: Department of Chemical Physics and Optics Supervisor: doc. Ing. Pavel Soldán, Dr. Abstract: Optical lattices are experimental devices that use laser light to confine ultracold neutral atoms to periodic spatial structures. A system of bosonic atoms in an optical lattice can be described by the Bose-Hubbard model. Although there exist powerful analytic and numerical methods to study this model in one dimension, their extensions to multiple dimensions have not been as successful yet. I present an original numerical method based on tree tensor networks to simulate time evolution in multidimensional lattice systems with a focus on the two-dimensional Bose-Hubbard model. The method is used to investigate phenomena accessible in current experiments. In particular, I have studied phase collapse and revivals, boson expansion, and many-body localization in two-dimensional optical lattices. The outcome of this work is TEBDOL - a program for modelling one-dimensional and two-dimensional lattice systems. Keywords: Bose-Hubbard model, multidimensional system, optical lattice, tensor networkNázev práce: Modelování velmi chladných plynů ve vícedimenzionálních optických mřížkách Autor: Miroslav Urbanek Katedra: Katedra chemické fyziky a optiky Vedoucí disertační práce: doc. Ing. Pavel Soldán, Dr. Abstrakt: Optické mřížky jsou experimentálními zařízeními, které využívají laserové světlo pro zachycení velmi chladných neutrálních atomů v periodických prostorových strukturách. Systém bosonových atomů v optické mřížce lze popsat Boseho- Hubbardovým modelem. Přestože existují pokročilé analytické a numerické metody ke studiu tohoto modelu v jedné dimenzi, jejich rozšíření do více rozměrů nebylo doposud příliš úspěšné. V této práci představuji původní numerickou metodu, založenou na stromových tenzorových sítích, určenou k simulaci časového vývoje ve vícedimenzionálních mřížkových systémech se zaměřením na dvoudimenzionální Boseho-Hubbardův model. Metoda je použita ke zkoumaní jevů pozorovaných v současných experimentech. Konkrétně jsem studoval kolaps a obnovu fázové koherence, rozpínaní bosonů a mnohočásticovou lokalizaci ve dvourozměrných optických mřížkách. Výsledkem této práce je TEBDOL - program pro modelování jednodimenzionálních a dvoudimenzionálních mřížkových systémů. Klíčová slova: Boseho-Hubbardův model, optická mřížka, tenzorová síť, vícedimenzionální sys- témKatedra chemické fyziky a optikyDepartment of Chemical Physics and OpticsFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Unfolding Quantum Computer Readout Noise

In the current era of noisy intermediate-scale quantum (NISQ) computers, noisy qubits can result in biased results for early quantum algorithm applications. This is a significant challenge for interpreting results from quantum computer simulations for quantum chemistry, nuclear physics, high energy physics, and other emerging scientific applications. An important class of qubit errors are readout errors. The most basic method to correct readout errors is matrix inversion, using a response matrix built from simple operations to probe the rate of transitions from known initial quantum states to readout outcomes. One challenge with inverting matrices with large off-diagonal components is that the results are sensitive to statistical fluctuations. This challenge is familiar to high energy physics, where prior-independent regularized matrix inversion techniques (`unfolding') have been developed for years to correct for acceptance and detector effects when performing differential cross section measurements. We study various unfolding methods in the context of universal gate-based quantum computers with the goal of connecting the fields of quantum information science and high energy physics and providing a reference for future work. The method known as iterative Bayesian unfolding is shown to avoid pathologies from commonly used matrix inversion and least squares methods.Comment: 13 pages, 16 figures; v2 has a typo fixed in Eq. 3 and a series of minor modification

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Several novel methods for performing calculations relevant to quantum chemistry on quantum computers have been proposed but not yet explored experimentally. Virtual quantum subspace expansion [T. Takeshita et al., Phys. Rev. X 10, 011004 (2020)] is one such algorithm developed for modeling complex molecules using their full orbital space and without the need for additional quantum resources. We implement this method on the IBM Q platform and calculate the potential energy curves of the hydrogen and lithium dimers using only two qubits and simple classical post-processing. A comparable level of accuracy would require twenty qubits with previous approaches. We also develop an approach to minimize the impact of experimental noise on the stability of a generalized eigenvalue problem that is a crucial component of the algorithm. Our results demonstrate that virtual quantum subspace expansion works well in practice

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Deformation under uniaxial tensile loading with using Digital Image Correlations (DIC) is the easiest way to analyze the material behavior in sheet metal forming. In order to determine the plastic parameters such as hardening, anisotropy and strain rate sensitivity at higher strain level, equi-biaxial stress state is prerequisite. As reported in the literature, Bulge tests are frequently used for this purpose, but in this work, stack compression test is used as an alternative. In this experiment, deformation in the middle layer where the friction effect is the lowest was monitored using two pairs of DIC systems in rolling and transversal directions. Uniaxial tensile tests as well as stack compression tests were performed on mild ferritic steel DC01 at different strain rates, from 0.001 −1 to 10 −1. Strain rate sensitivity parameter was investigated at different level of strains for both experiments and strain rate sensitivity profiles were obtained. Results show a decrease of material strain rate sensitivity with increasing the true strain

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The COVID-19 pandemic impacted the educational process since the teaching process has been forced to go online in many countries. This enforced change revealed the weaknesses and strengths of the national educational systems and particular institutions. This article aims to analyse the impact of COVID-19 at selected European universities and assess the satisfaction of students, teachers, IT staff and management. This study is unique for its systematicity and complexity – it aggregates the opinions of all interested groups of stakeholders, distinguishes several time periods (before, during and after the pandemic), and allows the respondents to express hesitance in their evaluation. The evaluation model uses fuzzy sets to capture the uncertainty and to aggregate the opinions of different stakeholder groups. The empirical results show that most of the satisfaction development is the same or similar for all institutions examined. Then, the pandemic strongly influenced the satisfaction of all stakeholder groups at the universities examined. This impact was mostly negative, however, several lessons learnt have been revealed. Therefore, it was shown that it is highly beneficial to include these aspects to obtain a reliable picture of overall satisfaction