Quantum computing algorithms for quantum chemistry

Název práce: Kvantově chemické algoritmy pro kvantové počítače Autor: Jakub Višňák Abstrakt: Práce se zabývá simulací kvantového výpočtu diagonalizace maticové reprezentace hamiltoniánu na klasickém počítači pro dva různé rozvoje vlnové funkce v rámci limited CI (LCI) metody pro popis všech elektronů molekuly SbH v rámci Dirac-Coulombova hamiltoniánu pro dva energeticky nejnižší elektronové stavy X 0+ a A 1 pomocí Iterative Phase Estimation Algortihm (IPEA). V simulacích je použita reprezentace evolučního operátoru exp(i Hˆ t) pomocí "compact mapping", v teoretické části je naznačeno jakým způsobem lze simulovat "direct mapping". Je studován vliv různé metodiky volby vstupního odhadu vlastního vektoru pro metody IPEA A a IPEA B pro které jsou rovněž porovnány hodnoty pravěpodobnosti úspěchu pm pro různé body disociačních křivek molekuly SbH. Je ukázáno, že pro použité LCI rozvoje a pro vstupní odhady vlastního vektoru vycházející z LCI rozvoje označovaného jako "CISD(2)" lze obě varianty metody IPEA použít až do mezijaderné vzálenosti1 R 6 a0. Byla zkoumána závislost hodnoty pm na překryvu vlastního vektoru se svým vstupním odhadem - 2 0 v případě metody IPEA B a diskutována použitelnost obou variant metody IPEA v dalších možných výpočtech. 1 a0 značí v celé práci Bohrův poloměr (viz seznam zkratek).Title: Quantum computing algorithms for quantum chemistry Author: Jakub Višňák Abstract: The topic of this study is the simulation of the quantum algorithm for the diagonalization of the matrix representation of the all-electron Dirac-Coulomb hamiltonian of the SbH molecule. Two different limited CI expansions were used to describe both the ground state (X 0+ ) and the first excited doublet (A 1) by simulating the Iterative Phase Estinamtion Algorith (IPEA). In the simulations numerically performed in this work, the "compact mapping" has been employed for the representation of the evolution operator exp(i Hˆ t); in the theoretical part of the work, the "direct mapping" is described as well. The influence of the metodics for choosing the initial eigenvector estimate is studied in both IPEA A and IPEA B variants. For those variants, the success probabilities pm are computed for different single-points on the SbH dissociation curves. The initial eigenvector estimates based on the "CISD(2)" method are found to be sufficient for both studied LCI-expansions up to internuclear distance R 6 a0. The pm dependence on the overlap between the eigenvector in question and its inital estimate - 2 0 is studied the for IPEA B method. The usability of the both variants of the IPEA in possible later calculations is...Department of Chemical Physics and OpticsKatedra chemické fyziky a optikyFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Towards DMRG-tailored coupled cluster method in the 4c-relativistic domain

There are three essential problems in computational relativistic chemistry: electrons moving at relativistic speeds, close lying states and dynamical correlation. Currently available quantum-chemical methods are capable of solving systems with one or two of these issues. However, there is a significant class of molecules, in which all the three effects are present. These are the heavier transition metal compounds, lanthanides and actinides with open d or f shells. For such systems, sufficiently accurate numerical methods are not available, which hinders the application of theoretical chemistry in this field. In this paper, we combine two numerical methods in order to address this challenging class of molecules. These are the relativistic versions of coupled cluster methods and density matrix renormalization group (DMRG) method. To the best of our knowledge, this is the first relativistic implementation of the coupled cluster method externally corrected by DMRG. The method brings a significant reduction of computational costs, as we demonstrate on the system of TlH, AsH and SbH

Relativistic quantum chemistry on quantum computers

Last years witnessed a remarkable interest in application of quantum computing for solving problems in quantum chemistry more efficiently than classical computers allow. Very recently, even first proof-of-principle experimental realizations have been reported. However, so far only the non-relativistic regime (i.e. Schroedinger equation) has been explored, while it is well known that relativistic effects can be very important in chemistry. In this letter we present the first quantum algorithm for relativistic computations of molecular energies. We show how to efficiently solve the eigenproblem of the Dirac-Coulomb Hamiltonian on a quantum computer and demonstrate the functionality of the proposed procedure by numerical simulations of computations of the spin-orbit splitting in the SbH molecule. Finally, we propose quantum circuits with 3 qubits and 9 or 10 CNOTs, which implement a proof-of-principle relativistic quantum chemical calculation for this molecule and might be suitable for an experimental realization

Multilinear analysis of Time-Resolved Laser-Induced Fluorescence Spectra of U(VI) containing natural water samples

Natural waters’ uranium level monitoring is of great importance for health and environmental protection. One possible detection method is the Time-Resolved Laser-Induced Fluorescence Spectroscopy (TRLFS), which offers the possibility to distinguish different uranium species. The analytical identification of aqueous uranium species in natural water samples is of distinct importance since individual species differ significantly in sorption properties and mobility in the environment. Samples originate from former uranium mine sites and have been provided by Wismut GmbH, Germany. They have been characterized by total elemental concentrations and TRLFS spectra. Uranium in the samples is supposed to be in form of uranyl(VI) complexes mostly with carbonate (CO32− ) and bicarbonate (HCO3− ) and to lesser extend with sulphate (SO42− ), arsenate (AsO43− ), hydroxo (OH− ), nitrate (NO3− ) and other ligands. Presence of alkaline earth metal dications (M = Ca2+ , Mg2+ , Sr2+ ) will cause most of uranyl to prefer ternary complex species, e.g. Mn(UO2)(CO3)32n-4 (n ∊ {1; 2}). From species quenching the luminescence, Cl− and Fe2+ should be mentioned. Measurement has been done under cryogenic conditions to increase the luminescence signal. Data analysis has been based on Singular Value Decomposition and monoexponential fit of corresponding loadings (for separate TRLFS spectra, the “Factor analysis of Time Series” (FATS) method) and Parallel Factor Analysis (PARAFAC, all data analysed simultaneously). From individual component spectra, excitation energies T00, uranyl symmetric mode vibrational frequencies ωgs and excitation driven U-Oyl bond elongation ΔR have been determined and compared with quasirelativistic (TD)DFT/B3LYP theoretical predictions to cross -check experimental data interpretation

Modelling of the LTDE-SD radionuclide diffusion experiment in crystalline rock at the Äspö Hard Rock Laboratory (Sweden)

Acknowledgement. The comments from Dr. Kersti Nilsson, the analytical work by VKTA (Dresden, Germany) for some of the rock samples, and the initial review by Dr. Anna-Maria Jakobsson are gratefully acknowledged. The constructive comments and suggestions by Dr. Jordi Cama and an anonymous reviewer contributed to a significant improvement of the manuscript. Funding was provided through the Task Force partner organisations participating in this modelling exercise (SKB, Sweden; POSIVA OY, Finland; SÚRAO, Czech Republic; BMWi, Germany; KAERI, Republic of Korea; NUMO and JAEA, Japan). IDAEA-CSIC is a Severo Ochoa Centre of Research Excellence (Spanish Ministry of Science and Innovation, Project CEX2018-000794-S). The contributions of TUL, CTU and PROGEO are the result of the SÚRAO project "Research support for Safety Evaluation of Deep Geological Repository". JAEA's modelling was performed as a part of "The project for validating assessment methodology in geological disposal system" funded by the METI of Japan. A.I., P.T., M.V., G.D., and D.B. gratefully acknowledge the computing time granted by the JARA Vergabegremium and provided on the JARA Partition part of the supercomputer JURECA at Forschungszentrum Jülich.This study shows a comparison and analysis of results from a modelling exercise concerning a field experiment involving the transport and retention of different radionuclide tracers in crystalline rock. This exercise was performed within the Swedish Nuclear Fuel and Waste Management Company (SKB) Task Force on Modelling of Groundwater Flow and Transport of Solutes (Task Force GWFTS).Task 9B of the Task Force GWFTS was the second subtask within Task 9 and focused on the modelling of experimental results from the Long Term Sorption Diffusion Experiment in situ tracer test. The test had been performed at a depth of about 410m in the Äspö Hard Rock Laboratory. Synthetic groundwater containing a cocktail of radionuclide tracers was circulated for 198 days on the natural surface of a fracture and in a narrow slim hole drilled in unaltered rock matrix. Overcoring of the rock after the end of the test allowed for the measurement of tracer distribution profiles in the rock from the fracture surface (A cores) and also from the slim hole (D cores). The measured tracer activities in the rock samples showed long profiles (several cm) for non- or weakly-sorbing tracers (Cl-36, Na-22), but also for many of the more strongly-sorbing radionuclides. The understanding of this unexpected feature was one of the main motivations for this modelling exercise. However, re-evaluation and revision of the data during the course of Task 9B provided evidence that the anomalous long tails at low activities for strongly sorbing tracers were artefacts due to cross-contamination during rock sample preparation. A few data points remained for Cs-137, Ba-133, Ni-63 and Cd-109, but most measurements at long distances from the tracer source (>10mm) were now below the reported detection limits.Ten different modelling teams provided results for this exercise, using different concepts and codes. The tracers that were finally considered were Na-22, Cl-36, Co-57, Ni-63, Ba-133, Cs-137, Cd-109, Ra-226 and Np-237. Three main types of models were used: i) analytical solutions to the transport-retention equations, ii) continuum-porous-medium numerical models, and iii) microstructure-based models accounting for small-scale heterogeneity (i.e. mineral grains, porosities and/or microfracture distributions) and potential centimetre-scale fractures. The modelling by the different teams led to some important conclusions, concerning for instance the presence of a disturbed zone (a few mm in thickness) next to the fracture surface and to the wall of the slim hole and the role of micro-fractures and cm-scale fractures in the transport of weakly sorbing tracers. These conclusions could be reached after the re-evaluation and revision of the experimental data (tracer profiles in the rock) and the analysis of the different sets of model results provided by the different team

Modelling of the LTDE-SD radionuclide diffusion experiment in crystalline rock at the Äspö Hard Rock Laboratory (Sweden)

This study shows a comparison and analysis of results from a modelling exercise concerning a field experiment involving the transport and retention of different radionuclide tracers in crystalline rock. This exercise was performed within the Swedish Nuclear Fuel and Waste Management Company (SKB) Task Force on Modelling of Groundwater Flow and Transport of Solutes (Task Force GWFTS). Task 9B of the Task Force GWFTS was the second subtask within Task 9 and focused on the modelling of experimental results from the Long Term Sorption Diffusion Experiment in situ tracer test. The test had been performed at a depth of about 410m in the Äspö Hard Rock Laboratory. Synthetic groundwater containing a cocktail of radionuclide tracers was circulated for 198 days on the natural surface of a fracture and in a narrow slim hole drilled in unaltered rock matrix. Overcoring of the rock after the end of the test allowed for the measurement of tracer distribution profiles in the rock from the fracture surface (A cores) and also from the slim hole (D cores). The measured tracer activities in the rock samples showed long profiles (several cm) for non-or weakly-sorbing tracers (Cl-36, Na-22), but also for many of the more strongly-sorbing radionuclides. The understanding of this unexpected feature was one of the main motivations for this modelling exercise. However, re-evaluation and revision of the data during the course of Task 9B provided evidence that the anomalous long tails at low activities for strongly sorbing tracers were artefacts due to cross-contamination during rock sample preparation. A few data points remained for Cs-137, Ba-133, Ni-63 and Cd-109, but most measurements at long distances from the tracer source (>10mm) were now below the reported detection limits. Ten different modelling teams provided results for this exercise, using different concepts and codes. The tracers that were finally considered were Na-22, Cl-36, Co-57, Ni-63, Ba-133, Cs-137, Cd-109, Ra-226 and Np-237. Three main types of models were used: i) analytical solutions to the transport-retention equations, ii) continuum-porous-medium numerical models, and iii) microstructure-based models accounting for small-scale heterogeneity (i.e. mineral grains, porosities and/or microfracture distributions) and potential centimetre-scale fractures. The modelling by the different teams led to some important conclusions, concerning for instance the presence of a disturbed zone (a few mm in thickness) next to the fracture surface and to the wall of the slim hole and the role of micro-fractures and cm-scale fractures in the transport of weakly sorbing tracers. These conclusions could be reached after the re-evaluation and revision of the experimental data (tracer profiles in the rock) and the analysis of the different sets of model results provided by the different teams.The comments from Dr. Kersti Nilsson, the analytical work by VKTA (Dresden, Germany) for some of the rock samples, and the initial review by Dr. Anna-Maria Jakobsson are gratefully acknowledged. The constructive comments and suggestions by Dr. Jordi Cama and an anonymous reviewer contributed to a significant improvement of the manuscript. Funding was provided through the Task Force partner organisations participating in this modelling exercise (SKB, Sweden; POSIVA OY, Finland; SÚRAO, Czech Republic; BMWi, Germany; KAERI, Republic of Korea; NUMO and JAEA, Japan). IDAEA-CSIC is a Severo Ochoa Centre of Research Excellence (Spanish Ministry of Science and Innovation, Project CEX2018-000794-S). The contributions of TUL, CTU and PROGEO are the result of the SÚRAO project “Research support for Safety Evaluation of Deep Geological Repository”. JAEA’s modelling was performed as a part of “The project for validating assessment methodology in geological disposal system” funded by the METI of Japan. A.I., P.T., M.V., G.D., and D.B. gratefully acknowledge the computing time granted by the JARA Vergabegremium and provided on the JARA Partition part of the supercomputer JURECA at Forschungszentrum Jülich.Peer reviewe

Quantum algorithms for computational nuclear physics

While quantum algorithms have been studied as an efficient tool for the stationary state energy determination in the case of molecular quantum systems, no similar study for analogical problems in computational nuclear physics (computation of energy levels of nuclei from empirical nucleon-nucleon or quark-quark potentials) have been realized yet. Although the difference between the above mentioned studies might seem negligible, it will be examined. First steps towards a particular simulation (on classical computer) of the Iterative Phase Estimation Algorithm for deuterium and tritium nuclei energy level computation will be carried out with the aim to prove algorithm feasibility (and extensibility to heavier nuclei) for its possible practical realization on a real quantum computer