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Optimizing quantum simulations and the DMRG method
Brandejs, Jan ; Pittner, Jiří (advisor) ; Zamastil, Jaroslav (referee)
Title: Optimizing quantum simulations and the DMRG method Author: Jan Brandejs Department: Department of Chemical Physics and Optics Supervisor: doc. Dr. rer. nat. Jiří Pittner, DSc., J. Heyrovský Institute of Physical Chemistry of the Czech Academy of Sciences Abstract: In this work, we explore the quantum information theoretical aspects of simulation of quantum systems on classical computers, in particular the many- electron strongly correlated wave functions. We describe a way how to reduce the amount of data required for storing the wavefunction by a lossy compression of quantum information. For this purpose, we describe the measures of quantum entanglement for the density matrix renormalization group method. We imple- ment the computation of multi-site generalization of mutual information within the DMRG method and investigate entanglement patterns of strongly correlated chemical systems. We present several ways how to optimize the ground state calculation in the DMRG method. The theoretical conclusions are supported by numerical simulations of the diborane molecule, exhibiting chemically interest- ing electronic structure, like the 3-centered 2-electron bonds. In the theoretical part, we give a brief introduction to the principles of the DMRG method. Then we explain the quantum informational...
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Density matrix renormalization group calculations and entanglement optimization in quantum chemistry
Antalík, Andrej ; Pittner, Jiří (advisor) ; Chalupský, Jaromír (referee)
Density matrix renormalization group is a powerful numerical approach originating in solid state physics. Since its introduction to quantum chemis- try it has been successfully applied to many challenging problems and proved especially efficient for systems with strong multi-reference character. As the method is not invariant to the change of orbital ordering, we implemented the automatic orbital ordering optimization procedure built around the entan- glement analysis and employing the Fiedler method. A technique for active space selection based on one-orbital entropy is introduced. We followed the study by Berardo et al. in which EOM-CC methods were applied to excited states of TiO2 clusters. Four lowest-lying singlet excited states of monomer, dimer and trimer were calculated by means of the DMRG method. In case of the monomer there was good agreement for two states, but the calculations suffered from insufficient treatment of dynamic correlation. For the dimer our results were in very good agreement with EOM-CCSDT results and for the trimer further study would be appropriate. 1
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Quantum computers, principles and latest development
Ješko, Eduard ; Skála, Lubomír (advisor) ; Pittner, Jiří (referee)
The main goal of this thesis is to give information on quantum computer principles and its latest development. In the first part we introduce quantum bits, quantum registers and quantum gates. We show basic operations acting on one and more qubits. On an example we present, how it is possible to construct an arbitrary gate using only elementary quantum gates. We describe a behaviour of quantum computers called quantum parallelism and show its application in Deutsch's algorithm. We define the quantum Fourier transform and its applications. In the last chapter we explain on what principle the D-Wave quantum computer works. In this thesis we compare classical and quantum computers in terms of algorithms and computational speed.
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Explicitly Correlated Multireference Coupled-Cluster Study of Molecules and Cations with Diradical Character
Jungwirth, Jakub ; Pittner, Jiří (advisor) ; Fišer, Jiří (referee)
Known and proposed helium chemistry embraces a large variety of small-size cationic species. Even though some of these species can be studied experimentally in the gas phase, the vast majority of contemporary studies are backed up or done entirely using high-level of theory calculations. The aim of this thesis is to present a theoretical introduction to ab initio computational chemistry from the basics (definition of the electronic problem, Born-Oppenheimer approximation, Hartree- Fock method) to the Brillouin-Wigner and Mukherjee Hilbert-space state-specific multireference coupled-cluster (MRCC) methods and their explicitly correlated versions. The thesis also contains a study of HeN2+ 2 using the mentioned MRCC methods. An important result has been, that Mukherjee's state-specific multireference coupled-cluster method with perturbative triexcitations Mk CCSD(Tu) gives results in very good agreement to conventional calculations (CASPT2 and MRCI) using a much smaller active space and smaller basis sets.
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Aplication of explicitly correlated multi-reference coupled cluster methods
Lang, Jakub ; Pittner, Jiří (advisor) ; Fišer, Jiří (referee)
Nowdays, coupled cluster method belongs to one of the most used quantum chemical methods. However, the single-reference coupled cluster methods are not able to describe systems where the static correlation have an important role. Multireference coupled cluster methods developed in our group can describe both static and dy- namic correlation and can be used for problematic systems. Together with explicitly correlated wavefunction, which can properly describe the electronic cusp and speed up the convergence to the complete ba- sis set limit, they are able to calculate computationally demanding diradicals. Multireference CC calculations of tetramethylenethane have been perforemd and the performance of explicitly correlated version is discussed. Calculations of the isomerization of bicyclobu- tane using the multireference approach are presented as well. 1
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Structure, dynamics and reactivity of the hydrated electron
Uhlig, Frank ; Jungwirth, Pavel (advisor) ; Pittner, Jiří (referee) ; Sebastiani, Daniel (referee)
Structure, dynamics and reactivity of the hydrated electron Frank Uhlig In this work, one of the products of ionization of water, namely the hydrated electron, has been investigated. The hydrated electron is a key-intermediate in aqueous radiation chemistry. Although known to exist for over 50 years, its structure remained elusive and under discussion up to the present day. We show in this work, that we can obtain a faithful picture of the hydrated electron, its equilibrium structure, dynamics after attachment to water, and its reactivity, using ab initio methods. To this end, small cluster models and extended bulk and slab geometries of water including an excess electron have been investigated.
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Quantum computing approach to non-relativistic and relativistic molecular energy calculations
Veis, Libor ; Pittner, Jiří (advisor) ; Skála, Lubomír (referee) ; Nagaj, Daniel (referee)
Quantum computers are appealing for their ability to solve some tasks much faster than their classical counterparts. In fact, they have a potential to perform the full configuration interaction (FCI) energy calculations with a polynomial scaling only. This is in contrast to con- ventional computers where FCI scales exponentially. We provide a detailed description of the quantum version of the FCI method and the results of numerical simulations of the ground and excited state energy calculations of the methylene molecule. We further generalize this method to the relativistic four component regime and show how to efficiently solve the eigenproblem of the Dirac-Coulomb(-Breit) Hamiltonian on a quantum computer. We demonstrate the func- tionality 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. 1
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Simulation of processes in cellular membranes
Timr, Štěpán ; Jungwirth, Pavel (advisor) ; Pittner, Jiří (referee)
Probing orientations of fluorescent molecules embedded in or attached to cell membranes has a great potential to reveal information on membrane structure and processes occurring in living cells. In this thesis, we first describe one- and two-photon linear dichroism measurements on a fluorescent probe embedded in a phospholipid membrane with a well- defined lipid composition. On the basis of experimental data, we determine the distribution of the angle between the one-photon transition dipole moment of the probe and the membrane normal. At the same time, we perform molecular dynamics simulations of the fluorescent probe and quantum calculations of its one-photon and two-photon absorption properties. By comparing the orientational distribution gained from experiments with that predicted by simulations, we test the ability of linear dichroism measurements to report on the orientation of a fluorescent molecule in a lipid membrane. We also examine the applicability of molecular simulations as a basis for the interpretation of experimental data.
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Study of Diradicals By Explicitly Correlated Multireference Coupled Cluster Methods
Švaňa, Matej ; Pittner, Jiří (advisor) ; Pitoňák, Michal (referee)
Title: Study of Diradicals by Explicitly Correlated Multireference Coupled Cluster Methods Author: Matej Švaňa Department: Department of Physical and Macromelecular Chemistry Supervisor: Mgr. Jiří Pittner, Dr. rer. nat., J. Heyrovský Institute of Physical Chemistry Abstract: Total energies of cyclopropane, trimethylene, and propylidene were calculated with conventional post-HF CCSD(T), BWCCSD(T), MkCCSD(T) methods and their explicitly correlated alternatives. Main aims of the the- sis were to compare the basis set convergence of total energies and relative energies between cyclopropane and trimethylene/propylidene, both at the conventional and the explicitly correlated levels. It was shown that use of explicit correlation accelerates the convergence of the total energy by one or- der of basis set quality, resulting in considerable savings in computational times. Also, the MkCCSD(T)-F12/QZ and the BWCCSD(T)-F12/QZ calcula- tions belong to the most sophisticated approaches employed for estimation of the relative energies of cyclopropane and trimethylene/propylidene to date. Keywords: explicitly correlated, coupled cluster, multi-reference, cyclopropane isomerisation, trimethylene, propylidene 1
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An Analytical Gradient of a Multireference Coupled Cluster Method
Šmydke, Jan ; Pittner, Jiří (advisor) ; Fišer, Jiří (referee) ; Neogrady, Pavel (referee)
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