Univ., Diss.--Göteborg, 2007. / Enth. außerdem 5 Zeitschriftenaufsätze.

Thesis (doctoral)--Göteborg University, 2007. / Includes bibliographical references.

In recent years, there has been a significant development in high performance computing, driven by advances in hardware and software technology. The performance of the computers to the present has improved in accordance with Moore’s law, on the other hand, it seems to be reaching the limits in the near future. The quantum computers, which have the potential to greatly exceed the capabilities of the classical computers, have been the focus of intense researches. In the present study, we investigate the difference of the classical random walk and the quantum walk based on theoretical point of view and the implementation in the simulation, and seek the applicability of the quantum walk in the future. We provide the overview of the fundamental theory in the classical random walk and the quantum walk, and compare the differences of the features, based on the behaviors between the classical random walk and the quantum walk, and the probability distributions. Also, we implement the quantum walk using the Qiskit as the quantum simulator. The quantum circuit representing the quantum walk is mainly composed of the three parts, the coin operator, the shift operator, and the quantum measurement. The coin operator represent the coin flip in the quantum walk, where we use the Hadamard operator. The shift operator indicates the movement of the quantum walk according to the result of the coin operator. The quantum measurement is the process of extracting the quantum state of qubits. In one-dimensional quantum walk, we prepare four cases, as the difference of the number of qubits for the position from two to five qubits. In all cases, the successful implementation of the quantum walk has been seen with respect to the number of qubits and the difference of the initial state. We then extensively investigate the implementation of the two-dimensional quantum walk. In two-dimensional quantum walk, three cases are prepared in terms of the number of qubits for the position in each x and y coordinates, from two to four qubits. Although the complexity of the problem setting is much increased compared to the one-dimensional case, the success of the quantum walk implementation can be seen. We also see that the behavior of the quantum walk and the spread of the probability distribution strongly depends on the initial condition in terms of both the initial coin state and the initial position. The present study has shown the applicability of the quantum walk as the tool for solving the complex problems in a wide range of future applications. In concluding remarks, we offer conceivable perspectives and future prospects of the present study.

<p>The blooming of quantum computer hardware provokes enormous enthusiasm seeking for applications in various fields.</p> <p>Particularly, it is always of great interest to study the chemical or physical systems with quantum enhanced learning process or quantum simulation in the NISQ era.</p> <p>Here we will present our recent research on chemical or physical systems based on quantum computing. </p> <p><br></p> <p>One main focus of this dissertation is the quantum classification algorithms development, especially for the entanglement classification.</p> <p>As a quantum mechanical property describing the correlation between quantum mechanical systems, entanglement has no classical analog.</p> <p>In the past 100 years, entanglement has been attracting enormous attentions in both the theoretical and experimental research.</p> <p>We investigate the entanglement classification in chemical reactions, generalizing the typical CHSH inequality from discrete measurement results into the continuous measurement results.</p> <p>Furthermore, we develop a quantum classification algorithm based on the typical instance-based learning algorithms, which in turn is applied into the entanglement classification problems.</p> <p>Additionally, the proposed quantum algorithm has a variety of applications, such as the prediction of phase transition. </p> <p><br></p> <p>Quantum-enhanced classification algorithm is never the only practicable application of quantum computer.</p> <p>Moreover, we propose a universal quantum circuit implementation to estimate a given one-dimensional functions with a finite Fourier expansion.</p> <p>We demonstrate the circuit implementation with the application on square wave function.</p> <p>Additionally, we present a quantum circuit for the typical time-independent perturbation theory.</p> <p>Perturbation theory is always one of the most powerful tools for physicists and chemists dealing with the eigenenergy problems in quantum mechanics.</p> <p>Though PT is quite popular today, it seems that the techniques for PT does not take a ride in the era of quantum computing.</p> <p>In this dissertation, we present a a universal quantum circuit implementation  for the time-independent PT method, which is often termed as Rayleigh–Schr\"odinger PT.</p> <p>In order to demonstrate the implementation of the proposed quantum circuit, the extended Fermi Hubbard Model is introduced as an example.</p> <p>In particular, the proposed quantum circuit shows considerable speedup comparing with the typical PT methods.</p>

Abstract Histidine acid phosphatases are characterized by the presence of a conserved RHGXRXP motif. One medically important acid phosphatase is the Prostatic Acid Phosphatase (PAP). PAP has been associated with prostate cancer for a long time and has been used as a marker to stage prostate carcinoma. Yet, there is no clear understanding on the functioning of the enzyme in vivo. This thesis work focuses on the characterization of putative ligands and elucidation of the reaction mechanism of PAP using computational methods. The ligand-enzyme complexes were generated by docking and molecular dynamics simulations. The complexes showed that the conserved arginines of RHGXRXP motif are important for binding the highly negatively charged phosphate group. The complexes also highlighted that the active site aspartate (Asp258) should be neutral in the complex and is involved as a general acid-base in the reaction. The studies support that PAP could dephosphorylate the growth factor receptors EGFR and ErbB-2. The studies also found that the majority of tyrosine phosphorylated peptides from these growth factor receptors could bind to PAP. The affinities were assessed based on theoretical calculations and were further confirmed by experimental measurements in the feasible cases. To clearly understand the mechanism of PAP, quantum mechanical methods were employed. The enzymatic reaction involves two steps. In the first step, the phosphate moiety is transferred from the ligand to the conserved histidine. The calculations on the first step of the reaction involved generating the transition state (TS) structures and estimating the respective barriers. The calculations clearly support that Asp258 becomes neutral by picking up the proton from the monoanionic ligand entering the binding site. The proton from neutral Asp258 is later transferred to the leaving group via a water bridge, restoring the negative state of Asp258. The second step involves the hydrolysis of phosphohistidine enzyme intermediate. Using hybrid quantum mechanics/molecular mechanics calculations, it was found that the Asp258 accepts a proton from the nucleophilic water only after the TS is crossed. This proton is possibly then transferred to the free phosphate while it leaves the binding site, restoring the enzyme to its free state. The study highlights the importance of active site arginines in the binding as well as the stabilization of TS. Further, the analysis of TS structures in both the steps showed an associative mechanism, based on the distance of the nucleophilic and the leaving atoms to the phosphate atom. These distances are much smaller than what has been found in other well studied nonmetallo-phopshatases. Thus, the study finds a novel mechanism of enzymic phosphotransfer in PAP mediated catalysis.

We investigate the energy levels of a particle confined in the isotropic oscillator potential with a magnetic and spatially varying electric field. Here we are able to exactly solve the Schrodinger equation, using matrix methods, for the first excited states. To this end we find that the spatial gradient of the electric field acts as a magnetic field in certain circumstances. Here we present the changes in the energy levels as functions of the electric field, and other parameters.

No description available.

We introduce the formalism of supersymmetric quantum mechanics, including super-symmetry charges,Z2-graded Hilbert spaces, the chirality operator and the Wittenindex. We show that there is a one to one correspondence of fermions and bosons forenergies different than zero, which implies that the Witten index measures the dif-ference of fermions and bosons at the ground state. We argue that the Witten indexis the index of an elliptic operator. Quantization of the supersymmetric non-linearsigma model shows that the Witten index equals the Euler characteristic of the un-derlying Riemannian manifold over which the theory is defined. Finally, the pathintegral representation of the Witten index is applied to derive the Gauss-Bonnettheorem. Apart from this we introduce elementary mathematical background in thesubjects of topological invariance, Riemannian manifolds and index theory / Vi introducucerar formalismen f ̈or supersymmetrisk kvantmekanik, d ̈aribland super-symmetryladdningar,Z2-graderade Hilbertrum, kiralitetsoperatorn och Wittenin-dexet. Vi visar att det r ̊ader en till en-korrespondens mellan fermioner och bosonervid energiniv ̊aer skillda fr ̊an noll, vilket medf ̈or att Wittenindexet m ̈ater skillnadeni antal fermioner och bosoner vid nolltillst ̊andet. Vi argumenterar f ̈or att Wittenin-dexet ̈ar indexet p ̊a en elliptisk operator. Kvantisering av den supersymmetriskaicke-linj ̈ara sigmamodellen visar att Wittenindexet ̈ar Eulerkarakteristiken f ̈or denunderliggande Riemannska m ̊angfald ̈over vilken teorin ̈ar definierad. Slutligenapplicerar vi v ̈agintegralrepresentationen av Wittenindexet f ̈or att h ̈arleda Gauss-Bonnets sats. Ut ̈over detta introduceras ocks ̊a grundl ̈aggande matematisk bakrundi ämnena topologisk invarians, Riemmanska m ̊angfalder och indexteori.

Plasmonic cavities confine optical fields at metal-dielectric interfaces via collective charge oscillations of free electrons within metals termed surface plasmon polaritons (SPPs). SPPs are confined in nanometre gaps formed between two metallic surfaces which creates an optical resonance. This optical resonance of the system is controlled by the geometry and the material of the nanogap. The focus of this work is to understand and utilize these confined optical modes to probe and manipulate the dynamics of single-molecules at room temperature. In this thesis, nanogap cavities are constructed by placing nanoparticles on top of a metal-film separated by molecular spacers. Such nanogaps act as cavities with confined optical fields in the gap. Precise position and orientation of single-molecules in the gap is obtained by supramolecular guest-host assembly and DNA origami breadboards. The interaction of light and single-molecules is studied in two different regimes of interaction strength. In the perturbative regime molecular light emission from electronic and vibrational states is strongly enhanced and therefore is used for the detection of single-molecules. In this regime the energy states remain unaltered, however profound effects emerge when the gap size is reduced to < 1 nm. New hybridized energy states which are half-light and half-matter are then formed. Dispersion of these energies is studied by tuning the cavity resonance across the molecular resonance, revealing the anti-crossing signature of a strongly coupled system. This dressing of molecules with light results in the modification of photochemistry and photophysics of single-molecules, opening up the exploration of complex natural processes such as photosynthesis and the possibility to manipulate chemical bonds.

Spatial confinement of electrons and their interactions as well as confinement of the spin dimensionality often yield drastic changes of the electronic and magnetic properties of solids. Novel quantum transport and optical phenomena, involving electronic spin degrees of freedom in semiconductor heterostructures, as well as a rich variety of exotic quantum ground states and magnetic excitations in complex transition metal oxides that arise upon such confinements, belong therefore to topical problems of contemporary condensed matter physics. In this work electron spin systems in reduced dimensions are studied with Electron Spin Resonance (ESR) spectroscopy, a method which can provide important information on the energy spectrum of the spin states, spin dynamics, and magnetic correlations. The studied systems include quasi onedimensional spin chain materials based on transition metals Cu and Ni. Another class of materials are semiconductor heterostructures made of Si and Ge. Part I deals with the theoretical background of ESR and the description of the experimental ESR setups used which have been optimized for the purposes of the present work. In particular, the development and implementation of axial and transverse cylindrical resonant cavities for high-field highfrequency ESR experiments is discussed. The high quality factors of these cavities allow for sensitive measurements on μm-sized samples. They are used for the investigations on the spin-chain materials. The implementation and characterization of a setup for electrical detected magnetic resonance is presented. In Part II ESR studies and complementary results of other experimental techniques on two spin chain materials are presented. The Cu-based material Linarite is investigated in the paramagnetic regime above T > 2.8 K. This natural crystal constitutes a highly frustrated spin 1/2 Heisenberg chain with ferromagnetic nearest-neighbor and antiferromagnetic next-nearestneighbor interactions. The ESR data reveals that the significant magnetic anisotropy is due to anisotropy of the g-factor. Quantitative analysis of the critical broadening of the linewidth suggest appreciable interchain and interlayer spin correlations well above the ordering temperature. The Ni-based system is an organic-anorganic hybrid material where the Ni2+ ions possessing the integer spin S = 1 are magnetically coupled along one spatial direction. Indeed, the ESR study reveals an isotropic spin-1 Heisenberg chain in this system which unlike the Cu half integer spin-1/2 chain is expected to possess a qualitatively different non-magnetic singlet ground state separated from an excited magnetic state by a so-called Haldane gap. Surprisingly, in contrast to the expected Haldane behavior a competition between a magnetically ordered ground state and a potentially gapped state is revealed. In Part III investigations on SiGe/Si quantum dot structures are presented. The ESR investigations reveal narrowlines close to the free electron g-factor associated with electrons on the quantum dots. Their dephasing and relaxation times are determined. Manipulations with sub-bandgap light allow to change the relative population between the observed states. On the basis of extensive characterizations, strain, electronic structure and confined states on the Si-based structures are modeled with the program nextnano3. A qualitative model, explaining the energy spectrum of the spin states is proposed.