This dissertation studies quantum decoherence in anharmonic oscillator systems to monitor and understand the way the systems evolve. It also explores methods to control the systems' evolution, and the effects of decoherence when applicable. We primarily do this by finding the time evolution of the systems using their Lie algebraic structures. We solve for a generalized Caldirola-Kanai Hamiltonian, and propose a general way to produce a desired evolution of the system. We apply the analysis to the effects of Dirac delta fluctuations in mass and frequency, both separately and simultaneously. We also numerically demonstrate control of the generalized Caldirola-Kanai system for the case of timed Gaussian fluctuations in the mass term. This is done in a way that can be applied to any system that is made up of a Lie algebra. We also explore the evolution of an optomechanical coupled mirror-laser system while maintaining a second order coupling. This system creates anharmonic effects that can produce cat states which can be used for quantum computing. We find that the decoherence in this system causes a rotational smearing effect in the Husimi function which, with the second order term added, causes rotational smearing after a squeezing effect. Finally, we also address the dynamic evolution and decoherence of an anharmonic oscillator with infinite coupling using the Born-Markov master equation. This is done by using the Lie algebraic structure of the Born-Markov master equation's superoperators when applying a strategic mean field approximation to maintain dynamic flexibility. The system is compared to the Born-Markov master equation for the harmonic oscillator, the regular anharmonic oscillator, and the dynamic double anharmonic oscillator. Throughout, Husimi plots are provided to visualize the dynamic decoherence of these systems.

In this dissertation, we develop two novel methods for studying the nature of the Milky Way's dark matter halo. In both cases, we rely on the relationship between the dark matter halo's gravitational potential and the orbital structure it supports. The first method explores the morphology of stellar streams orbiting in non-spherical gravitational potentials. When globular clusters or dwarf galaxies fall into the Milky Way, tidal forces shred them into long filaments of stars called stellar streams. We show that in non-spherical potentials, stream morphologies are heavily dependent on the characteristics of the progenitor's orbit. Flattened axisymmetric galactic potentials, for example, are known to host minor orbit families surrounding special orbits with commensurable frequencies. The behavior of orbits that belong to these orbit families is fundamentally different from that of typical orbits with non-commensurable frequencies. We show that streams evolving near the boundaries, or separatrices, between orbit families, may become fanned out, develop a bifurcation, or both. We utilize perturbation theory to estimate the timescale of this effect and the likelihood of a stream evolving close enough to a separatrix to be affected by it. Next, we study the dynamical reasons for stream fanning and bifurcations near resonances, and find that each morphological outcome has a slightly different dynamical cause. Using a novel numerical approach for measuring the libration frequencies of resonant and near-resonant orbits, we reveal that fans come about due to a large spread in the libration frequencies near a separatrix, whereas bifurcations arise when a separatrix splits the orbital distribution of the stellar stream between two (or more) distinct orbit families. We then demonstrate how these features can arise in streams on realistic galactic orbits, in realistic galactic potentials, over timescales as short as 2-3 Gyr, and discuss how this might be used to constrain the global shape of the Milky Way's gravitational potential. The second method studied in this dissertation enables dynamical tests of a dark matter candidate known as Fuzzy (or Ultra-Light) Dark Matter. Our method relies on a wave generalization of the classic Schwarzschild approach for constructing self-consistent halos -- such a halo consists of a suitable superposition of waves instead of particle orbits, chosen to yield a desired mean density profile. As an illustration, we apply the method to spherically symmetric halos. We derive an analytic relation between the particle distribution function and the wave superposition amplitudes, and show how it simplifies in the high energy (WKB) limit. We verify the stability of such constructed halos by numerically evolving the Schrodinger-Poisson system. The proposed algorithm provides an efficient and accurate way to simulate the time-dependent halo substructures from wave interference, and to test how they will affect dynamical tracers or other observables in a galaxy. The dissertation concludes with a brief discussion of the future prospects of these two methods, especially in the context of upcoming ground- and space-based missions like Rubin LSST and the Roman Space Telescope.

Plants and bacteria both have specialized light-harvesting pigment-protein complexes, composed of a network of chromophores encompassed by a protein scaffold, that are involved in photosynthesis. While chromophore, as well as protein, composition and arrangement vary in these light-harvesting complexes, chromophores transfer energy as molecular excitation energy through their complex multi-chromophoric network with near perfect efficiency. Understanding the efficiency of this excitation energy transfer process has been the focus of many interdisciplinary studies. By elucidating the mechanisms involved in efficient excitation energy transfer in biological systems, we are able to guide the design of novel organic materials for their application in photovoltaic systems. Interdisciplinary studies of light-harvesting biological systems leverage advanced spectroscopic techniques and theoretical models to help explain the interaction be- tween excited electronic states. Difficulties in assigning the origin of spectral features in spectroscopy experiments arise from both homogeneous and inhomogeneous effects. Various computational studies have been able to provide theoretical models that help disentangle these effects and provide insight into the origin of some these spectral features. In this work, we present a computational approach that is used to calculate an ensemble of model Hamiltonians for a light-harvesting pigment-protein complex found in algae. To verify the reliability of our model, we compare various computed spec- tra with experimental measurements. Next, we extend our computational approach for parameterizing an ensemble of Hamiltonians for two configurationally unique or- ganic dimers. Finally, we examine the error of some of the approximations made while partitioning “system” and “bath” degrees of freedom when computing molecu- lar properties. Using these methods we are able to provide mechanistic interpretations and explanations of spectral signatures observed in various linear and nonlinear ex- perimental spectra.

Quantum annealing represents an essential milestone towards the goal of adiabatic quantum computing. In quantum annealing, the computation involves finding the ground state of a classical Ising-like Hamiltonian realized as interactions between qubits. Quantum fluctuations are introduced to allow the wavefunction of the qubits to explore the energy landscape, the hope being that the wavefunction finds a minimum energy configuration and possibly giving the result of the computation. While quantum annealing likely may not be as powerful as adiabatic quantum computing, it is possible that it may be better at optimization compared to analogous classical algorithms. In physical realizations of quantum annealing, there are still questions as to the role of quantum fluctuations in the operation of a device given the short coherence times of the individual qubits. These questions have consistently posed a serious theoretical challenge making it difficult to verify experimental results. Here we simplify the problem by considering a system of qubits with ferromagnetic interactions, modeling the decoherence effects as classical noise in the transverse-field of each qubit. We compare the calculations to data collected from a system of manufactured qubits produced by D-wave Systems by performing a finite-size scaling analysis that captures the competition between quantum fluctuations of the transverse-field and bit-flip errors from the noise. We argue that on time-scales larger than the single-qubit decoherence time, the device produces the expected quantum fluctuations for the many-body system. Using this finite-size scaling, one can diagnose sources of noise in the system. Hopefully, in the near future, these devices will not only be realizing coherent quantum annealing but will likely be useful as another example of synthetic quantum matter.

<p>Qudit, a multi-level computational unit for quantum computing, provides a larger state space for information processing, and thus can reduce the circuit complexity, simplify the experimental setup. We promote the qudit-based quantum computing by providing an overview that covers a variety of qudit topics ranging from gate universality, circuit building, algorithm design, to physical realization methods. Among all the important qudit algorithms, we perform the first experimental realization of a qudit-based phase estimation algorithm(PEA) on a photonic platform, utilizing the high dimensionality in time and frequency degrees of freedom (DoFs) in a single photon. In our scheme the controlled-unitary gates can be realized in a deterministic fashion, as the control and target registers are now represented by two DoFs in a single photon. Next we improve the PEA by introducing a new statistical and variational approach to the PEA that we called SPEA. The SPEA can determine any unknown eigenstate-eigenphase pair from a given unitary matrix  by treating the probabilistic output of an Iterative PEA (IPEA)-like circuit as an eigenstate-eigenphase proximity metric, using this metric to estimate the proximity of the input state and input phase to the nearest eigenstate-eigenphase pair and approaching this pair via a variational process on the input state and phase. The SPEA can search over the entire computational space as well as some specified given range efficiently and thus outperforms the original PEA.</p> <p> </p> <p><br></p> <p>The simulation of open quantum dynamics has attracted wide interests recently with a variety of quantum algorithms developed and demonstrated. The second half of the thesis focus on the simulation of the open quantum dynamics which is a useful application for quantum computer based on qudit as well as qubit. We perform the first quantum simulations of the  radical pair mechanism(RPM) in the avian compass with a Sz.-Nagy dilation theorem-based quantum algorithm to demonstrate the generality of the quantum algorithm and to open new opportunities for studying the avian compass with quantum computing devices. Next we apply the same quantum algorithm to simulate open quantum dynamics based on the Generalized Quantum Master Equation (GQME). This approach overcomes the limitations of the Lindblad equation by providing a rigorous derivation of the equations of motion for any subset of elements of the reduced density matrix. We validate our quantum algorithm as applied to the spin-boson benchmark model by analyzing the impact of the quantum circuit depth on the accuracy of the results when the subset is limited to the diagonal elements of the reduced density matrix.  Our findings demonstrate that our approach yields reliable results on  noisy intermediate-scale quantum (NISQ) computers.</p>

京都大学 / 新制・課程博士 / 博士(理学) / 甲第24437号 / 理博第4936号 / 新制||理||1705(附属図書館) / 京都大学大学院理学研究科化学専攻 / (主査)教授 谷村 吉隆, 教授 林 重彦, 教授 鈴木 俊法 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

京都大学 / 新制・課程博士 / 博士(理学) / 甲第23717号 / 理博第4807号 / 新制||理||1688(附属図書館) / 京都大学大学院理学研究科化学専攻 / (主査)教授 谷村 吉隆, 教授 林 重彦, 教授 渡邊 一也 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

In this thesis we introduce a new quantity which we call the dynamic fidelity susceptibility (DFS). We show that it is relevant to out-of-equilibrium dynamics in many-particle quantum systems, taking the problem of an impurity in a Bosonic Josephson junction, and the transverse field Ising model, as examples. Both of these systems feature quantum phase transitions in their ground states and understanding the dynamics near such critical points is currently an active area of research. In particular, sweeping a system through a quantum critical point at finite speed leads to non-adiabatic dynamics. A simple theoretical tool for describing such a scenario is the celebrated Kibble-Zurek theory which predicts that the number of excitations is related to the speed of sweep via the phase transition’s critical exponents at equilibrium. Another theoretical tool, useful in describing the static properties of quantum phase transitions, is the fidelity susceptibility. Our DFS generalizes the concept of fidelity susceptibility to nonequilibrium dynamics, reproducing its results in the static limit, whilst also displaying universal scaling properties, akin to those found in Kibble-Zurek theory, in the non-adiabatic regime. Furthermore, we show that the DFS is the same quantity as the time-dependent quantum Fisher information which provides a measure of multi-partite entanglement, as well as being closely related to out-of-time-order correlators (OTOCs). / Thesis / Master of Science (MSc)

We study numerical methods for time-dependent partial differential equations describing wave propagation, primarily applied to problems in quantum dynamics governed by the time-dependent Schrödinger equation (TDSE). We consider both methods for spatial approximation and for time stepping. In most settings, numerical solution of the TDSE is more challenging than solving a hyperbolic wave equation. This is mainly because the dispersion relation of the TDSE makes it very sensitive to dispersion error, and infers a stringent time step restriction for standard explicit time stepping schemes. The TDSE is also often posed in high dimensions, where standard methods are intractable. The sensitivity to dispersion error makes spectral methods advantageous for the TDSE. We use spectral or pseudospectral methods in all except one of the included papers. In Paper III we improve and analyse the accuracy of the Fourier pseudospectral method applied to a problem with limited regularity, and in Paper V we construct a matrix-free spectral method for problems with non-trivial boundary conditions. Due to its stiffness, the TDSE is most often solved using exponential time integration. In this thesis we use exponential operator splitting and Krylov subspace methods. We rigorously prove convergence for force-gradient operator splitting methods in Paper IV. One way of making high-dimensional problems computationally tractable is low-rank approximation. In Paper VI we prove that a splitting method for dynamical low-rank approximation is robust to singular values in the approximation approaching zero, a situation which is difficult to handle since it implies strong curvature of the approximation space. / eSSENCE

Propriedades dinâmicas de sistemas quânticos de muitos corpos é um tópico de grande interesse em física da matéria condensada. Estas propriedades nos dão informação sobre a propagação de excitações elementares e de mecanismos de relaxação em sistemas interagentes. Neste contexto, as funções de correlação tem se tornado ainda mais relevantes devido a experimentos em sistemas de átomos frios e íons armadilhados que medem diretamente no domínio temporal os comportamentos assintóticos no tempo. No entanto, até o momento a maioria dos estudos em cadeias de spin quânticas focaram-se em correlações de um único spin. Utilizando a cadeia de spin XX unidimensional, nós estudamos métodos exatos para calcular as funções de correlação das componentes do tensor de dois spins, Tabi,j = SaiSbj. Estes operadores aparecem, por exemplo, como a resposta da seção de choque de espalhamento inelástico de raios X. Baseados no teorema de Wick, nós mostramos que algumas funções de correlação das componentes locais do tensor de dois operadores de spins de sítios vizinhos, na representação de férmions, podem ser escritas como uma combinação de funções de Green de uma única partícula. Utilizamos diagramas de Feynman para organizar esta combinação e calcular as funções de correlação. Em seguida, considerando esses propagadores para tempos longos e grandes distâncias ao longo do cone de luz, encontramos o comportamento dessas funções de correlação como leis de potência oscilatórias que decaem com o tempo e distância. Uma aplicação direta das funções de correlação é para o estudo de quantidades conservadas e não conservadas, uma análise sobre algumas dessas quantidades foi feita. Discutimos também as funções de correlação das componentes do tensor que não são locais na representação fermiônica. Nesse caso os cálculos foram mais desafiadores, mas usamos o fato que funções de correlação dependente do tempo podem ser expressadas em termos dos determinantes de Fredholm. / Dynamical properties of quantum many body systems is a major topic of interest in condensed matter physics. These properties tell us about the propagation of elementary excitation and mechanisms of relaxation in interacting systems. In this context correlation functions have became even more relevant due the experiments in systems of cold atoms and trapped ions that measure real time dependence directly out to relatively long times. However, most studies in quantum spins chains so far have focused on correlations of single spins. Using the one dimensional XX spin chain, we study exact methods to calculate the correlation functions of the components of the tensor operator involving two spins, Tabi,j = SaiSbj. This operator appear, for example, as a response of inelastic x-ray scattering cross section. Based on Wick\'s theorem, we show that some correlation functions of local components of the tensor operator of two pairs of neighbor sites, in the fermion space, can be written as a combination of Greens functions of a single particle. We have used Feynman diagrams to organize this combination and calculate the correlation functions. Then, considering these propagators for long times and large distances along the light cone, we found the behavior of these correlation functions as a oscillatory and power law decay on time. A direct application of correlation functions is to study conserved and non-conserved quantities, and such analysis has been made. We also considered other two-spin operators which are not local in the fermionic representation. In this case the calculation is more challenging, but the time-dependent correlation functions can be expressed in terms of Fredholm determinants.