Hybrid optimization schemes for quantum control

Optimal control theory is a powerful tool for solving control problems in quantum mechanics, ranging from the control of chemical reactions to the implementation of gates in a quantum computer. Gradient-based optimization methods are able to find high fidelity controls, but require considerable numerical effort and often yield highly complex solutions. We propose here to employ a two-stage optimization scheme to significantly speed up convergence and achieve simpler controls. The control is initially parametrized using only a few free parameters, such that optimization in this pruned search space can be performed with a simplex method. The result, considered now simply as an arbitrary function on a time grid, is the starting point for further optimization with a gradient-based method that can quickly converge to high fidelities. We illustrate the success of this hybrid technique by optimizing a geometric phase gate for two superconducting transmon qubits coupled with a shared transmission line resonator, showing that a combination of Nelder-Mead simplex and Krotov’s method yields considerably better results than either one of the two methods alone.

Entanglement analysis of atomic processes and quantum registers

During recent years, quantum information processing and the study of N−qubit quantum systems have attracted a lot of interest, both in theory and experiment. Apart from the promise of performing efficient quantum information protocols, such as quantum key distribution, teleportation or quantum computation, however, these investigations also revealed a great deal of difficulties which still need to be resolved in practise. Quantum information protocols rely on the application of unitary and non–unitary quantum operations that act on a given set of quantum mechanical two-state systems (qubits) to form (entangled) states, in which the information is encoded. The overall system of qubits is often referred to as a quantum register. Today the entanglement in a quantum register is known as the key resource for many protocols of quantum computation and quantum information theory. However, despite the successful demonstration of several protocols, such as teleportation or quantum key distribution, there are still many open questions of how entanglement affects the efficiency of quantum algorithms or how it can be protected against noisy environments. To facilitate the simulation of such N−qubit quantum systems and the analysis of their entanglement properties, we have developed the Feynman program. The program package provides all necessary tools in order to define and to deal with quantum registers, quantum gates and quantum operations. Using an interactive and easily extendible design within the framework of the computer algebra system Maple, the Feynman program is a powerful toolbox not only for teaching the basic and more advanced concepts of quantum information but also for studying their physical realization in the future. To this end, the Feynman program implements a selection of algebraic separability criteria for bipartite and multipartite mixed states as well as the most frequently used entanglement measures from the literature. Additionally, the program supports the work with quantum operations and their associated (Jamiolkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. As an application of the developed tools we further present two case studies in which the entanglement of two atomic processes is investigated. In particular, we have studied the change of the electron-ion spin entanglement in atomic photoionization and the photon-photon polarization entanglement in the two-photon decay of hydrogen. The results show that both processes are, in principle, suitable for the creation and control of entanglement. Apart from process-specific parameters like initial atom polarization, it is mainly the process geometry which offers a simple and effective instrument to adjust the final state entanglement. Finally, for the case of the two-photon decay of hydrogenlike systems, we study the difference between nonlocal quantum correlations, as given by the violation of the Bell inequality and the concurrence as a true entanglement measure.

Development of hybrid UV VCSEL with organic active material and dielectric DBR mirrors for medical, sensoric and data storage applications

Lasers play an important role for medical, sensoric and data storage devices. This thesis is focused on design, technology development, fabrication and characterization of hybrid ultraviolet Vertical-Cavity Surface-Emitting Lasers (UV VCSEL) with organic laser-active material and inorganic distributed Bragg reflectors (DBR). Multilayer structures with different layer thicknesses, refractive indices and absorption coefficients of the inorganic materials were studied using theoretical model calculations. During the simulations the structure parameters such as materials and thicknesses have been varied. This procedure was repeated several times during the design optimization process including also the feedback from technology and characterization. Two types of VCSEL devices were investigated. The first is an index coupled structure consisting of bottom and top DBR dielectric mirrors. In the space in between them is the cavity, which includes active region and defines the spectral gain profile. In this configuration the maximum electrical field is concentrated in the cavity and can destroy the chemical structure of the active material. The second type of laser is a so called complex coupled VCSEL. In this structure the active material is placed not only in the cavity but also in parts of the DBR structure. The simulations show that such a distribution of the active material reduces the required pumping power for reaching lasing threshold. High efficiency is achieved by substituting the dielectric material with high refractive index for the periods closer to the cavity. The inorganic materials for the DBR mirrors have been deposited by Plasma- Enhanced Chemical Vapor Deposition (PECVD) and Dual Ion Beam Sputtering (DIBS) machines. Extended optimizations of the technological processes have been performed. All the processes are carried out in a clean room Class 1 and Class 10000. The optical properties and the thicknesses of the layers are measured in-situ by spectroscopic ellipsometry and spectroscopic reflectometry. The surface roughness is analyzed by atomic force microscopy (AFM) and images of the devices are taken with scanning electron microscope (SEM). The silicon dioxide (SiO2) and silicon nitride (Si3N4) layers deposited by the PECVD machine show defects of the material structure and have higher absorption in the ultra violet range compared to ion beam deposition (IBD). This results in low reflectivity of the DBR mirrors and also reduces the optical properties of the VCSEL devices. However PECVD has the advantage that the stress in the layers can be tuned and compensated, in contrast to IBD at the moment. A sputtering machine Ionsys 1000 produced by Roth&Rau company, is used for the deposition of silicon dioxide (SiO2), silicon nitride (Si3N4), aluminum oxide (Al2O3) and zirconium dioxide (ZrO2). The chamber is equipped with main (sputter) and assisted ion sources. The dielectric materials were optimized by introducing additional oxygen and nitrogen into the chamber. DBR mirrors with different material combinations were deposited. The measured optical properties of the fabricated multilayer structures show an excellent agreement with the results of theoretical model calculations. The layers deposited by puttering show high compressive stress. As an active region a novel organic material with spiro-linked molecules is used. Two different materials have been evaporated by utilizing a dye evaporation machine in the clean room of the department Makromolekulare Chemie und Molekulare Materialien (mmCmm). The Spiro-Octopus-1 organic material has a maximum emission at the wavelength λemission = 395 nm and the Spiro-Pphenal has a maximum emission at the wavelength λemission = 418 nm. Both of them have high refractive index and can be combined with low refractive index materials like silicon dioxide (SiO2). The sputtering method shows excellent optical quality of the deposited materials and high reflection of the multilayer structures. The bottom DBR mirrors for all VCSEL devices were deposited by the DIBS machine, whereas the top DBR mirror deposited either by PECVD or by combination of PECVD and DIBS. The fabricated VCSEL structures were optically pumped by nitrogen laser at wavelength λpumping = 337 nm. The emission was measured by spectrometer. A radiation of the VCSEL structure at wavelength 392 nm and 420 nm is observed.

Efficient Characterisation and Optimal Control of Open Quantum Systems - Mathematical Foundations and Physical Applications

Since no physical system can ever be completely isolated from its environment, the study of open quantum systems is pivotal to reliably and accurately control complex quantum systems. In practice, reliability of the control field needs to be confirmed via certification of the target evolution while accuracy requires the derivation of high-fidelity control schemes in the presence of decoherence. In the first part of this thesis an algebraic framework is presented that allows to determine the minimal requirements on the unique characterisation of arbitrary unitary gates in open quantum systems, independent on the particular physical implementation of the employed quantum device. To this end, a set of theorems is devised that can be used to assess whether a given set of input states on a quantum channel is sufficient to judge whether a desired unitary gate is realised. This allows to determine the minimal input for such a task, which proves to be, quite remarkably, independent of system size. These results allow to elucidate the fundamental limits regarding certification and tomography of open quantum systems. The combination of these insights with state-of-the-art Monte Carlo process certification techniques permits a significant improvement of the scaling when certifying arbitrary unitary gates. This improvement is not only restricted to quantum information devices where the basic information carrier is the qubit but it also extends to systems where the fundamental informational entities can be of arbitary dimensionality, the so-called qudits. The second part of this thesis concerns the impact of these findings from the point of view of Optimal Control Theory (OCT). OCT for quantum systems utilises concepts from engineering such as feedback and optimisation to engineer constructive and destructive interferences in order to steer a physical process in a desired direction. It turns out that the aforementioned mathematical findings allow to deduce novel optimisation functionals that significantly reduce not only the required memory for numerical control algorithms but also the total CPU time required to obtain a certain fidelity for the optimised process. The thesis concludes by discussing two problems of fundamental interest in quantum information processing from the point of view of optimal control - the preparation of pure states and the implementation of unitary gates in open quantum systems. For both cases specific physical examples are considered: for the former the vibrational cooling of molecules via optical pumping and for the latter a superconducting phase qudit implementation. In particular, it is illustrated how features of the environment can be exploited to reach the desired targets.

Large Numerical Models in Continuous Hybrid Simulation

Hybrid simulation is a technique that combines experimental and numerical testing and has been used for the last decades in the fields of aerospace, civil and mechanical engineering. During this time, most of the research has focused on developing algorithms and the necessary technology, including but not limited to, error minimisation techniques, phase lag compensation and faster hydraulic cylinders. However, one of the main shortcomings in hybrid simulation that has pre- vented its widespread use is the size of the numerical models and the effect that higher frequencies may have on the stability and accuracy of the simulation. The first chapter in this document provides an overview of the hybrid simulation method and the different hybrid simulation schemes, and the corresponding time integration algorithms, that are more commonly used in this field. The scope of this thesis is presented in more detail in chapter 2: a substructure algorithm, the Substep Force Feedback (Subfeed), is adapted in order to fulfil the necessary requirements in terms of speed. The effects of more complex models on the Subfeed are also studied in detail, and the improvements made are validated experimentally. Chapters 3 and 4 detail the methodologies that have been used in order to accomplish the objectives mentioned in the previous lines, listing the different cases of study and detailing the hardware and software used to experimentally validate them. The third chapter contains a brief introduction to a project, the DFG Subshake, whose data have been used as a starting point for the developments that are shown later in this thesis. The results obtained are presented in chapters 5 and 6, with the first of them focusing on purely numerical simulations while the second of them is more oriented towards a more practical application including experimental real-time hybrid simulation tests with large numerical models. Following the discussion of the developments in this thesis is a list of hardware and software requirements that have to be met in order to apply the methods described in this document, and they can be found in chapter 7. The last chapter, chapter 8, of this thesis focuses on conclusions and achievements extracted from the results, namely: the adaptation of the hybrid simulation algorithm Subfeed to be used in conjunction with large numerical models, the study of the effect of high frequencies on the substructure algorithm and experimental real-time hybrid simulation tests with vibrating subsystems using large numerical models and shake tables. A brief discussion of possible future research activities can be found in the concluding chapter.