This thesis focuses on pioneering a scalable route to fabricate quantum information devices based upon single InAs/InP quantum dots emitting in the telecommunications wavelength band around 1550 nm. Using metallic gates in combination with nanotemplate, site-selective epitaxy techniques, arrays of single quantum dots are produced and electrostatically tuned with a high degree of control over the electrical and optical properties of each individual quantum dot. Using metallic gates to apply local electric fields, the number of electrons within each quantum dot can be tuned and the nature of the optical recombination process controlled. Four electrostatic gates mounted along the sides of a square-based, pyramidal nanotemplate in combination with a flat metallic gate on the back of the InP substrate allow the application of electric fields in any direction across a single quantum dot. Using lateral fields provided by the metallic gates on the sidewalls of the pyramid and a vertical electric field able to control the charge state of the quantum dot, the exchange splitting of the exciton, trion and biexciton are measured as a function of gate voltage. A quadrupole electric field configuration is predicted to symmetrize the product of electron and hole wavefunctions within the dot, producing two degenerate exciton states from the two possible optical decay pathways of the biexciton. Building upon these capabilities, the anisotropic exchange splitting between the exciton states within the biexciton cascade is shown to be reversibly tuned through zero for the first time. We show direct control over the electron and hole wavefunction symmetry, thus enabling the entanglement of emitted photon pairs in asymmetric quantum dots. Optical spectroscopy of single InAs/InP quantum dots atop pyramidal nanotemplates in magnetic fields up to 28T is used to examine the dispersion of the s, p and d shell states. The g-factor and diamagnetic shift of the exciton and charged exciton states from over thirty single quantum dots are calculated from the spectra. The g-factor shows a generally linear dependence on dot emission energy, in agreement with previous work on this subject. A positive linear correlation between diamagnetic coefficient and g-factor is observed.

Logic gates are the fundamental building blocks of digital circuits. In this episode, we take a look at the four most basic gates: AND, OR, exclusive-OR, and the inverter, and show how an XOR gate can be used to compare two digital values. Click here to read the show transcript.

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This thesis deals with the possibilities of digital circuit test optimization using multifunctional logic gates. The most important part of this thesis is the explanation of the optimization principle, which is also described by a formal mathematical apparatus. Based on this apparatus, the work presents several options. The optimization of testability analogous to inserting test points and  simple methodology based on SCOAP is shown. The focus of work is a methodology created to optimize circuit tests. It was implemented in the form of software tools. Presented in this work are the results of using these tools to reduce the test vectors volume while maintaining fault coverage on various circuits, including circuits from the ISCAS 85 test set. Part of the work is devoted to the various principles and technology of creating multifunctional logic gates. Some selected gates of these technologies are subject to simulations of electronic properties in SPICE. Based on the principles of presented methodology and results of multifunctional gates simulations, analysis of various problems such as validity of the modified circuit test and the suitability of each multifunctional gate technology for the methodology was also made. The results of analysis and experiments confirm it is possible for the multifunctional logic gate to optimize circuit diagnostic properties in such a way that has achieved the required circuit test parameter modification with minimum impact on the quality and credibility of these tests.

We study the possibility of constructing quantum gates using topological phases, which originate from local SU(2) evolution of entangled multiqubit systems. For this purpose, logical codewords using two-, three- and nine-qubit entangled states are defined and possible implementations of topological gates on these codes, are examined. For two-qubit systems, it is shown that for only two of the Pauli gates, a topological implementation is possible, the third must be non-topological. Furthermore, it is shown that a topological implementation of Hadamard gate is also possible on the two-qubit code. For the three-qubit code, the logical Pauli gates are found to be topologically implementable and a topological implementation of the logical S gate seems to be possible as well. Lastly, for the nine-qubit code, the logical Pauli gates, the logical S gate and the logical T gate are shown to be implementable topologically on the code. It remains an open question whether topological implementation of logical Hadamard gate by invertible local operators is possible on the nine-qubit code.

This thesis is concerned with studying the fascinating quantum properties of real-world nanostructures embedded in a noisy condensed matter environment. The interaction with light is used for controlling and manipulating the quantum state of the systems considered here. In some instances, laser pulses also provide a way of actively probing and controlling environmental interactions. The first two research chapters assess two different ways of performing all-optical spin qubit gates in self-assembled quantum dots. The principal conclusion is that an `adiabatic' control technique holds the promise of achieving a high fidelity when all primary sources of decoherence are taken into account. In the next chapter, it is shown that an optically driven quantum dot exciton interacting with the phonons of the surrounding lattice acts as a heat pump. Further, a model is developed which predicts the temperature-dependent damping of Rabi oscillations caused by bulk phonons, finding an excellent agreement with experimental data. A different system is studied in the following chapter: two electron spin qubits with no direct interaction, yet both exchange-coupled to an optically active mediator spin. The results of this study show that these general assumptions are sufficient for generating controlled electron spin entanglement over a wide range of parameters, even in the presence of noise. Finally, the Radical Pair model of the avian compass is investigated in the light of recent experimental results, leading to the surprising prediction that the electron spin coherence time in this molecular system seems to approach the millisecond timescale.

Doctor of Philosophy / Electrical and Computer Engineering / Sanjoy Das / Quantum circuit synthesis is one of the major areas of current research in the field of quantum computing. Analogous to its Boolean counterpart, the task involves constructing arbitrary quantum gates using only those available within a small set of universal gates that can be realized physically. However, unlike the latter, there are an infinite number of single qubit quantum gates, all of which constitute the special unitary group SU(2). Realizing any given single qubit gate using a given universal gate family is a complex task. Although gates can be synthesized to arbitrary degree of precision as long as the set of finite strings of the gate family is a dense subset of SU(2), it is desirable to accomplish the highest level of precision using only the minimum number of universal gates within the string approximation. Almost all algorithms that have been proposed for this purpose are based on the Solovay-Kitaev algorithm. The crux of the Solovay-Kitaev algorithm is the use of a procedure to decompose a given quantum gate into a pair of group commutators with the pair being synthesized separately. The Solovay-Kitaev algorithm involves group commutator decomposition in a recursive manner, with a direct approximation of a gate into a string of universal gates being performed only at the last level, i.e. in the leaf nodes of the search tree representing the execution of the Solovay-Kitaev algorithm. The main contribution of this research is in integrating conventional optimization procedures within the Solovay-Kitaev algorithm. Two specific directions of research have been studied. Firstly, optimization is incorporated within the group commutator decomposition, so that a more optimal pair of group commutators are obtained. As the degree of precision of the synthesized gate is explicitly minimized by means of this optimization procedure, the enhanced algorithm allows for more accurate quantum gates to be synthesized than what the original Solovay-Kitaev algorithm achieves. Simulation results with random gates indicate that the obtained accuracy is an order of magnitude better than before. Two versions of the new algorithm are examined, with the optimization in the first version being invoked only at the bottom level of Solovay-Kitaev algorithm and when carried out across all levels of the search tree in the next. Extensive simulations show that the second version yields better results despite equivalent computation times. Theoretical analysis of the proposed algorithm is able to provide a more formal, quantitative explanation underlying the experimentally observed phenomena. The other direction of investigation of this research involves formulating the group commutator decomposition in the form of bi-criteria optimization. This phase of research relaxed the equality constraint in the previous approach and with relaxation, a bi-criteria optimization is proposed. This optimization algorithm is new and has been devised primarily when the objective needs to be relaxed in different stages. This bi-criteria approach is able to provide comparably accurate synthesis as the previous approach.

There remains limited research on the gap between the participation and persistence to graduation rates for American Indian students in higher education. It is pertinent to explore the experiences of these students who did not persist to graduation to be able to gain a better understanding of the factors involved in this gap. The primary purpose of this qualitative study was to gain a greater understanding of why twenty American Indian college students who were high-achieving and received the Gates Millennium scholarship (AIGMS) did not persist to graduation. To achieve this greater understanding from an Indigenous perspective, it was important to utilize existing theoretical frameworks developed by Native scholars that employed critical, culturally sensitive lenses for the analysis. Through the lenses of Tribal Critical Race Theory, Cultural Models of Education and the Family Education Model, the research questions were developed with a critical focus on the institutional influence of the participants' experiences. This study employed a phenomenological qualitative approach guided by an Indigenous research paradigm. The findings of this research inquiry were broken down into five main sections. The first section discussed the pre-collegiate experiences of AIGMS. This set of findings emerged throughout the interviews as participants shared their experiences in college, they often referred back to influential moments with their families and tribal communities leading up to college. The second section highlighted the conditions that impeded AIGMS' success in institutions of higher education. What emerged as the major factors of AIGMS' non persistence within higher education was GMSP's inflexible deferment policy and missing structures on campus to represent participants’ Native and Gates scholar identities, such as space for AIGMS to practice their cultural spirituality and direct support on campus for being a Gates scholar. The third section reveals the push-pull factors influential to AIGMS' experiences on campus and back home in their tribal communities. The main push factor from the institution was the lack of support they felt from key institutional agents, such as from a multicultural center director, financial aid officer or academic advisor. The fourth section describes the impact of the campus racial climate on AIGMS' experiences on their respective campuses. Some AIGMS assumed that being awarded this prestigious scholarship would be acknowledged either through their faculty or staff on campus. Instead they described examples of exclusion, lack of belonging, marginalization, isolation and invisibility on campus. The final section described the experiences of AIGMS who returned to higher education, including those who have found success in tribal colleges as well as those who have since completed their degrees without funding from GSMP. This finding is of particular importance because it demonstrates that the loss of financial aid affected the type of institution AIGMS' returned. Principally, AIGMS were thoughtful and rational about their decision to defer from higher education, taking into account the factors pulling them from outside the institution – such as family/medical/health issues. They were also impacted by their experiences within their institutions that pushed them out from within – such as experiences with invisibility and marginalization on campus. Faculty, institutional agents and their peers played into these experiences. The Gates Millennium Scholarship Program and institutions’ lack of cultural understanding of how to serve these AIGMS led to a disconnection with these students. These AIGMS’ experiences with push and pull factors places more responsibility on the institution and the scholarship program for their non-persistence.