At the dawn of the twentieth century, the underpinnings of centuries-old classical physics were beginning to be unravelled by the advent of quantum mechanics. As well as fundamentally shifting the way we understand the very nature of reality, this quantum revolution has subsequently shaped and created entire fields, paving the way for previously unimaginable technology. The quintessential instance of such technology is the quantum computer, whose building blocks - quantum bits, or qubits - are premised on the uniquely quantum principles of superposition and entanglement. It is predicted that quantum computers will be capable of efficiently solving certain classically intractable problems. To build a quantum computer, it is necessary to find a system which exhibits these uniquely quantum phenomena. The success of silicon-based integrated circuits for classical computing made semiconductors an obvious architecture in which to focus experimental quantum computing efforts. The two-dimensional electron gas which forms at the interface of GaAs/AlGaAs heterostructures constitutes an ideal platform for isolating and controlling single electrons, encoding quantum information in their spin and charge states. This thesis broadly addresses three key challenges to quantum computing with GaAs qubits: scalability, particularly in the context of readout, unwanted interactions between fragile quantum states and their environment, and the facilitation of controllable, strong interactions between separated qubits as a means of generating entanglement. These significant, unavoidable challenges must be addressed in order for a future solid-state quantum computer to be viable.
At the dawn of the twentieth century, the underpinnings of centuries-old classical physics were beginning to be unravelled by the advent of quantum mechanics. As well as fundamentally shifting the way we understand the very nature of reality, this quantum revolution has subsequently shaped and created entire fields, paving the way for previously unimaginable technology. The quintessential instance of such technology is the quantum computer, whose building blocks - quantum bits, or qubits - are premised on the uniquely quantum principles of superposition and entanglement. It is predicted that quantum computers will be capable of efficiently solving certain classically intractable problems. To build a quantum computer, it is necessary to find a system which exhibits these uniquely quantum phenomena. The success of silicon-based integrated circuits for classical computing made semiconductors an obvious architecture in which to focus experimental quantum computing efforts. The two-dimensional electron gas which forms at the interface of GaAs/AlGaAs heterostructures constitutes an ideal platform for isolating and controlling single electrons, encoding quantum information in their spin and charge states. This thesis broadly addresses three key challenges to quantum computing with GaAs qubits: scalability, particularly in the context of readout, unwanted interactions between fragile quantum states and their environment, and the facilitation of controllable, strong interactions between separated qubits as a means of generating entanglement. These significant, unavoidable challenges must be addressed in order for a future solid-state quantum computer to be viable.
The understanding of quantum mechanics enabled the development of technology such as transistors and has been the foundation of today’s information age. Actively using quantum mechanics to build quantum technology may cause a second revolution in handling information. However, to execute meaningful algorithms, largescale quantum computers have to be built. Such systems are constructed from many qubits, the quantum version of the classical bit. While exciting progress is being made across a range of different qubit platforms, achieving the radical scalability that is necessary to build a largescale processor could be a roadblock. Huge challenges are put on reproducibility, inand output connectivity and material quality. Qubits based on the spins of electrons and holes confined in semiconductor quantum dots may have an important advantage in constructing quantum processors. This platform can profit from the advanced semiconductor industry that was responsible for the first computing revolution. Group IV semiconductors such as silicon and germanium have a high compatibility with industrial semiconductor manufacturing and contain stable isotopes with zero nuclear spin. The materials can be isotopically purified and serve as excellent hosts for spins with long quantum coherence. In Chapter 3 we present quantum dot arrays in silicon metaloxidesemiconductor (SiMOS), strained silicon (Si/SiGe) and strained germanium (Ge/SiGe). A nearly identical integration scheme based on an overlapping gate structure can be used to define quantum dots in each platform. Each platform has its own opportunities, which are carefully assessed. By employing charge sensing we confirm that all quantum dots can be depleted to the singleelectron regime. We compare capacitive crosstalk and find it to be the smallest in SiMOS, relevant for the tuning of quantum dot arrays. Using this crossplatform integration, we can study qubits in each platform with minimal overhead. Long coherence times, excellent singlequbit gate fidelities and twoqubit logic have been demonstrated with SiMOS spin qubits, making it one of the leading platforms for quantum information processing. However, due to the high disorder at the Si/SiO2 interface compared to Ge/SiGe and Si/SiGe interface, quantum dots defined in SiMOS are small and achieving sufficient control over single electrons has been a long standing challenge. In Chapter 5 we show experiments on a double quantum dot that can be isolated from its reservoir. We demonstrate a tunable tunnel coupling between single electrons up to 13 GHz and tunable tunnel rates down to below 1 Hz. These results mark an important step towards the required degree of control over the location of and coupling between quantum dots, necessary for the operation of a large array.
Quantum computing represents a transformative leap in computational power, capable of solving problems beyond the reach of classical computers. This chapter focuses on the crucial role of semiconductor advancements in developing quantum computing, highlighting key technological breakthroughs and engineering challenges. It begins with an overview of quantum computing principles, emphasizing qubits' unique properties like superposition and entanglement, which enable parallel computations. The chapter then delves into semiconductor-based qubits, including silicon-based quantum dots, superconducting qubits, and spin qubits, exploring their operational principles, fabrication techniques, and performance metrics. It also examines material science innovations such as isotopically purified silicon and silicon-germanium heterostructures, essential for qubit stability and scalability. Additionally, the chapter addresses engineering challenges like quantum error correction and the integration of quantum and classical computing systems.
The computer industry has seen an immense development in the last decades. \nPersonal computers have become available for everybody living in industrialized \ncountries with rapidly increasing performance in terms of speed and storage capacities. \nHowever, the performance of nowadays' computers is fundamentally limited by the \nlaws of classical physics: a classical bit can only take on either of the two distinct \nvalues `0' or `1'. \nIn contrast, a quantum computer could, in principle, make direct use \nof quantum phenomena, such as state superpositions \n-- a quantum bit can be in both states `0' and `1' simultaneously --, \nto perform complex computational tasks much faster than any classical computer. \n \nThe idea of building computers that work according to the laws of quantum physics \nhas opened various fields of research, one of which is the search for the best \nphysical system to use as a quantum bit (qubit). One important criterion for determining \nthe optimal qubit system is the lifetime of state superpositions. \nTypically, once initialized, such superpositions are destroyed on remarkably short \ntimescales due to interactions with the environment -- a process which is referred to \nas decoherence --, posing the question which physical qubit candidate system might show a high-enough robustness against the \ninfluence of the `outside world' to allow for viable quantum computation. \n \nIn this thesis, we will consider three particular realizations of one specific and \nvery promising type of qubit candidate system: \nan electron (or hole) confined to a quantum dot -- a nanoscale structure \nwithin a (typically semiconducting) material --, where the spin states `down' \nand `up' of our electron (or hole) encode the logical states `0' and `1'. \nOur task will be to study the decay of spin-state superpositions in such quantum-dot \nsystems. The main objective of this thesis is to understand the most important physical \nprocesses that lead to spin decoherence and to show ways to suppress this undesirable effect. \nIt turns out that at low temperatures, the main source of decoherence \nis the coupling of the electron (hole) to the surrounding nuclear spins. \n \nThis thesis is divided into three logical parts, corresponding to the three qubit candidate \nsystems under consideration. First we will study electron-spin qubits in III-V semiconductor \nquantum dots, where the electron spin interacts with the nuclear spins of the semiconducting \nhost material \nvia the isotropic Fermi contact hyperfine interaction. Second we consider quantum-dot-confined \nheavy holes and the decoherence of their (pseudo-)spin states due to anisotropic interactions with the \nnuclear spins. Third and last, we study electron-spin qubits made from carbon-nanotube and \ngraphene quantum dots. Quantum dots made of carbon have the advantage of a low abundance \nof spin-carrying nuclear isotopes, therefore reducing decoherence effects significantly. \n \nFor each of the systems under consideration, we will carry out analytical calculations on \nthe nuclear-spin interactions and the spin dynamics of the qubit. Although one main goal of \nthis thesis is to show ways to extend spin decoherence times, we will also focus on physically more \nfundamental questions. Not only the timescale of the decay is relevant for \nthe system's applicability as a qubit, but also the form of the decay which can vary \nsignificantly from system to system. For example, the decay of spin-state superpositions \ncan follow an exponential, super-exponential or power-law decay, and can even pass through \nvarious stages. This is not only of academic interest, but also important for practical \npurposes, such as the implementation of quantum error-correction schemes in a potential \nquantum computer. \n
Quantum physics describes the universe on a microscopic scale. Even though this scale is not accessible without complex experimental setups, quantum effects are respon- sible for the properties of matter and in some instances we have learned to exploit them technologically. A modern computer constituted of transistors passively utilizes the quantum nature of charge carriers in the band structure of semiconductors to encode and process information. Although such a classical computer is a formidable tool already, what could be achieved with active control over the quantum states in the computer is an intriguing question. This is the idea of the quantum computer, which offers an entirely new paradigm of computing by encoding information in quantum binary digits (qubits). Indeed, for several applications it has been shown that a quantum computer is superior to its classical counterpart, even though its realization remains elusive up to date. One candidate to host qubits are gate-defined semiconductor quantum dots, confin- ing single or few charge carriers with spin. The spin of a single confined electron is a quantum two-level system which can be manipulated and measured, allowing the storage and processing of quantum information. This thesis can be viewed as part of the endeavor to give birth to quantum computers based on semiconductor spin qubits. It primarily focuses on the challenge to enable scalable architectures of well-characterized qubits. In the first part, spin shuttling is investigated. This denotes the coherent transport of a single spin between spatially separate nodes of a quantum processor, driven by a time-dependent electric potential. The object of study is a minimal version of a bucket- brigade-like spin shuttling between two quantum dots. The probability of maintaining the spin state is identified as figure of merit and the effect of spin-orbit interaction and the Zeeman effect in an inhomogeneous magnetic field is explored with analytical and numerical methods. Special attention is paid to the repercussions of near-degenerate valleys. The second part of the thesis addresses the challenge to probe the microscopic properties of a quantum dot array, which is a crucial first step before any quantum operation can be performed. The transmission of a microwave resonator coupled to a triple quantum dot occupied by two electrons is investigated, and a scheme to infer the exchange interaction between electrons in adjacent quantum dots is proposed. By means of analytical derivations it is shown that the transmission profile of the resonator directly reveals the value of the exchange coupling strength between two electrons. This holds even if magnetic gradients or a valley splitting comparable to the inter-dot tunnel coupling are included. Subsequently, quantum transport measurements in the Pauli blockade regime are modelled in the presence of a microwave resonator, bringing together two powerful techniques to probe quantum dots. Based on generalized input-output theory, a theoretical framework is derived to investigate how a double quantum dot in a transport setup interacts with a coupled microwave resonator while the current through the double qauntum dot is rectified by Pauli blockade. It is shown that the output field of the resonator can be used to infer the leakage current and thus obtain insight into the blockade mechanisms and to estimate a large number of parameters of the quantum dots. Furthermore, the back-action of the resonator photons on the steady state leakage current is described and quantified. In the context of Pauli blockade, the spin and valley physics of bilayer graphene quantum dots in the few-electron regime is touched upon, describing a situation where spin blockade is observed despite the presence of the valleys. In the final part of the thesis, the attention is shifted towards the readout of the spin qubits. A new paradigm of dispersive readout is devised, which is performed while the qubit dephases, implementing a measurement in the x-basis. Laplace transforming the time dependent cavity response allows a separation of contributions from multiple qubits coupled to the same resonator. Thus, they can be read out simultaneously in a single shot. Modelling silicon spin qubits, as an example, results in in a readout time that compares favourably to conventional dispersive readout with comparable fidelity, even for a single qubit. With an auxiliary qubit the readout scheme can be extended to a quantum non-demolition measurement.
A quantum computer would exploit the phenomena of quantum superposition and entanglement in its functioning and with them offer pathways to solving problems that are too hard or complex to even the best classical computers built today. The implementation of a large-scale working quantum computer could bring about a change in our society rivaling the one started by the digital computer. However, the field is still in its infancy and there are many theoretical and practical issues needing to be solved before large-scale quantum computing can become reality. In digital computers, data is stored in bits. The quantum equivalent is called a qubit (quantum bit) and it is basically a quantum mechanical two-level system that can be in a superposition of its two basis states. There are many different proposals for implementing qubits, but one of the most promising ones is to encode the qubit using electron spins trapped in semiconductor quantum dots. Singlet-triplet qubits are spin qubits where the two-electron spin eigenstates are used as the qubit's basis. The required one and two-qubit operations have already been demonstrated experimentally by several research groups around the world in this qubit architecture. The most severe factor limiting the implementation of larger systems of qubits is decoherence. The qubits are not isolated systems, they interact with their environment, which can lead to the loss of quantum information. Few-electron systems can be simulated accurately using first principle methods that become too taxing when the particle number increases. The topic of this thesis is the simulation of quantum dot singlet-triplet qubit systems using accurate exact diagonalization based methods. The emphasis is on the realistic description of qubit operations, both single-qubit ones and those involving the interaction between neighboring qubits. The decoherence effects are also discussed alongside with certain proposals to alleviate their effects.
The recent discovery of efficient quantum algorithms for factoring and database search has shown that quantum computing would allow to solve important problems which are intractable with conventional computers. In contrast to the very demanding task of building a large-scale quantum computer, there are quantum communication protocols, e.g. quantum key distribution for cryptography, which—though still difficult—require much less effort and can be implemented with current technology. Apart from the technological motivation, the study of quantum information offers (at least) two additional benefits. First, new insight into fundamental questions on quantum mechanics, e.g. concerning non-locality and entanglement, are gained from an information-theoretical approach. And second, investigating a particular physical implementation of quantum information can give rise to independent physical results. Spintronics, the use of spin as opposed to charge in (classical) electronics is a new field for which some results presented here could be relevant. In this dissertation we investigate several theoretical aspects of the physical implementation of quantum computation and communication in which the fundamental unit of quantum information, the qubit, is represented by the spin of electrons in semiconductor quantum dots. The required coupling between the spins can be obtained by allowing for tunneling of electrons between adjacent dots, leading to a Heisenberg exchange coupling J S1 · S2 between the spins, a scenario which we study for laterally coupled quantum dots in a two-dimensional electron system, and for a three-dimensional setup with vertically coupled quantum dots. Furthermore, an alternative scheme to couple the spins via the interaction with an optical cavity mode is presented. Quantum error correction represents one of the important ingredients for the physical implementation of a quantum computer by protecting \nit from the e�ects of a noisy environment. As a �rst test for errorcorrection \nin a solid-state device using spins, we propose an optimized \nimplementation of the most primitive error correction scheme (the threebit \ncode). In this context, we introduce parallel switching, allowing \nto operate a quantum computer more e�ciently than the usual serial \nswitching. \nCoupling spins with the exchange interaction J S1 �S2 is not su�cient \nfor quantum computation; the spins also have to be addressed individually \nusing controllable local magnetic �elds or g-factors giBi �Si in order \nto allow for single-qubit operations. On the one hand, we discuss several \nschemes for overcoming the di�culty of applying local magnetic �elds \n(requiring large gradients), e.g. g-factor engineering, which allows for \nall-electric operation of the device. On the other hand, we show that \nat the expense of additional devices (spins) and switching operations, \nsingle-spin rotations can be dispensed with completely. \nAddressing the feasibility of quantum communication with entangled \nelectrons in mesoscopic wires, i.e. interacting many-body environments, \nwe propose an interference experiment using a scattering set-up with an \nentangler and a beam splitter. The current noise for electronic singlet \nstates turns out to be enhanced (bunching), while it is reduced for triplets \n(antibunching). Due to interactions, the �delity of the entangled singlet \nand triplet states is reduced by z4F \nin a conductor described by Fermi \nliquid theory, zF being the quasiparticle weight factor. \nFinally, we study the related but more general problem of the noise of \nthe cotunneling current through one or several tunnel-coupled quantum \ndots in the Coulomb blockade regime. The various regimes of weak and \nstrong, elastic and inelastic cotunneling are analyzed for quantum-dot \nsystems (QDS) with few-level, nearly-degenerate, and continuous electronic \nspectra. In contrast to sequential tunneling, the noise in inelastic \ncotunneling can be super-Poissonian. In order to investigate strong cotunneling \nwe develop a microscopic theory of cotunneling based on the \ndensity-operator formalism and using the projection operator technique. \nWe have derived the master equation for the QDS and the current and \nnoise in cotunneling in terms of the stationary state of the QDS. These \nresults are then applied to QDS with a nearly degenerate and continuous \nspectrum.