Low-dimensional complex oxides offer new opportunities for small-scale electronic devices where diverse spin, charge and orbital correlations can be suitably adapted by manipulating many-body interactions, geometries, disorder, fields, strain, etc. Therefore, oxides may be viewed as one of the promising candidates for replacing semiconductors in future devices. Maintaining coherence and control in a qubit is an important necessity for quantum computation. In this review, we discuss an example of oxide devices: decoherence-free oxide-based qubits. We present recent progress in demonstrating that long coherence times can be achieved at easily accessible temperatures in charge qubits of oxide double quantum dots. For treating strong coupling to the environment, we describe a nonperturbative approach that is useful for oxides. We illustrate ways to enhance the coherence times: increasing the electron–phonon coupling, detuning the dots to a fraction of the optical phonon energy, decreasing the temperature or reducing the adiabaticity.
Low-dimensional complex oxides offer new opportunities for small-scale electronic devices where diverse spin, charge and orbital correlations can be suitably adapted by manipulating many-body interactions, geometries, disorder, fields, strain, etc. Therefore, oxides may be viewed as one of the promising candidates for replacing semiconductors in future devices. Maintaining coherence and control in a qubit is an important necessity for quantum computation. In this review, we discuss an example of oxide devices: decoherence-free oxide-based qubits. We present recent progress in demonstrating that long coherence times can be achieved at easily accessible temperatures in charge qubits of oxide double quantum dots. For treating strong coupling to the environment, we describe a nonperturbative approach that is useful for oxides. We illustrate ways to enhance the coherence times: increasing the electron–phonon coupling, detuning the dots to a fraction of the optical phonon energy, decreasing the temperature or reducing the adiabaticity.
Scalable fault-tolerant quantum computer architectures require quantum gates that operate within a small fraction of the qubit decoherence time and with high accuracy over a bandwidth set by the decoherence rate. Electron spin quantum bits in Si are promising because of long decoherence times (∼0.5 ms), but electrical gating schemes still seem problematic. Oxide–semiconductor heterostructures have the potential for precise electrical control of gate operations in the semiconductor, using optical rectification in the ferroelectric oxide. Accurate (∼80 dB), local (∼10 nm), dynamic (>THz) and programmable optical control over electric polarization in the ferroelectric can be achieved using existing technology. Optical techniques may also be useful in rapid initialization of the quantum computer, and for providing a source of initialized qubits to use for quantum error correction. Advantages of optical methods will be discussed within a framework proposed for a quantum information processor using ferroelectrically coupled electron spins and Ge quantum dots in Si.
The spin of an electron confined into a lateral semiconductor quantum dot has been proposed as a possible physical realization of a qubit. While the spin has the advantage of large decoherence times, operations with more than one qubit will necessarily involve orbital degrees of freedom, namely, charge, which is much more prone to decoherence. There are also alternative quantum dot qubit proposals that are entirely based on charge. We have used a realistic model to quantify the limitations imposed by acoustic phonons on the operation of quantum dot-based qubits. Our treatment includes essential aspects of the setup geometry, wave function profile and materials characteristics. The time dependence of the qubit density matrix is the presence of a phonon bath solved within the Born-Markov approximation. We find that the inclusion of geometric form factors makes the phonon-induced decoherence rates in double dot charge qubits nearly one order of magnitude lower than estimates previously in the literature. Moreover, our theoretical prediction for the quality factor of coherent charge oscillations based on phonon decoherence are higher than the values recently observed experimentally. This allows us to conclude that phonons are not the primary source of decoherence in double quantum dot qubits.
Since the development of microsized devices is moving forward at enormous speed, there is huge amount of new industrial opportunities. However such devices also require high precision and understanding of the operating of their constituent parts up to the quantum level. The device of the purely quantum nature being developed so far is quantum computer. However the physical realization of it is still not performed, as the requirements for it are very rigorous. \n \nIn the pioneering work by Loss and DiVincenzo it was suggested to use a spin of electron placed in a quantum dot as an information qubit. Following this work the study of electron or hole spin qubits developed. Both experimental and theoretical tools for studying them greatly advanced. \n \nIn the first part of the thesis we study the phonon-induced decoherence and relaxation of singlet-triplet qubits in the double quantum dots. First of all we consider AlGaAs/GaAs double quantum dots. The important result we present here is the strong dephasing that occurs at large detuning. This dephasing is due to two-phonon process that affects mainly singlet state of the qubit and consequently changes the splitting between singlet and triplet leading to dephasing. Remarkably at small detuning this dephasing process is suppressed and the decoherence time is by orders of magnitude longer than in case of large detuning and is mainly defined by one-phonon process. We also present the dependence of relaxation time and decoherence time on the strength of spin-orbit interaction and different directions of the system. Our results provide a deeper insight into the recently obtained experimental data. \n \nWe also studied Si/SiGe quantum dots as a potential candidate for a qubit. Apart from the absence of hyperfine interaction and bulk spin-orbit interaction in the isotopically purified 28Si, its electron-phonon interaction is different from GaAs that also leads to longer qubit lifetimes. We study S-T− qubit near the anticrossing of the basis states. This particular region is interesting due to possibilities in operating the qubit. We show that the type of singlet plays a crucial role, i.e. whether it is a singlet with each dot singly occupied or a singlet with only one dot doubly occupied. Depending on the type of singlet the qubit lifetimes change by several orders of magnitude. We also study the influence of a micromagnet, usually used in experiments to operate the qubit, on the relaxation time and decoherence time and present the regime where its effect is negligible. We suggest how to test experimentally our theory of one-phonon and two-phonon processes separately. We also show how the relaxation and decoherence time depend on different system parameters for S-T0 qubits. \n \nThe second part of the thesis is devoted to the other important constituent part of microsized devices, namely nanowires. We are interested in the dynamic of polarization of localized spins in the nanowires, as it can affect such important device characteristics as e.g. conductance. \n \nWe studied Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction-induced polarization in the nanowire in case when the voltage is applied to it. It was already proposed theoretically that in the ground state the localized spins in 1D systems align in a helix due to RKKY interaction. This polarization is still present until some critical temperature. The presence of such polarization acts as a spin filter for electrons, that most likely affects the conductance of the nanowire. Therefore we studied how this helical polarization changes when the voltage is applied. The key result is the appearance of the uniform polarization perpendicular to the helix plane, that occurs due to backscattering of electrons that is accompanied by flip-flop process with localized spins. When this uniform polarization is formed, the helix starts to rotate as a whole around the direction of the uniform polarization. We present the dependence of polarization of the localized spins on temperature and voltage. Remarkably the uniform polarization grows both with voltage and temperature in the given range of parameters. \n \nWe also considered the electron-induced relaxation of the nuclear spins. As the electron spins and nuclear spins interact via hyperfine interaction, the nuclear relaxation time reflects some properties of electron bath. Namely, we see a strong dependence of nuclear relaxation time on spin-orbit interaction strength. We present here the dependence of the nuclear relaxation time on the external magnetic field and chemical potential of the wire, that can be experimentally varied via gate. The dependences for the strong spin-orbit interaction and for the weak one are substantially different. Moreover, they have distinct peaks, that allow to get the value of spin-orbit interaction amplitude with the high precision.
Hole spin qubits in semiconductor quantum dots (QDs) are promising candidates for quantum information processing due to their weak hyperfine coupling to nuclear spins, and to the strong spin-orbit coupling, which allows for rapid operation time. We propose a coherent control on two heavy-hole spin qubits in a double QD by a fast adiabatic driving protocol, which helps to achieve higher fidelities than other experimentally commonly used protocols as linear ramping, $\ensuremath{\pi}$ pulses or Landau-Zener passages. Using fast quasiadiabatic driving via spin-orbit coupling, it is possible to reduce charge noise significantly for qubit manipulation and achieve high robustness for the qubit initialization. We also implement one- and two-qubit gates, in particular, not, cnot, and swaplike gates, of hole spins in a double QD achieving fidelities above $99\mathrm{%}$, exhibiting the capability of hole spins to implement universal gates for quantum computing.
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.
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