Quantum Computing With Spin Qubits In Lithium Doped Silicon

Quantum information processing (QIP) is one of the most promising and exciting areas of nanoscience and nanotechnology. Silicon-based quantum computers have become popular candidates for QIP partly because the needed nanoscale manufacturing techniques are well-established for modern silicon electronics. Furthermore, electron spins bound to donors in Si have proven to be some of the most, if not the most, coherent quantum structures among proposed solid state QIP systems to date. Unfortunately, a serious obstacle impeding the physical implementation of quantum computing technology is the ability to readily control quantum bits (qubits). The unique inverted electronic structure of the lithium donor in silicon makes these quantum structures not only strongly coherent, but also readily manipulable. The goal of this work is the development of a complete quantum computing scheme allowing for electrical and piezoelastic control of lithium spin qubits in silicon. To achieve our goal and to enable electrical control of lithium spin qubits, we study the effect of a static electric field on lithium donor spins in silicon. We demonstrate that the anisotropy of the effective mass leads to the anisotropy of the quadratic Stark susceptibility. Using the Dalgarno-Lewis exact summation method, we are able to calculate the Stark susceptibilities and analyze several important physical effects. We show the energy level shifts due to the quadratic Stark effect are equivalent to, and can be mapped onto, those produced by an external stress. Furthermore, we show the energy level shifts, combined with the unique valley-orbit splitting of the Li donor in Si, spin-orbit interaction and specially tuned external stress, leads to a very strong modulation of the donor spin g-factor and electron spin resonance (ESR) lines by the electric field. We propose a complete quantum computing scheme based on Li donors in Si. With the system under external biaxial stress, the qubits are encoded on a ground state Zeeman doublet and arc coupled via the acoustic-phonon-mediated long-range spin-spin interaction. We utilize g-factor control of the qubits to perform a specially-designed sequence of electric field impulses in order to execute both the cz gate and the universal CNOT gate. Using the quadratic Stark effect calculations and electron-phonon decoherence times, we estimate that the typical two-qubit gate time is on the order of ~ 1 [us] with a quality factor of [~ 10 -6]. A possible extension to these results is the piezoelastic control of spin qubits in semiconductors, which may open new avenues in solid state quantum information processing. This work has been supported by the following agencies: the National Security Agency (NSA), the Army Research Office (ARO) and the National Aeronautics and Space Administration (NASA).

The project goals are to fabricate qubits in quantum dots in Si/SiGe modulation-doped heterostructures, to characterize and understand those structures, and to develop the technology necessary for a Si/SiGe quantum dot quantum computer. The physical qubit in our approach is the spin of an electron confined in a top-gated silicon quantum dot in a Si/SiGe modulation-doped heterostructure. Operations on such a qubit may be performed by controlling the voltages on gates in-between neighboring quantum dots. A quantum computer and qubits in silicon offer potential advantages, both fundamental and practical. Electron spins in silicon quantum dots are expected to have long coherence times. Silicon has an isotope, Si, which has zero nuclear spin and thus no nuclear magnetic moment. As a result, electron spins in silicon have longer coherence times than they would in the presence of a fluctuating nuclear spin background. From a practical perspective, modern classical computers are made in silicon, and one hopes that this will lead to synergy in the future with a silicon quantum computer. This QCCM includes both theory and experiment focusing on (i) the development of qubits in the form of electron spins in silicon quantum dots, (ii) the measurement and manipulation of those qubits, and (iii) the science essential for understanding the properties of such qubits.

Nuclear spins are highly coherent quantum objects that were featured in early ideas and demonstrations of quantum information processing. In silicon, the high-fidelity coherent control of a single phosphorus (31-P) nuclear spin I=1/2 has demonstrated record-breaking coherence times, entanglement, and weak measurements. In this thesis, we demonstrate the coherent quantum control of a single antimony (123-Sb) donor atom, whose higher nuclear spin I = 7/2 corresponds to eight nuclear spin states. However, rather than conventional nuclear magnetic resonance (NMR), we employ nuclear electric resonance (NER) to drive nuclear spin transitions using localized electric fields produced within a silicon nanoelectronic device. This method exploits an idea first proposed in 1961 but never realized experimentally with a single nucleus, nor in a non-polar crystal such as silicon. We then present a realistic proposal to construct a chaotic driven top from the nuclear spin of 123-Sb. Signatures of chaos are expected to arise for experimentally realizable parameters of the system, allowing the study of the relation between quantum decoherence and classical chaos, and the observation of dynamical tunneling. These results show that high-spin quadrupolar nuclei could be deployed as chaotic models, strain sensors, hybrid spin-mechanical quantum systems, and quantum-computing elements using all-electrical controls.

In the race for quantum computing, these last years silicon has become a material of choice for the implementation of spin qubits. Such devices are fabricated in CEA using CMOS technologies, in order to facilitate their large-scale integration. This thesis covers the modeling of these qubits andin particular the manipulation of the spin state with an electric field. To that end, we use a set numerical tools to compute the potential and electronic structure in the qubits (in particular tightbinding and k.p methods), in order to be as close as possible to the experimental devices. These simulations allowed us to study two important experimental results: on one hand the observation of the electrical manipulation of an electron spin, and on the other hand the characterization of the anisotropy of the Rabi frequency of a hole spin qubit. The first one was rather unexpected, since the spin-orbit coupling is very low in the silicon conduction band. We develop a model, confirmed by thesimulations and some experimental results, that highlights the essential role of the intervalley spinorbit coupling, enhanced by the low symmetry of the system. We use these results to propose and test numerically a scheme for electrical manipulation which consists in switching reversibly betweena spin qubit and a valley qubit. Concerning the hole qubits, the relatively large spin-orbit coupling allows for electrical spin manipulation. However the experimental measurements of Rabi frequency anisotropy show a complex physics, insufficiently described by the usual models. Therefore we developa formalism which allows to characterize simply the Rabi frequency as a function of the magnetic field, and that can be applied to other types of spin-orbit qubits. The simulations reproduce the experimental features, underline the important role of strain.

"Electron spins in gate-defined quantum dots have emerged as a leading candidate for quantum-information-processing applications, including quantum computation. Long coherence times and compatibility with conventional semiconductor-manufacturing techniques contribute to the appeal of implementing these devices as quantum bits, or qubits. Recent research efforts have demonstrated many of the fundamental requirements for their utilization in a future quantum processor. Despite this, further development in the performance of these devices is necessary if the goal is truly to realize a universal quantum computer. Improvements will likely come in the form of both device-engineering advancements as well as novel qubit-operation and qubit-measurement schemes. This thesis describes a number of experiments carried out in gate-defined quantum dots in Si/SiGe, including demonstrations of high-fidelity spin-measurement, multiple studies of environmental noise, and coherent control of electron-spin qubits. This work represents the first realization of such devices in the Nichol Group at the University of Rochester. Together, the results represent the advancement of our understanding of silicon-based quantum dots and spin qubits"--Page xii.

Nanomagnetism is a rapidly expanding area of research which appears to be able to provide novel applications. Magnetic molecules are at the very bottom of the possible size of nanomagnets and they provide a unique opportunity to observe the coexistence of classical and quantum properties. The discovery in the early 90's that a cluster comprising twelve manganese ions shows hysteresis of molecular origin, and later proved evidence of quantum effects, opened a new research area which is still flourishing through the collaboration of chemists and physicists. This book is the first attempt to cover in detail the new area of molecular nanomagnetism, for which no other book is available. In fact research and review articles, and book chapters are the only tools available for newcomers and the experts in the field. It is written by the chemists originators and by a theorist who has been one of the protagonists of the development of the field, and is explicitly addressed to an audience of chemists and physicists, aiming to use a language suitable for the two communities.

This book provides a self-contained undergraduate course on quantum computing based on classroom-tested lecture notes. It reviews the fundamentals of quantum mechanics from the double-slit experiment to entanglement, before progressing to the basics of qubits, quantum gates, quantum circuits, quantum key distribution, and some of the famous quantum algorithms. As well as covering quantum gates in depth, it also describes promising platforms for their physical implementation, along with error correction, and topological quantum computing. With quantum computing expanding rapidly in the private sector, understanding quantum computing has never been so important for graduates entering the workplace or PhD programs. Assuming minimal background knowledge, this book is highly accessible, with rigorous step-by-step explanations of the principles behind quantum computation, further reading, and end-of-chapter exercises, ensuring that undergraduate students in physics and engineering emerge well prepared for the future.

This volume presents information about several topics in the field of electron paramagnetic resonance (EPR) study of carbon-containing nanomaterials. It introduces the reader to an array of experimental and theoretical approaches for the analysis of paramagnetic centers (dangling bonds, interface defects, vacancies, and impurities) usually observed in modern carbon-containing materials such as nanographites, graphene, disordered onion-like carbon nanospheres (DOLCNS), single-walled carbon nanotubes (SWCNTs), multi-walled carbon nanotubes (MWCNT), graphene oxide (GO), reduced graphene oxide (rGO), nanodiamonds, silicon carbonitride (SiCN) and silicon carbide (SiC) based composites and thin films. In particular, the book describes in detail: • The fundamentals of EPR spectroscopy and its application to the carbon-containing materials; • The resolution of the EPR signals from different species in carbon materials; • EPR characterization of spin dynamics in carbon nanomaterials; • Magnetic properties of DWCNTs and MWCNTs polymer composites; • EPR investigations on GO, rGO and CNTs with different chemical functionalities; • EPR spectroscopy of semiconducting SWCNTs thin films and their transistors; • In-situ EPR investigations of the oxygenation processes in coal and graphene materials; • The two-temperature EPR measurement method applied to carbonaceous solids; • Characterization of impurities in nanodiamonds and SiC nanomaterials and related size effects by CW and pulse EPR techniques; • Application of multifrequency EPR to the study of paramagnetic defects in a-Si1-xCx:H thin films and a-SiCxNy based composites. This volume is a useful guide for researchers interested in the EPR study of paramagnetic centers in the carbon-containing thin films, nanomaterials, ceramics, etc. It is also a valuable teaching tool at graduate and postgraduate levels for advanced courses in analytical chemistry, applied sciences and spectroscopy.