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.

The past few decades of research and development in solid-state semicon ductor physics and electronics have witnessed a rapid growth in the drive to exploit quantum mechanics in the design and function of semiconductor devices. This has been fueled for instance by the remarkable advances in our ability to fabricate nanostructures such as quantum wells, quantum wires and quantum dots. Despite this contemporary focus on semiconductor "quantum devices," a principal quantum mechanical aspect of the electron - its spin has it accounts for an added quan largely been ignored (except in as much as tum mechanical degeneracy). In recent years, however, a new paradigm of electronics based on the spin degree of freedom of the electron has begun to emerge. This field of semiconductor "spintronics" (spin transport electron ics or spin-based electronics) places electron spin rather than charge at the very center of interest. The underlying basis for this new electronics is the intimate connection between the charge and spin degrees of freedom of the electron via the Pauli principle. A crucial implication of this relationship is that spin effects can often be accessed through the orbital properties of the electron in the solid state. Examples for this are optical measurements of the spin state based on the Faraday effect and spin-dependent transport measure ments such as giant magneto-resistance (GMR). In this manner, information can be encoded in not only the electron's charge but also in its spin state, i. e.

A Si:P electron-spin qubit architecture was developed in 2008, based upon research outcomes over the four-year QCCM grant. Single-shot spin readout will proceed via spin-dependent tunneling to a Si MOS rf-SET, which we have demonstrated to posses charge sensitivities equal to or better than Al rf-SETs. Spin manipulation will occur using local electron-spin resonance (ESR), which we have used to observe hyperfine-split electron spin resonances in P-doped Si MOSFETs. This spin qubit concept has been incorporated into the bi-linear array quantum computer design developed in parallel over 2004-2008 by the theory programs, which was one of the first quantum computer architectures quantitatively analyzed for the fault-tolerant threshold. Preliminary measurements on ion-implanted spin qubit devices have demonstrated transfer of P-donor electrons to a Si-SET detector with a large signal of ~0.2e, while tunneling structures have enabled transport spectroscopy of singly occupied (D0) and doubly occupied (D- ) P-donor electron states. These measurements are strongly supported by the NEMO-TCAD program allowing donor species and position to be determined through transport spectroscopy. Single-ion implantation using on-chip PIN detectors now routinely produces Si:P devices with accurately positioned single donors, such as a 2-P-atom charge qubit device, in which electron transfer events and charge-state relaxation times have been measured. Using STM atom-scale lithography the narrowest conducting doped wires in silicon have been demonstrated and used to fabricate the first in-plane-gated dot architecture. Measurements of these dots highlight the stability of in-plane gates compared with top gates and provide a pathway to atomically precise single donor architectures. Ab-initio and self-consistent tight-binding approaches have made progress in describing the essential physics of these highlydoped nanostructures.

This book highlights state-of-the-art qubit implementations in semiconductors and provides an extensive overview of this newly emerging field. Semiconductor nanostructures have huge potential as future quantum information devices as they provide various ways of qubit implementation (electron spin, electronic excitation) as well as a way to transfer quantum information from stationary qubits to flying qubits (photons). Therefore, this book unites contributions from leading experts in the field, reporting cutting-edge results on spin qubit preparation, read-out and transfer. The latest theoretical as well as experimental studies of decoherence in these quantum information systems are also provided. Novel demonstrations of complex flying qubit states and first applications of semiconductor-based quantum information devices are given, too.

Quantum mechanics, the subfield of physics that describes the behavior of very small (quantum) particles, provides the basis for a new paradigm of computing. First proposed in the 1980s as a way to improve computational modeling of quantum systems, the field of quantum computing has recently garnered significant attention due to progress in building small-scale devices. However, significant technical advances will be required before a large-scale, practical quantum computer can be achieved. Quantum Computing: Progress and Prospects provides an introduction to the field, including the unique characteristics and constraints of the technology, and assesses the feasibility and implications of creating a functional quantum computer capable of addressing real-world problems. This report considers hardware and software requirements, quantum algorithms, drivers of advances in quantum computing and quantum devices, benchmarks associated with relevant use cases, the time and resources required, and how to assess the probability of success.

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.

"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.

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.

The finding of algorithms for factoring and data base search that promise substantially increased computational power, as well as the expectation for efficient simulation of quantum systems have spawned an intense interest in the realization of quantum information processors [1]. Solid state implementations of quantum computers scaled to>1000 quantum bits ('qubits') promise to revolutionize information technology, but requirements with regard to sources of decoherence in solid state environments are sobering. Here, we briefly review basic approaches to impurity spin based qubits and present progress in our effort to form prototype qubit test structures. Since Kane's bold silicon based spin qubit proposal was first published in 1998 [2], several groups have taken up the challenge of fabricating elementary building blocks [3-5], and several exciting variations of single donor qubit schemes have emerged [6]. Single donor atoms, e. g. {sup 31}P, are 'natural quantum dots' in a silicon matrix, and the spins of electrons and nuclei of individual donor atoms are attractive two level systems for encoding of quantum information. The coupling to the solid state environment is weak, so that decoherence times are long (hours for nuclear spins, and {approx}60 ms for electron spins of isolated P atoms in silicon [7]), while control over individual spins for one qubit operations becomes possible when individual qubits are aligned to electrodes that allow shifting of electron spin resonances in global magnetic fields by application of control voltages. Two qubit operations require an interaction that couples, and entangles qubits. The exchange interaction, J, is a prime candidate for mediation of two qubit operations, since it can be turned on and off by variation of the wave function overlap between neighboring qubits, and coherent manipulation of quantum information with the exchange interaction alone has been shown to be universal [8]. However, detailed band structure calculations and theoretical analysis of J coupling between electrons bound to phosphorus atoms at low temperatures in silicon revealed strong oscillations of the coupling strength as a function of donor spacing on a sub-nm length scale [9]. These oscillations translate into scattering of interaction strength for ensembles of qubit spacings which in turn poses a serious obstacle to scalability [10]. Two alternatives to J coupling are dipolar coupling [11] and spin coherent shuttling of electrons between donor sites [12]. Readout of single electron spins poses another critical challenge [13, 14], and inferring spin orientations from charge measurements in spin dependent charge transfer reactions seems to be viable route to single shot single spin readout. This readout can be accomplished with single electron transistors, which are used as sensitive electrometers [15]. Impurity spin based qubit schemes in silicon have to overcome a significant nanofabrication challenge so that a test bed regime can be entered where fundamental properties and rudimentary operations can be investigated. In order to form such test devices, three key components have to be integrated: (1) an array of single dopant atoms has to be formed; (2) single dopant atoms are aligned to control gates; and (3) single dopant atoms are also aligned to a readout device.