Theoretical Issues In Silicon Quantum Dot Qubits

Electrically-gated quantum dots in semiconductors is an excellent architecture on which to make qubits for quantum information processing. Silicon is attractive because of the potential for excellent manipulability, scalability, and for integration with classical electronics. This thesis describes several aspects of the theoretical issues related to quantum dot qubits in silicon. It may be broadly divided into three parts -- (1) the hybrid qubit and quantum gates, (2) decoherence and (3) charge transport. In the first part, we present a novel architecture for a double quantum dot spin qubit, which we term the hybrid qubit, and demonstrate that implementing this qubit in silicon is feasible. Next, we consider both AC and DC quantum gating protocols and compare the optimal fidelities for these protocols that can be achieved for both the hybrid qubit and the more traditional singlet-triplet qubit. In the second part, we present evidence that silicon offers superior coherence properties by analyzing experimental data from which charge dephasing and spin relaxation times are extracted. We show that the internal degrees of freedom of the hybrid qubit enhance charge coherence, and demonstrate tunable spin loading of a quantum dot. In the last part, we explain three key features of spin-dependent transport -- spin blockade, lifetime-enhanced transport and spin-flip cotunneling. We explain how these features arise in the conventional two-electron as well as the unconventional three-electron regimes, using a theoretical model that captures the key characteristics observed in the data.

This thesis explores several different aspects in theoretical quantum computing, including problems in application, implementation and fundamental theories. First, we investigate the spin bus problem. We primarily focus on the non-local multi-qubit entanglement state generation and unitary gate construction using the new type of gates we proposed, the mediated gates. We build a complete set of toolbox to solve and optimize this problem using all the different mediated gates spin bus could offer. Specifically, we compare the quantum circuit efficiency with the conventional serial gate implementation method using a nearest-neighbor SWAP gate and demonstrate that in most cases, using mediate gates through a spin bus will provide a significant improvement in terms of circuit depth. As a consequence, it provides a viable and robust solution to the challenges we face when considering scalability in quantum circuits. We then turn our attention to a specific implementation of encoded logical qubit, the exchange-only qubit in a semiconductor triple quantum dot. It has plenty of advantages compare to other encoded qubit, such as fast gate operations via pure electrical control, and robustness against global magnetic noise when encoding happens in decoherence free subspace, etc. We show that there are more things we could do to further improve the quality of gate operations on such encoded logical qubits. The general idea is similar as in the context of singlet-triplet qubits and hybrid qubits. One thing is to take full advantage of the true ``sweet spot'' of its energy level diagram as the optimal working point, which provides protection against charge noise. The other is that we could optimize the tunnable parameters in the pulse sequence by taking into account the knowledge we have about the device, such as the strength of nuclear field bath (for GaAs triple quantum dot) and the dephasing rate. Our result shows the upper bounds you could anticipate for specific gate operations using DC pulse sequences. Finally, we discuss a more theoretically fundamental problem in quantum computation, the property of two partite entanglement space. We calculate the separability probability in the high dimensional space of two rebits, two qubits, and two quaterbits using Monte Carlo Sampling methods. Our results match the analytical conjecture almost perfectly for such three systems. Our method of probing such problems provides a simple but efficient way to explore the geometrical structure of high dimensional two partite system, such as the distribution of physical, separable and entanglement states. And the connection between our numerical simulations and the analytical conjecture proposed earlier might imply something more fundamental yet to be uncovered.

Quantum computing - leveraging quantum phenomena to perform complex and otherwise intractable computational problems - has rapidly progressed from a theoretical aspiration to a potential reality. Currently, there are many competing approaches to the way the physical qubits (quantum bits) are built, from trapped ions, to superconducting circuits, to semiconductor quantum dots, and beyond. Here, we focus on quantum dots, where electrons or holes are confined within a semiconductor and the quantized nature of charge and spin are utilized for computation. Within the field of quantum dots, heterostructures made of silicon and silicon-germanium are especially enticing due to their low density of defects and nuclear spin. Although quantum dots are a promising avenue for quantum computation because of their intrinsically small size and similarity to classical transistors, nearly every aspect of their design, realization, and control has yet to be fully optimized.This thesis explores modifications to the heterostructure, fabrication, and measurement of Si/SiGe quantum dots in the pursuit of improved quantum dot qubits. The valley splitting in silicon quantum dots, a near degeneracy of the lowest lying energy states, is critical to the formation and performance of silicon qubits. In this work, we present several modifications to the Si/SiGe heterostructure in an effort to enhance this splitting. In particular, we investigate the effects of introducing germanium to the silicon quantum well by the inclusion of a single spike in germanium concentration or an oscillatory concentration throughout the well. We present experimental measurements of the energy spectrum arising from both modifications and, coupled with theoretical support, demonstrate enhancements to the valley splitting. Next, we present several fabrication techniques with the goal of improved quantum dot functionality and lowered charge noise, a major barrier to higher quality devices. We report a new strategy for etched-palladium fabrication and discuss the current progress. Finally, we present work towards the automation of quantum dot tuning. As quantum dot devices increase in the number of qubits, so do the number of electrostatic gates which control the device. We discuss the development of automated tuning procedures and present a procedure for the formation of well-controlled quantum dots from initial voltage settings.

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.

Quantum computing has the potential to achieve better scaling for factoring large numbers, simulating quantum behavior of molecules, and sampling random number distributions. Quantum dot qubits in silicon show strong promise as a qubit platform due to the long decoherence times measured as well as the possibility of leveraging techniques from classical processor fabrication towards scaling to large qubit systems. We examine coupling quantum dot qubits to a superconducting coplanar waveguide, which functions as a single-photon resonator, and this system enables coherent communications between qubit systems. We are concerned with both the hardware and low-level software of quantum computation. We examine geometric modifications to the heterostructure and the electrode geometry to boost the capacitive coupling between a triple dot system and a resonator. We find decreasing the vertical separation between the electrode connected to the resonator and the dots has a positive impact on the coupling strength. Continuing hardware simulations, we consider the issue of low device yield in Si-MOS devices, where despite large singlet-triplet splittings, there was no evidence of Pauli spin blockade. We attributed this to impurities within the oxide and performed a series of simulations that allowed us to determine the required impurity density to lift spin blockade, and found this density consistent with the device yield. Switching to considering different qubit encodings, we compared and contrasted the behavior of three qubits that are resonantly coupled to a superconducting resonator. The three encodings were the charge dipole (CD) qubit, the charge quadrupole (CQ) qubit, and the quantum dot hybrid qubit (QDHQ). In terms of entangling a one photon state with a qubit state, the CD qubit and the CQ qubit behaved similarly, however the CQ qubit does allow arbitrary single qubit gates while being protected from quasistatic charge noise. The QDHQ exhibited better performance (measured by infidelity) when operated at a second-order-sweet spot than both other encodings in the typical charge noise regime. Furthermore, the quantum dot hybrid qubit enables multiple operating points, offering greater tuning flexibility when considering implementation in actual devices.

Despite knowing the fundamental equations in most of the physics research areas, still there is an unceasing need for theoretical method development, thanks to the more and more challenging problems addressed by the research community. The investigation of post-silicon, non-classical information processing is one of the new and rapidly developing areas that requires tremendous amount of theoretical support, new understanding, and accurate theoretical predictions. My thesis focuses on theoretical method development for solid-state quantum information processing, mainly in the field of point defect quantum bits (qubits) in silicon carbide (SiC) and diamond. Due to recent experimental breakthroughs in this field, there are diverse theoretical problems, ranging from functional development for accurate first principles description of point defects, through complete theoretical characterization of qubits, to the modeling and simulation of actual quantum information protocols, that are needed to be addressed. The included articles of this thesis cover the development of (i) hybrid-DFT+Vw approach for the first principles description of mixed correlated and uncorrelated systems, (ii) zero-field-splitting tensor calculation for solid-state quantum bit characterization, (iii) a comprehensive model for dynamic nuclear spin polarization of solid-state qubits in semiconductors, and (iv) group theoretical description of qubits and novel twodimensional materials for topologically protected states.

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.

Semiconductor Quantum Dots presents an overview of the background and recent developments in the rapidly growing field of ultrasmall semiconductor microcrystallites, in which the carrier confinement is sufficiently strong to allow only quantized states of the electrons and holes. The main emphasis of this book is the theoretical analysis of the confinement induced modifications of the optical and electronic properties of quantum dots in comparison with extended materials. The book develops the theoretical background material for the analysis of carrier quantum-confinement effects, introduces the different confinement regimes for relative or center-of-mass motion quantization of the electron-hole-pairs, and gives an overview of the best approximation schemes for each regime. A detailed discussion of the carrier states in quantum dots is presented and surface polarization instabilities are analyzed, leading to the self-trapping of carriers near the surface of the dots. The influence of spin-orbit coupling on the quantum-confined carrier states is discussed. The linear and nonlinear optical properties of small and large quantum dots are studied in detail and the influence of the quantum-dot size distribution in many realistic samples is outlined. Phonons in quantum dots as well as the influence of external electric or magnetic fields are also discussed. Last but not least the recent developments dealing with regular systems of quantum dots are also reviewed. All things included, this is an important piece of work on semiconductor quantum dots not to be dismissed by serious researchers and physicists.

The concept of quantum computing is based on two fundamental principles of quantum mechanics: superposition and entanglement. Instead of using bits, qubits are used in quantum computing, which is a key indicator in the high level of safety and security this type of cryptography ensures. If interfered with or eavesdropped in, qubits will delete or refuse to send, which keeps the information safe. This is vital in the current era where sensitive and important personal information can be digitally shared online. In computer networks, a large amount of data is transferred worldwide daily, including anything from military plans to a country’s sensitive information, and data breaches can be disastrous. This is where quantum cryptography comes into play. By not being dependent on computational power, it can easily replace classical cryptography. Limitations and Future Applications of Quantum Cryptography is a critical reference that provides knowledge on the basics of IoT infrastructure using quantum cryptography, the differences between classical and quantum cryptography, and the future aspects and developments in this field. The chapters cover themes that span from the usage of quantum cryptography in healthcare, to forensics, and more. While highlighting topics such as 5G networks, image processing, algorithms, and quantum machine learning, this book is ideally intended for security professionals, IoT developers, computer scientists, practitioners, researchers, academicians, and students interested in the most recent research on quantum computing.