My work on singlet-triplet spin qubits has bridged between the eras of two different semiconductors, gallium arsenide (GaAs) and silicon germanium (SiGe), that have been used in the Yacoby Lab. I have chosen to report my work in chronological order as it fits best with developments in the field but this leaves it with a structure inverted to most experimental physics theses with the main scientific achievements front loaded and the engineering stages at the end. The first chapter will provide background on spin qubits in semiconductors and will focus on major developments in singlet-triplet qubits that supported and motivated my own work. The second chapter discusses an advancement in two qubit coupling based on using large magnetic field gradients to mitigate charge noise. The third chapter is technical details about a new readout mechanism that allowed for the measurements presented in the second chapter. The fourth chapter discusses the transition from GaAs to SiGe and highlights the main difference between these two materials. The fifth chapter details the Crassula Quantum Dot Simulator that was written to aid in designing devices in SiGe. The sixth chapter discusses the progress made towards qubits in SiGe. The seventh chapter discusses overcoming the difficulties of RF reflectometry that are introduced by SiGe. The thesis concludes with experiment ideas that I was not able to complete before graduation but that I wish to note down so that some later generation of students may try them.
My work on singlet-triplet spin qubits has bridged between the eras of two different semiconductors, gallium arsenide (GaAs) and silicon germanium (SiGe), that have been used in the Yacoby Lab. I have chosen to report my work in chronological order as it fits best with developments in the field but this leaves it with a structure inverted to most experimental physics theses with the main scientific achievements front loaded and the engineering stages at the end. The first chapter will provide background on spin qubits in semiconductors and will focus on major developments in singlet-triplet qubits that supported and motivated my own work. The second chapter discusses an advancement in two qubit coupling based on using large magnetic field gradients to mitigate charge noise. The third chapter is technical details about a new readout mechanism that allowed for the measurements presented in the second chapter. The fourth chapter discusses the transition from GaAs to SiGe and highlights the main difference between these two materials. The fifth chapter details the Crassula Quantum Dot Simulator that was written to aid in designing devices in SiGe. The sixth chapter discusses the progress made towards qubits in SiGe. The seventh chapter discusses overcoming the difficulties of RF reflectometry that are introduced by SiGe. The thesis concludes with experiment ideas that I was not able to complete before graduation but that I wish to note down so that some later generation of students may try them.
There is a huge, worldwide effort to build a quantum computer due to its potential to perform chemical and materials simulations and to break current cryptography schemes. While there has been incredible progress in recent years, each potential platform still faces meaningful obstacles. The singlet-triplet qubit in gallium arsenide, which is based on electric spin, boasts several advantages, including fast single-gate times and readout, long lifetimes, and a clear path to large-scale integration using current semiconductor manufacturing techniques. However, it also suffers from electric and magnetic field noise that limits coherence time and weak two-qubit interactions, which have prevented the construction of multi-qubit systems so far. In this thesis, I will discuss my research measuring and working to improve noise and entangling gates in singlet-triplet qubits and will examine the viability of the singlet-triplet qubit as the building block for a quantum computer. \nBy measuring the dynamics of the electric and magnetic field noise that the singlet-triplet experiences, we can develop an understanding of their origins and how to reduce their impact. The singlet-triplet can be operated rapidly enough to use it as a sensor and directly measure the fluctuating magnetic field arising from the nuclear spins in the semiconductor heterostructure surrounding it. We use Hamiltonian parameter estimation, a technique that maximizes the rate at which we learn information, given the strange properties of quantum measurement, to measure magnetic noise to within 15 μT at a rate of 2 kHz, and we use these measurements to provide real-time feedback to system controls, increasing the coherence time by a factor of 30. Charge noise has much larger high-frequency components than magnetic noise, and thus requires use of dynamical decoupling methods borrowed from NMR to measure it. We measure its power spectrum up to 1 MHz and find that it has a 1/f spectrum. We perform these measurements for several different devices and have begun to determine how our growth and fabrication processes affect dephasing. \nPlacing a high-impedance resonator between two singlet-triplet qubits to mediate their interaction shows promise as way to create long-distance entanglement and to increase the speed of the entangling gate. We analyze this gate theoretically, finding that we expect the fidelity to be over 95%, with a straightforward path to increasing it to above 99% with improved resonator parameters. However, because the singlet-triplet qubit is extremely sensitive to changes in its electrostatic environment, which can be affected both by the resonator’s fabrication process and the presence of the proximal resonator gate, implementing this gate experimentally is challenging. We have developed processes for fabricating narrow, thin, NbN resonators directly adjacent to the double quantum dots that compose singlet-triplet qubits. These processes yield quantum dots that can be tuned into low-noise, stable singlet-triplet qubits, and superconducting resonators with impedances over 1 kOhm.
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.
Electron spins confined in semiconductor quantum dots are emerging as a promising system to study quantum information science and to perform sensitive metrology. Their weak interaction with the environment leads to long coherence times and robust storage for quantum information, and the intrinsic tunability of semiconductors allows for controllable operations, initialization, and readout of their quantum state. These spin qubits are also promising candidates for the building block for a scalable quantum information processor due to their prospects for scalability and miniaturization. owever, several obstacles limit the performance of quantum information experiments in these systems. For example, the weak coupling to the environment makes inter-qubit operations challenging, and a fluctuating nuclear magnetic field limits the performance of single-qubit operations.\n\n\n\nThe focus of this thesis will be several experiments which address some of the outstanding problems in semiconductor spin qubits, in particular, singlet-triplet (S-T0) qubits. We use these qubits to probe both the electric field and magnetic field noise that limit the performance of these qubits. The magnetic noise bath is probed with high bandwidth and precision using novel techniques borrowed from the field of Hamiltonian learning, which are effective due to the rapid control and readout available in S-T0 qubits. These findings allow us to effectively undo the undesired effects of the fluctuating nuclear magnetic field by tracking them in real-time, and we demonstrate a 30-fold improvement in the coherence time T2*.\n\n\n\nWe probe the voltage noise environment of the qubit using coherent qubit oscillations, which is partially enabled by control of the nuclear magnetic field. We find that the voltage noise bath is frequency- dependent, even at frequencies as high as 1MHz, and it shows surprising and, as of yet, unexplained temperature dependence. We leverage this knowledge of the voltage noise environment, the nuclear magnetic field control, as well as new techniques for calibrated measurement of the density matrix in a singlet-triplet qubit to entangle two adjacent single-triplet qubits. We fully characterize the generated entangled states and prove that they are, indeed, entangled.\n\n\n\nThis work opens new opportunities to use qubits as sensors for improved metrological capabilities, as well as for improved quantum information processing. The singlet-triplet qubit is unique in that it can be used to probe two fundamentally different noise baths, which are important for a large variety of solid state qubits. More specifically, this work establishes the singlet-triplet qubit as a viable candidate for the building block of a scalable quantum information processor.
There is currently a worldwide effort towards the realisation of large-scale quantum computers that exploit quantum phenomena for information processing. While these computing systems could potentially redefine the technological landscape, harnessing quantum effects is challenging due to their inherently fragile nature and the experimentally demanding environments in which they arise. In order for quantum computation to be viable it is first necessary to demonstrate the operation of two-level quantum systems (qubits) which have long coherence times, can be quickly read out, and can be controlled with high fidelity. Focusing on these key requirements, this thesis presents four experiments towards scalable solid state quantum computing using gate-defined quantum dot devices based on gallium arsenide (GaAs) heterostructures. The first experiment investigates a phonon emission process that limits the charge coherence in GaAs and potentially complicates the microwave control of multi-qubit devices. We show that this microwave analogy to Raman spectroscopy can provide a means of detecting the unique phonon spectral density created by a nanoscale device. Experimental results are compared to a theoretical model based on a non-Markovian master equation and approaches to suppressing electron-phonon coupling are discussed. The second experiment demonstrates a technique involving in-situ gate electrodes coupled to lumped-element resonators to provide high-bandwidth dispersive read-out of the state of a double quantum dot. We characterise the charge sensitivity of this method in the few-electron regime and benchmark its performance against quantum point contact charge sensors. The third experiment implements a low-loss, chip-level frequency multiplexing scheme for the readout of scaled-up spin qubit arrays. Dispersive gate-sensing is realised in combination with charge detection based on two radio frequency quantum point contacts to perform multiplexed readout of a double quantum dot in the few-electron regime. Demonstration of a 10-channel multiplexing device is achieved and limitations in scaling spin qubit readout to large numbers using multiplexed channels discussed. The final experiment ties previously presented results together by realising a micro-architecture for controlling and reading out qubits during the execution of a quantum algorithm. The basic principles of this architecture are demonstrated via the manipulation of a semiconductor qubit using control pulses that are cryogenically routed using a high-electron mobility transistor switching matrix controlled by a field programmable gate array. Finally, several technical results are also presented including the development of printed circuit board solutions to allow the high-frequency measurement of nanoscale devices at cryogenic temperatures and the design of on-chip interconnects used to suppress electromagnetic crosstalk in high-density spin qubit device architectures.
Charge separation from the (4,0) to the (3,1) state in a Si/SiGe double quantum dot is commonly used for initialization of spin qubits and Pauli-spin-blockade readout. It was used in recent experiments involving creation of the (3,1) singlet, and subsequent shuttling of one of the electrons. We present a theoretical description of the process of charge separation and singlet-triplet mixing, arriving at expressions for the singlet return probability that take into account experimentally observed finite probabilities of the creation of singlets with various patterns of valley occupations. In our analysis we focus on magnetic fields for which the electron spin Zeeman splitting is close to the valley splitting in one of the dots, when the spin-valley coupling causes a strong renormalization of the frequency of oscillations of singlet return probability. The latter effect has been recently used to perform valley splitting mapping by shuttling of one quantum dot to various locations with respect to the other. We give a detailed description of singlet-triplet dynamics near these spin-valley resonances and compare the results of calculations with measurements on double quantum dots in two distinct Si/SiGe heterostructures. Comparison of theory with experiments in which the presence of a few valley occupation patterns is visible, gives insight into the valley dependence of g-factors in these structures, providing support for a recently proposed theoretical model of this dependence. We also discuss how dephasing of singlet return probability oscillations near the spin-valley resonances is affected by valley splitting fluctuations caused by electric field noise.