Abstract : Artificial two-level quantum systems are widely investigated as the fundamental building blocks of future quantum computers. These quantum bits (qubits) can be realized in many solid state systems, including Josephson junction based devices, nitrogen vacancy centers in diamond, and electron spins in semiconductor quantum dots. Among these systems, Si is very promising since it can be isotopically purified to eliminate random fluctuating hyperfine fields from lattice nuclei, leading to ultra-long quantum coherence times. However, lower heterostructure quality, higher electron effective mass and valley degeneracy present many challenges in realizing high quality qubits in Si. This thesis demonstrates consistent realization of robust single-electron silicon qubits with high yield. With optimized device designs and DC/RF measurement techniques developed at Petta lab in Princeton University, we have achieved versatile quantum control of a single electron, as well as sensitive read-out of its quantum state. By applying microwave radiation to the gate electrodes, we can probe the energy level structure of the system with 1 mu-eV resolution. We apply bursts of microwave radiation to extract the qubit lifetime, T1 . By experimentally tuning the qubit, we demonstrate a four order of magnitude variation of T1 with gate voltage. We show that our experimental results are consistent with a theory that takes into account phonon-mediated charge relaxation.
Abstract : Artificial two-level quantum systems are widely investigated as the fundamental building blocks of future quantum computers. These quantum bits (qubits) can be realized in many solid state systems, including Josephson junction based devices, nitrogen vacancy centers in diamond, and electron spins in semiconductor quantum dots. Among these systems, Si is very promising since it can be isotopically purified to eliminate random fluctuating hyperfine fields from lattice nuclei, leading to ultra-long quantum coherence times. However, lower heterostructure quality, higher electron effective mass and valley degeneracy present many challenges in realizing high quality qubits in Si. This thesis demonstrates consistent realization of robust single-electron silicon qubits with high yield. With optimized device designs and DC/RF measurement techniques developed at Petta lab in Princeton University, we have achieved versatile quantum control of a single electron, as well as sensitive read-out of its quantum state. By applying microwave radiation to the gate electrodes, we can probe the energy level structure of the system with 1 mu-eV resolution. We apply bursts of microwave radiation to extract the qubit lifetime, T1 . By experimentally tuning the qubit, we demonstrate a four order of magnitude variation of T1 with gate voltage. We show that our experimental results are consistent with a theory that takes into account phonon-mediated charge relaxation.
Logical qubits are essential for utility scale universal quantum computation and require stable, high-fidelity physical qubits. In this thesis we consider three factors that can affect the performance of phosphorus atom qubits in silicon. Specifically, we determined the number of phosphorus atoms in few-atom qubit registers using the charging energy. We then explored if a new silicon encapsulation recipe could reduce charge noise under realistic qubit operating conditions. Finally, we performed experiments on few qubit devices to identify the dominant causes of qubit decoherence. To attain high-fidelity control requires characterising the underlying atomic structure of qubit registers (≤4P). By combining precise (≤5% error) experimentally measured charging energies with high quality STM images and theoretically modelled charging energies, we show the number of phosphorus atoms present can be determined confidently. Previously, our all-epitaxial nat-Si devices have demonstrated record low charge noise (0.17µeV). In this thesis we consider a new Si-28 growth recipe to assess if introducing an annealed ∼1nm silicon locking layer grown at room temperature can further increase the silicon encapsulation quality, whilst minimising P segregation. We first optimised the geometry of SET charge sensors fabricated in Si-28 to obtain high current contrast (≫1nA). For the locking layer (standard recipe) single electron transistors we found high (low) levels of charge noise at 0V (2.1µeV) that increased with the applied voltage (at 0V (0.29µeV) and 0.5V (0.23µeV)). In addition, we found that the electrical behaviour of the locking layer sensors was highly sensitive to the applied voltage. Since qubits are typically operated at ∼0.5V, further work is needed to assess the viability of this new growth recipe. Finally, we investigated different charge and magnetic noise sources that cause qubit decoherence in a 3P register using a modified Hahn echo experiment. Here, we use resonant drive at the frequencies of different nuclear spin species to identify P-31 in the SET island as causing qubit decoherence. Further, we found that the dominant charge noise source for electron spin qubits was the Stark shift of the g-factor. We also found the spin flip rate of phosphorus nuclei in the spin bath was affected by a change in the mechanical noise coupling into the fridge. For nuclear spin qubits we found the dominant noise source to be the Stark shift of the hyperfine interaction.
Abstract : As classical computers begin to reach their fundamental performance limits, quantum computers will be an invaluable tool for the advance of science and technology. The trillion dollar silicon electronics industry sets the perfect stage for the evolution of quantum computation, yet it has so far proved to be a tough challenge to implement all the elements needed to build a scalable quantum computer in silicon. This thesis presents the first experimental demonstration of the full operation of single-spin qubits in Si. Our qubits consist of the electron and nuclear spins of a single phosphorus atom, implanted in a Si substrate, and controlled by a gated nanostructure. We describe an experimental setup tailored to minimise electron temperature and perform realtime data acquisition, analysis and instrument control. We present modeling, simulation and characterisation of a novel nanoscale coplanar antenna for spin control, designed to work at frequencies up to 50 GHz. These tools have allowed us to demonstrate the first ever single-atom spin-qubits in natural silicon, leading the way to demonstrating record qubit performances in isotopically purified 28Si: an electron spin qubit with measurement and control fidelities 97% and coherence times of 0.5 seconds; and a nuclear spin qubit with fidelities 99.99% and a record single-spin coherence of 30 s. We have performed noise spectroscopy in our system and concluded that decoherence is currently limited by magnetic noise originating from our broadband antenna.
Spin is a quantum mechanical property that describes the magnetic orientation of elementary and composite particles such as electrons and nuclei. For spin-half particles placed in a magnetic field, two states with differing energies are defined. Proposals exist for developing a revolutionary kind of computer that encodes bits of information on the states of a simple quantum two-level system - like those of a spin in a magnetic field. These quantum computers exploit the fundamental principles of quantum mechanics in order to perform certain calculations exponentially faster than their classical counterparts. Key to the development of such a device is the identification of potential systems that are suitable for employment as a quantum bit (qubit). This thesis explores quantum bits constructed from the spin states of single atoms hosted in silicon semiconductor devices. Silicon is an exceptional platform for spin-based quantum computing - in addition to being the dominant material in the microelectronic industry, it is also predominantly composed of nuclear spin-zero isotopes, providing very little background magnetic disturbance. The donor-atom phosphorus (31P) is investigated here. It possesses a nucleus that binds an additional electron to its positive charge, providing two distinct spin qubits. Here, several world-first experimental milestones in spin-based quantum information processing are reported. First, the readout of the electron spin is demonstrated in single-shot, using a silicon device which combines implanted phosphorus donors with a sensitive nanoscale electrometer. Then, the electron spin is coherently operated as a qubit by delivering on-chip microwave excitations. Combining the electron spin detection and control capabilities enables a quantum non-demolition measurement of the single 31P nuclear spin. Experiments yield exceptional nuclear readout fidelities - the highest for any solid-state qubit. Through an application of nuclear magnetic resonance, high-fidelity quantum control of the nuclear spin qubit is demonstrated. Finally, a single spin-bearing silicon nucleus (29Si) coupled to the electron spin is detected in single-shot and operated as a qubit. These results, along with the clear pathways identified for improving device performance, illustrate that single-atom electron and nuclear spin qubits in silicon constitute an excellent basis on which to construct a quantum computer.
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.
This dissertation describes a set of experiments with the goal of creating a super-conductor-semiconductor hybrid circuit quantum electrodynamics architecture with single electron spins. Single spins in silicon quantum dots have emerged as attractive qubits for quantum computation. However, how to scale up spin qubit systems remains an open question. The hybrid architecture considered here could provide a route to realizing large networks of quantum dot–based spin qubit registers. The first experiment in this thesis is aimed at achieving strong coupling between a single electron spin and a single microwave photon. The electron is trapped in a gate-defined double quantum dot in a Si/SiGe heterostructure and the photon is stored in an on-chip superconducting high-impedance NbTiN cavity. The photon is coupled directly to the electron charge, and indirectly to the electron spin, mediated through a synthetic spin-orbit field. We observe a vacuum Rabi splitting that depends on the spin-charge hybridization. The ratio of spin-photon coupling strength to decoherence rates of the spin and cavity combined is larger than unity, confirming the strong coupling regime has been reached. In addition, we find an optimal degree of spin-charge hybridization for which this ratio is maximized. The demonstration of strong spin-photon coupling not only opens a new range of physics experiments, but fulfills also a crucial requirement for coupling spin qubits at a distance via a cavity. The second experiment is focused on spin readout with the on-chip cavity. Instead of the direct dispersive readout of a single spin, we use the cavity to detect whether the electron is allowed to tunnel between the two dots or not. We benchmark the charge sensitivity and bandwidth of the detector and find that rapid detection of the electron charge with high SNR is possible. In the two-electron regime, electron tunneling is contingent on the total spin state (Pauli spin blockade). This spin-to-charge conversion scheme enables single-shot detection of singlet states with high-fidelity. The demonstration of single-shot spin readout with a cavity is an essential step towards readout in dense spin qubit arrays, such as the crossbar network, where it is not possible to integrate electrometers and accompanying reservoirs adjacent to the qubit dots. In the third experiment, we develop on-chip microwave filters to suppress microwave photon leakage from the cavity through the gate electrodes that are necessary to form quantum dots. We introduce a new cavity design that is compatible with long-distance connectivity between spins, but is also more susceptible to microwave leakage. We test and compare two low-pass filter variations in terms of performance, footprint and integrability. They use the same nanowire inductor, but different implementations of the capacitor: one with a planar interdigitated capacitor and one novel design with an overlapping thin-film capacitor. We find that both approaches are effective against microwave leakage. However, the large footprint of the interdigitated capacitor makes this solution inconvenient as the number of gate lines increases. The thin-film capacitor, with its much smaller footprint, is better suited for our devices. The final part of this dissertation contains concluding remarks and possible future directions are proposed.
Semiconductor quantum dots in silicon demonstrate exceptionally long spin lifetimes as qubits and are therefore promising candidates for quantum information processing. However, control and readout techniques for these devices have thus far employed low frequency electrons, in contrast to high speed temperature readout techniques used in other qubit architectures, and coupling between multiple quantum dot qubits has not been satisfactorily addressed.This dissertation presents the design and characterization of a semiconductor charge qubit based on double quantum dot in silicon with an integrated microwave resonator for control and readout. The 6 GHz resonator is designed to achieve strong coupling with the quantum dot qubit, allowing the use of circuit QED control and readout techniques which have not previously been applicable to semiconductor qubits. To achieve this coupling, this document demonstrates successful operation of a novel silicon double quantum dot design with a single active metallic layer and a coplanar stripline resonator with a bias tee for dc excitation.Experiments presented here demonstrate quantum localization and measurement of both electrons on the quantum dot and photons in the resonator. Further, it is shown that the resonator-qubit coupling in these devices is sufficient to reach the strong coupling regime of circuit QED. The details of a measurement setup capable of performing simultaneous low noise measurements of the resonator and quantum dot structure are also presented here.The ultimate aim of this research is to integrate the long coherence times observed in electron spins in silicon with the sophisticated readout architectures available in circuit QED based quantum information systems. This would allow superconducting qubits to be coupled directly to semiconductor qubits to create hybrid quantum systems with separate quantum memory and processing components.