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(2023)ThesisSilicon spin qubits are strong candidates in the efforts to build a universal quantum computer. They can be fabricated on the nanometer scale, have low noise and long coherence times. To date, efforts for fabricating donor quantum dots in silicon have only focused on two qubits or less. Presented in this thesis is the design, fabrication, and measurement of a twenty-quantum dot Si:P device, the basis of a 10-qubit singlet-triplet architecture. To individually address each qubit, we designed and manufactured superconducting NbTiN frequency division multiplexing chips. These chips were demonstrated to be reproducible and could be used to readout up to 20 quantum dots using only one input and one output line, an important step for increasing device scalability. This multiplexing chip was characterised under magnetic field and used to demonstrate single shot readout of the 𝑆−𝑇− state with 90% readout fidelity using in-situ gate-based dispersive readout, the highest fidelity readout to date for this system. We then fabricated the largest integrated Si:P qubit circuit using scanning tunnelling microscope (STM) lithography to date, five times larger than previous devices. This scale-up required improvements to the manufacturing process, including extension of electron beam lithography capabilities for defining ohmic structures. A custom cryogenic printed circuit board was designed for the device and demonstrated to have low crosstalk of less than -40 dB up to 4 GHz. The device was characterised at millikelvin in a dilution fridge with charge readout performed on 8 of the 10 double dots. Finally, a scalable measurement system based on the PCI eXtensions for Instrumentation (PXI) platform was created, enabling simultaneous multitone digital signal generation and filtering. This system reduced the hardware requirements of previous analogue setups by 80% and enabled four times better signal to noise (SNR) ratio for charge readout as a result of improved low pass digital filtering. The first demonstration of simultaneous readout of neighbouring qubits in the Si:P platform is presented and used to correlate noise sources in the device showing that noise is strongly correlated across four double dots separated by 300 nm.
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(2023)ThesisQuantum networks are the quantum analogue of the modern internet, offering the ability to employ more secure protocols than modern communication. At the base of these quantum networks are so-called qubits: physical entities that can be in a simultaneous superposition of two states. For quantum networks, qubits should contain states that can be optically accessed and can store quantum properties for a long time. Nowadays, a number of qubit platforms exist, with spin qubits in Si offering long coherence times due to the low number of nuclear spins in the host crystal. Si is a widely used semiconductor in modern electronic devices and the maturated micro- and nanofabrication techniques can be exploited to miniaturise quantum devices. Additionally, Si and SiO2 form an attractive photonic material system because they provide a large contrast in the refractive index, which is critical for achieving efficient optical confinement. To minimise the photon losses and leverage on the well-established telecommunication networks, the photons excited from the spin states should emit within the telecommunication C-band. In this sense, Er3+:Si is an attractive system because Er3+ ions exhibit a spin transition that can be accessed by photons with frequencies within the telecommunication C-band. Moreover, the optical transition of Er3+ takes place within an inner shell, meaning that the outer shells electrically shield this transition, resulting in narrow and stable optical transitions within the telecommunication C-band. The upper bounds on the coherence times of the optical and spin transitions of Er3+:Si are, thus far, still unknown. In this thesis, these optical and spin properties of Er3+ ions in Si are investigated with the aim to create an interface between a spin qubit and a flying qubit. Here, the optical measurements include the extraction of inhomogeneous and homogeneous broadening of Er3+:Si over various samples, observing linewidths down to less than 100 MHz and 500 kHz, respectively. The low Er3+ density in natural Si samples showed characteristics of long-lived electron spin states for two sites. The electron spin coherence time of an Er3+ site in a nuclear-spin-free Si crystal was measured to be 0.5 ms by employing a Hahn echo sequence, and this was further extended up to 9 ms using a Carr–Purcell Meiboom–Gill sequence. These optical and spin properties establish that Er3+:Si exhibits fundamentally promising properties for quantum networks.
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(2023)ThesisStrongly correlated materials can display exotic quantum phenomena relevant to the emergence of quantum technologies. Yet, many questions have remained open because of the difficulty in modelling the underlying physics beyond a few lattice sizes. Therefore, a continuing effort has been made to develop quantum simulation platforms, where these many-body states can be artificially emulated with a great degree of control in bespoke hardware implementations. This thesis focuses on the use of dopant-based atomic-scale devices in silicon to build artificial quantum matter probed by a low-temperature scanning tunnelling microscope (STM). We combine STM hydrogen lithography with phosphine doping for the placement of phosphorus donors in our silicon devices with atomic precision and perform spatially resolved measurements using the STM tip. We first establish the experimental platform by characterising strongly correlated states found in single and pairs of quantum dots made of a few donors each. Using these building blocks, we create devices based on dimerised chains to perform an analogue quantum simulation of the Su-Schrieffer-Hegger model, a topological quantum system that classical computers cannot solve effectively. As a preliminary result, we demonstrate the formation of 25 nm-long electronic bands in chains of 5 and 7 sites. These results demonstrate the viability of using silicon as a base for the realisation of Fermi-Hubbard analogue quantum simulators inside a low-temperature STM, with the tip as a tuneable local probe.
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(2022)ThesisIn this thesis we assess the design and optimisation of critical device requirements for the realisation of three qubit parity error detection in donor spin qubits in silicon. Three key results are presented: (i) the capacitative modelling and design of triple donor dot architectures needed to realise a parity device, highlighting the need for multi-donor quantum dots (ii) optimisation of the geometry of the donor charge sensor and noise levels required for reproducible high fidelity spin readout, and (iii) understanding how the configurations of the additional donor nuclear spins in these multi-donor dots impact the electron spin resonance (ESR) spectra observed and how this will affect the operation of the parity measurement. Using electrostatic simulations of the different device geometries we show that either a 1P-2P-1P or 1P-3P-1P configuration of donors in each of the individual quantum dots is needed to achieve the required (1,1)↔(2,0) equivalent interdot charge transitions with the available gate space. Using such a higher donor number ancilla qubit, we then compared the sequence of logical gates required to perform the parity measurement using single qubit rotations and different 2-qubit gates. This analysis highlighted the need for isotopically pure silicon-28 to maintain coherence within the time frame of the measurement and stable, high fidelity single shot spin read-out. We then conducted a series of experiments of how to achieve stable, high fidelity single shot spin read out in our triple dot devices. It is known that read-out fidelity is improved by increasing the signal to noise of the charge sensor and by reducing the electron temperature. As such we investigated two triple dot device designs to investigate the interplay between these two requirements. The first design had the donor dots tunnel coupled to the single electron transistor (SET) charge sensor and the second had the donor dots capacitively coupled to an independent reservoir 50nm away from the SET charge sensor. We showed that under high bias of the SET (1mV) where we achieve a good signal to noise (1nA) of the charge sensor, electron-electron interactions within the tunnel coupled SET lead to heating of the qubits (680mK) compared with the independent reservoir qubits (170mK). Ultimately we showed that this heating limits spin read-out fidelities at high power where the signal to noise of the charge sensor is greatest. We simulated the spin readout fidelity for both designs and found the independent reservoir parity design can achieve above 99% fidelities over a greater range of SET resistances (up to 10MΩ) and tunnel rates (up to 100kHz), whereas the tunnel coupled design is limited to ≈100kΩ SET resistances with tunnel rates below 100Hz. i To further investigate the reproducibility of our SET charge sensors we then investigated the optimal tunnel barrier dimensions in a series of STM-patterned devices to achieve high fidelity single shot spin read-out. We found a simple width dependent exponential model describes the optimal tunnel barrier lengths for different lead widths. For tunnel barriers with 6±0.5nm lead widths, tunnel gap lengths of 11±0.5nm were found to give reliable SET resistances of 100KΩ optimal for providing good S/N. We then measured the charge noise in several SET devices and found that charge noise is correlated with high (> 350W) powers on the SUSI cell giving rise to an increase in pressure in the growth chamber (> 1×10−10mbar). We investigated the impact of charge noise on the ability to perform high fidelity spin readout and determined a noise threshold limit (0.03meV2) to achieve fidelities above 99%. In the final chapter we integrated an antenna on a triple dot device aiming for a 1,3,1 donor dot configuration. Using a detailed analysis of STM image height profiles, charging energies from gate-gate maps, capacitance triangulation and T1 measurements we determined that the final donor number was 0,3,2 indicating that no donor had incorporated in the lefthand dot. Despite this we were able to perform single shot spin read-out of the middle (≈92%) and right dots (92%) and confirmed the donor number of the right dot to be a 2P donor molecule using ESR resonance spectrum. We measured different hyperfine couplings of A1 = 189MHz and A2 = 83MHz to each of the donors within the dot, which under different slightly electric fields of 3.2MV/m and 3.8MV/m gave rise to a Stark shift of 41±31MHz/(MV/m). Using the ESR spectra, Stark shift measurements and tight binding simulations of the donor hyperfine Hamiltonian we are able to locate the exact configuration of the phosphorus atoms within the 2P donor molecule with the second donor being [0.5 1.5 0]a0 from the first donor. From these results we identified that a (3,2) donor configuration for the ancilla/data qubit does provide an equivalent (1,1) ↔ (2,0) interdot charge transitions with the available gate space. We then present a detailed outlook, with specific device recommendations as to how to achieve the parity measurement in donor qubits going forward.
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(2023)ThesisIn the pursuit of realising a full-scale universal quantum computer, the phosphorus donor in silicon platform provides a simple, low magnetic and low charge noise environment. In this thesis we consider the singlet-triplet (T0) qubit encoding in this system which allows for fast all electrical control. In a first scalable, double quantum dot design, we optimised the readout circuit to achieve single-shot single-gate RF dispersive readout of the singlet and triplet (T-) states with a fidelity of 90% at 5 kHz bandwidth. By atomic engineering of the donor number and positions, we optimised the tunnel coupling between the two dots to 3 GHz, ideal to observe coherent interaction of the qubit states. However surprisingly this was not observed due to the fast relaxation rate (>1 MHz) of the triplet T0 to the singlet ground state. This fast rate is a result of the large difference in Zeeman energy between the two electrons (ΔEZ ~ 200 MHz) present which induces mixing between the triplet T0 and singlet states, exceeding the readout bandwidth of the dispersive sensor. Motivated by this discovery, we designed 2 different charges sensors to map the short-lived triplet (1,1)T0 state to a longer lived (2,1) charge state in a process called latched readout. In the first device, we designed a novel single lead quantum dot (SLQD) sensor. Despite realising an operational sensor, the charge noise in this device was found to be too high. In the second device, we used an single electron transistor (SET) charge sensor where we were able to demonstrate latched readout for the first time in the Si:P platform with a fidelity of 99.7%. We showed that the latched method is robust at higher temperatures, with a 97.1% fidelity measured at 3.7 K. Using this sensor we were able to observe coherent oscillations around the Z-axis of an all donor singlet-triplet qubit with a coherence time of T2*~ 23 ns. Finally the role of phosphorus donor nuclear spins on X-gate operations are discussed.