Silicon quantum dots for quantum information processing

This thesis focuses on the development and demonstration of silicon metal-oxide-semiconductor (MOS) quantum dots (QDs) for spin-based quantum information processing. Firstly, by measuring the transport current through a MOS quantum dot, its multi-electron spin state was determined as the electron occupancy was reduced from twenty-seven electrons down to the single-electron limit. In particular, kinks observed in the electron addition energy as a function of magnetic field demonstrated that a valley-orbit excited state existed 100 μeV above the ground state. Secondly, by incorporating a silicon single-electron transistor (SET) charge sensor next to a quantum dot, the electron occupancy of the dot was probed via the sensor output signal. By applying a digitally-controlled dynamic feedback loop to the charge sensor, robust detection of the QD charge state was achieved, even in the presence of charge drifts and random charge upset events. Next, the excited states of a silicon MOS quantum dot were studied in detail. The electron occupancy and excited-state energy levels were detected using a SET charge sensor, with the aid of pulsed-voltage spectroscopy. The energy of the first orbital excited state was found to decrease rapidly as the electron occupancy increased from N = 1 to 4. By monitoring the sequential spin filling of the dot a valley splitting of ~230 μeV was extracted, which was found to be independent of electron number. Finally, by performing single-shot spin readout on a silicon MOS quantum dot, spin lifetimes were extracted for different electron occupancies and valley splitting configurations, with a maximum one-electron spin lifetime exceeding 2 seconds. We also demonstrated the ability to tune the valley splitting energy via electrostatic gate control, with a splitting that increased linearly with applied electric field over the range 0.3 - 0.8 meV. The spin relaxation rates were found to be highly dependent on the valley splitting energy, with a dramatic rate enhancement (or hot-spot) when the Zeeman and valley splittings coincided, a process that had not previously been anticipated for silicon quantum dots

Charge Offset Stability in Si Single Electron Devices with Al Gates

We report on the charge offset drift (time stability) in Si single electron devices (SEDs) defined with aluminum (Al) gates. The size of the charge offset drift (0.15 $e$) is intermediate between that of Al/AlO$_x$/Al tunnel junctions (greater than 1 $e$) and Si SEDs defined with Si gates (0.01 $e$). This range of values suggests that defects in the AlO$_x$ are the main cause of the charge offset drift instability

Accessing the Full Capabilities of Filter Functions: A Tool for Detailed Noise and Control Susceptibility Analysis

The filter function formalism from quantum control theory is typically used to determine the noise susceptibility of pulse sequences by looking at the overlap between the filter function of the sequence and the noise power spectral density. Importantly, the square modulus of the filter function is used for this method, hence directional and phase information is lost. In this work, we take advantage of the full filter function including directional and phase information. By decomposing the filter function with phase preservation before taking the modulus, we are able to consider the contributions to $x$-, $y$- and $z$-rotation separately. Continuously driven systems provide noise protection in the form of dynamical decoupling by cancelling low-frequency noise, however, generating control pulses synchronously with an arbitrary driving field is not trivial. Using the decomposed filter function we look at the controllability of a system under arbitrary driving fields, as well as the noise susceptibility, and also relate the filter function to the geometric formalism

Real-time feedback protocols for optimizing fault-tolerant two-qubit gate fidelities in a silicon spin system

Recently, several groups have demonstrated two-qubit gate fidelities in semiconductor spin qubit systems above 99%. Achieving this regime of fault-tolerant compatible high fidelities is nontrivial and requires exquisite stability and precise control over the different qubit parameters over an extended period of time. This can be done by efficiently calibrating qubit control parameters against different sources of micro- and macroscopic noise. Here, we present several single- and two-qubit parameter feedback protocols, optimised for and implemented in state-of-the-art fast FPGA hardware. Furthermore, we use wavelet-based analysis on the collected feedback data to gain insight into the different sources of noise in the system. Scalable feedback is an outstanding challenge and the presented implementation and analysis gives insight into the benefits and drawbacks of qubit parameter feedback, as feedback related overhead increases. This work demonstrates a pathway towards robust qubit parameter feedback and systematic noise analysis, crucial for mitigation strategies towards systematic high-fidelity qubit operation compatible with quantum error correction protocols

Spatio-temporal correlations of noise in MOS spin qubits

In quantum computing, characterising the full noise profile of qubits can aid the efforts towards increasing coherence times and fidelities by creating error mitigating techniques specific to the type of noise in the system, or by completely removing the sources of noise. Spin qubits in MOS quantum dots are exposed to noise originated from the complex glassy behaviour of two-level fluctuators, leading to non-trivial correlations between qubit properties both in space and time. With recent engineering progress, large amounts of data are being collected in typical spin qubit device experiments, and it is beneficiary to explore data analysis options inspired from fields of research that are experienced in managing large data sets, examples include astrophysics, finance and climate science. Here, we propose and demonstrate wavelet-based analysis techniques to decompose signals into both frequency and time components to gain a deeper insight into the sources of noise in our systems. We apply the analysis to a long feedback experiment performed on a state-of-the-art two-qubit system in a pair of SiMOS quantum dots. The observed correlations serve to identify common microscopic causes of noise, as well as to elucidate pathways for multi-qubit operation with a more scalable feedback system.Comment: updated referenc

Gate-based single-shot readout of spins in silicon

Electron spins in silicon quantum dots provide a promising route towards realizing the large number of coupled qubits required for a useful quantum processor 1–7 . For the implementation of quantum algorithms and error detection 8–10 , qubit measurements are ideally performed in a single shot, which is presently achieved using on-chip charge sensors, capacitively coupled to the quantum dots 11 . However, as the number of qubits is increased, this approach becomes impractical due to the footprint and complexity of the charge sensors, combined with the required proximity to the quantum dots 12 . Alternatively, the spin state can be measured directly by detecting the complex impedance of spin-dependent electron tunnelling between quantum dots 13–15 . This can be achieved using radiofrequency reflectometry on a single gate electrode defining the quantum dot itself 15–19 , significantly reducing the gate count and architectural complexity, but thus far it has not been possible to achieve single-shot spin readout using this technique. Here, we detect single electron tunnelling in a double quantum dot and demonstrate that gate-based sensing can be used to read out the electron spin state in a single shot, with an average readout fidelity of 73%. The result demonstrates a key step towards the readout of many spin qubits in parallel, using a compact gate design that will be needed for a large-scale semiconductor quantum processor