Quantum computers can solve specific problems with practical applications efficiently faster than classical computers. Spin qubits in semiconductor quantum dots are one of the most promising physical realizations of the quantum computers. This thesis aims to investigate the dynamics of semiconductor spin qubits in their actual environment. Specifically, we aim to understand how the actual environment of the spin qubits give rise to nonlinear response of the qubits to external driving, crosstalk, dephasing (T2 processes), and the temperature-dependence of the qubit frequency.
Chapter 3 reports on experimental observation of the nonlinear response of the spin qubits to external driving as well as the crosstalk effect, where the Rabi frequency of an adjacent qubit changes as the target qubit is driven. We propose a phenomenological model that relates the external drivings to the observed dynamics of the spin qubits. The physical mechanism that give rise to these phenomena could not be reproduced in our analysis.
Given the progress in reducing noise sources in the spin qubits environment, it is pertinent to investigate the dephasing of spin qubits in a sparse bath of defects. In Chapter 4, we theoretically investigate the qubit dephasing, as measured in the Ramsey and Hahn echo experiments, in a sparse bath of two-level fluctuators (TLFs) with 1/f spectral density. We find that although the spectral density remains approximately unchanged, the coherence times become more variable as the bath becomes more sparse. We also find that in a sparse bath the qubit decoherence is dominated by only a fraction of TLF defects. Removing these defects results in a significant improvement of the coherence times.
Chapter 5 explores the potential of a bath of TLFs in elucidating the frequency shifts of spin qubits with temperature and the temperature insensitivity of Ramsey and echo decay times. These effects have been observed in experiments. By tuning the bath parameters, we are able to replicate the observed qubit frequency shift. However, our simulations reveal a decrease in qubit decoherence with temperature, which is inconsistent with the experimental findings.
On the whole, Chapters 3 and 5 aim to refine the models that we use to describe the dynamics of spin qubit in their environment. On the other hand, the theoretical work in Chapter 4 is inspired by the experimental observation of the variability of qubit decoherence and offers suggestions to improve coherence times in certain parameter regimes.@en

Progress in fabrication of semiconductor and superconductor qubits has greatly diminished the number of decohering defects, thus decreasing the devastating low-frequency 1/f noise and extending the qubits' coherence times (dephasing time T2∗ and the echo decay time T2). However, large qubit-to-qubit variation of the coherence properties remains a problem, making it difficult to produce a large-scale register where all qubits have a uniformly high quality. In this work, we show that large variability is a characteristic feature of a qubit dephased by a sparse bath made of many (n≫1) decohering defects, coupled to the qubit with similar strength. We model the defects as two-level fluctuators (TLFs) whose transition rates γ are sampled from a log-uniform distribution over an interval [γm,γM], which is a standard model for 1/f noise. We investigate decoherence by such a bath in the limit of high-quality qubit, i.e., when the TLF density d is small (the limit of sparse bath, with d=n/w≪1, where n is the number of TLFs and w=ln[γM/γm] is the log-width of the distribution). We show that different realizations of the bath produce very similar noise power spectra S(f)∼1/f, but lead to drastically different coherence times T2∗ and T2. Thus the spectral density S(f) does not determine coherence of a qubit coupled to a sparse TLF bath, as opposed to a dense bath; instead, decoherence is controlled by only a few exceptional fluctuators, determined by their value of γ. We show that removing only two of these TLFs greatly increases T2 and T2∗ times. Our findings help theoretical understanding and further improvements in the coherence properties of semiconductor and superconductor qubits, battling the 1/f noise in these platforms.

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Micromagnet-based electric dipole spin resonance offers an attractive path for the near-term scaling of dense arrays of silicon spin qubits in gate-defined quantum dots while maintaining long coherence times and high control fidelities. However, accurately controlling dense arrays of qubits using a multiplexed drive will require an understanding of the cross-talk mechanisms that may reduce operational fidelity. We identify an unexpected cross-talk mechanism whereby the Rabi frequency of a driven qubit is drastically changed when the drive of an adjacent qubit is turned on. These observations raise important considerations for scaling single-qubit control.

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As spin-based quantum processors grow in size and complexity, maintaining high fidelities and minimizing crosstalk will be essential for the successful implementation of quantum algorithms and error-correction protocols. In particular, recent experiments have highlighted pernicious transient qubit frequency shifts associated with microwave qubit driving. Work-Arounds for small devices, including prepulsing with an off-resonant microwave burst to bring a device to a steady state, wait times prior to measurement, and qubit-specific calibrations all bode ill for device scalability. Here, we make substantial progress in understanding and overcoming this effect. We report a surprising nonmonotonic relation between mixing chamber temperature and spin Larmor frequency which is consistent with observed frequency shifts induced by microwave and baseband control signals. We find that purposefully operating the device at 200 mK greatly suppresses the adverse heating effect while not compromising qubit coherence or single-qubit fidelity benchmarks. Furthermore, systematic non-Markovian crosstalk is greatly reduced. Our results provide a straightforward means of improving the quality of multispin control while simplifying calibration procedures for future spin-based quantum processors.

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