Shuttling is expected to play a vital role in scaling up quantum computing based on semiconductor spin qubits. Decoherence, caused by interactions between the qubit and its environment, remains a major obstacle to maintaining qubit fidelity. For stationary qubits, decoherence is typically described using standard random processes. However, trajectories such as forth-back shuttling give rise to random processes with nontrivial correlations. We develop and benchmark a numerical method to analyse the effect of 3D random magnetic fields on shuttled spins, particularly relevant to Ge-based devices where the direction of the effective magnetic field varies significantly. Building on this, we design new dynamical decoupling (DD) sequences for shuttling, incorporating a central pulse to suppress the effect of mirror symmetry between the forward and backwards paths. Using realistic parameters for Si and Ge devices with the developed numerical method, we evaluate the effectiveness of DD sequences at suppressing decoherence during shuttling. In particular, we find that the XY8-Z sequence significantly improves fidelity during forth-back shuttling, and outperforms the standard XY8 sequence commonly used for stationary qubits.

Synchronisation refers to the tendency of coupled oscillators to move in phase with one another over time, departing from their own natural frequency. This phenomenon occurs in almost all branches of science, engineering, and social life. Synchronisation is a well understood concept in classical mechanics. Quantum synchronisation involves attempting to extend this concept to quantum mechanics, where there are number of phenomena such as damping that are more difficult to realise. This thesis focuses on two things. Firstly, it explores the bridge between classical and quantum synchronisation. Both the equivalencies as well as the difficulties that must be overcome. This is initially done by looking at a simple classical model for two coupled oscillators and extending this to a quantum model, and subsequently by exploring the derivation of a master equation for a damped quantum harmonic oscillator with non-linear damping. Secondly, it explore the synchronisation of four coupled quantum van der Pol oscillators. To this purpose, the six different systems (tree, chain, loop, tower, spade, all-to-all) with four coupled classical van der Pol oscillators first analysed and the Arnold tongues are determined, showing for what parameters synchronisation is expected to occur. The equivalent systems with four quantum van der Pol oscillators are explored to determine whether the classical Arnold tongues give a good indication of when quantum synchronisation is expected to occur. An alternative measure for synchronisation is also investigated for these systems based on the relative entropy of coherence. The Arnold tongues for each of the four classical oscillator systems were determined. For some systems (chain and loop) the Arnold tongues were much smaller than for the three oscillator system while for others (tree, all-to-all) they were only slightly smaller. The quantum Arnold tongues showed very similar behaviour to the classical Arnold tongues. Furthermore, when investigating the correlations between different pairs of oscillators, it was found that the correlation decreased as the number of connections separating two oscillators increased. In the chain system, an expected symmetry was found. The relative entropy of coherence is found to be a good measure of synchronisation, better than the more frequently used complex correlator. This is because the relative entropy can take into account the entire system, while the correlator describes the synchronisation between two individual oscillators in the system.