Quantum-Bath Decoherence of Hybrid Electron-Nuclear Spin Qubits

A major problem facing the realisation of scalable solid-state quantum computing is that of overcoming decoherence -- the process whereby phase information encoded in a quantum bit (`qubit') is lost as the qubit interacts with its environment. Due to the vast number of environmental degrees of freedom, it is challenging to accurately calculate decoherence times T2, especially when the qubit and environment are highly correlated. Hybrid or mixed electron-nuclear spin qubits, such as donors in silicon, are amenable to fast quantum control with pulsed magnetic resonance. They also possess `optimal working points' (OWPs) which are sweet-spots for reduced decoherence in magnetic fields. Analysis of sharp variations of T2 near OWPs was previously based on insensitivity to classical noise, even though hybrid qubits are situated in highly correlated quantum environments, such as the nuclear spin bath environment of 29Si impurities. This presented limited understanding of the underlying decoherence mechanism and gave unreliable predictions for T2. In this thesis, I present quantum many-body calculations of the qubit-bath dynamics, which (i) yield T2 for hybrid qubits in excellent agreement with experiments in multiple regimes, (ii) elucidate the many-body nature of the nuclear spin bath and (iii) expose significant differences between quantum-bath and classical-field decoherence. To achieve these results, the cluster correlation expansion was adapted to include electron-nuclear state mixing. In addition, an analysis supported by experiment was carried out to characterise the nuclear spin bath for a bismuth donor as the hybrid qubit, a simple analytical formula for T2 was derived with predictions in agreement with experiment, and the established method of dynamical decoupling was combined with operating near OWPs in order to maximise T2. Finally, the decoherence of a 29Si spin in proximity to the hybrid qubit was studied, in order to establish the feasibility for its use as a quantum register