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 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, 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 of ²⁹Si impurities. This presented limited understanding of the decoherence mechanism and gave unreliable predictions for T₂. 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, 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.