Open quantum dynamics of spin qubits on graphene nanoribbons

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The next generation of quantum computers will need to make use of new materials to realise higher temperature operation and all-electrical control of qubits. Strong contenders for achieving these goals are atomically precise graphene nanoribbons, whose true potential has only recently been uncovered with ground-breaking developments in nanofabrication. Due to their molecular precision, these auspicious graphene nanoribbons boast spin relaxation times on the order of milliseconds at temperatures as large as 10 K [1], offering exciting prospects for further investigations. This project will investigate a spin-qubit framework that exploits proximity effects to enable ultra-fast all-electrical single-qubit control with Rabi frequencies breaking the GHz barrier [2]. The overall aim is to understand the effects of spin-phonon coupling upon qubit stability by using a combination of theoretical and numerical methods. The ability to identify and characterise the spin decoherence channels will provide a stepping stone to understand the resilience of spin-qubit encoding strategies in graphene nanoribbons. The main objectives are to determine the effects of electron-phonon coupling and common random sources of elastic scattering upon qubit stability and model the open quantum dynamics of proximitised graphene nanoribbons(GNRs). Benefiting from the team's expertise, we will use many-body perturbation theory and numerically exact methods to obtain a robust microscopic theory applicable to realistic systems. The following effects will be considered. (i) Spin-phonon coupling. Electron-phonon coupling is the main charge relaxation mechanism in gate-defined graphene quantum dots [3] and is likely to be the main factor in setting the spin coherence time in bottom-up GNRs as evidenced by pulse electron paramagnetic resonance experiments [4]. (ii) Disorder. The most common imperfection in bottom-up GNRs are "bite defects" (i.e. missing C rings) at the edge [5]. We shall map out the open dephasing channels for (i) and (ii), calculating the microscopic relaxation times and the ensuing T1 and T2 times. The secondary objectives are: (1) characterise spin-phonon relaxation processes due to spin-orbit admixture; and (2) determine the impact of magnetic noise.