Recent progress in atomistic modelling and simulations of donor spin qubits in silicon

Abstract

Electron or nuclear spins associated with dopant atoms, such as phosphorus impurities in silicon (Si:P), have been shown to form excellent qubits with promising potential for scale-up towards a fault-tolerant quantum computer architecture. The remarkable progress in the design and characterisation of Si:P qubits and quantum gates has been led by recent experimental demonstrations. Equally importantly, advances in theoretical modelling and simulations over a number of years have underpinned the experimental efforts through the fundamental understanding of dopant physics and by providing crucial interpretation of the experimental evidence. This brief review article provides highlights of our research on developing atomistic theoretical methods and their application to the understanding, characterisation and scale-up of Si:P qubits in silicon. We have established a state-of-the-art theoretical framework which is capable of performing electronic structure simulations over millions of atoms. This includes a comprehensive set of central-cell corrections within atomistic tight-binding theory to simulate dopant energy spectra and electronic wave functions with high precision. When integrated with Bardeen’s tunnelling formalism and Chen’s derivative rule, the theoretical simulations were able to reproduce the measured spatially resolved scanning tunnelling microscope (STM) images of dopant wave functions, providing an unprecedented access to the dopant physics in silicon. A systematic examination of the STM image features (brightness and symmetry) allowed pinpointing of the dopant atom positions in silicon lattice with an exact atom precision and for dopant depths up to 5 nm below the silicon surface. The scale-up of the metrology technique was demonstrated by training a machine learning algorithm such as convolutional neural network. For the design and implementation of high-fidelity two-qubit quantum gates, we investigated exchange interaction between dopant pairs and showed that the application of a small lattice strain could provide a full control in the presence of one-lattice site donor position variations. The state-of-the-art computational capability developed by our team is a culmination of more than five years of research efforts – it has been well-benchmarked against several different experimental measurements and is expected to play an important role in design and characterisation of quantum gates and scale-up architectures in the coming years.