Quantum gates with donors in germanium

Recent work has shown that electron spins in germanium (Ge) nanoscale transistors can be electrically tuned and have encouraging coherence times. Based on a novel, complete and validated theory of Ge-donor electron states, we propose that Ge spin qubits could have significant advantages over silicon (Si) in the implementation of a donor-based quantum processor architecture. Our work shows that the intrinsic features of the Ge band structure allow for a speedup of selective (local) one-qubit gates of up to two orders of magnitude as compared to Si. Further, we find that fast, robust two-qubit gates in Ge pose less stringent fabrication constraints than in Si devices: Ge-donors spaced three times farther apart than in Si show comparable exchange couplings, allowing more space for readout and control gates. In addition, for realistic position uncertainty in donor placement, Ge:P spin couplings have a 33\% chance of being within an order of magnitude of the largest coupling, compared with only 10\% in Si:P. It is therefore possible that a Ge based platform would enable fast, parallel and robust architectures for quantum computing.