Quantum gates in donor based silicon qubits*

Recently, new types of qubits based on donors in silicon have been proposed, e.g. the flip-flop qubit and the electrically controlled nuclear spin qubit. These proposals provide potential advantages in terms of the speed and range of certain interactions, leading to promising quantum gate quality. Nevertheless, the qubit states are two levels out of a larger Hilbert space, and thus coherent errors and leakage can occur during control. Here we derive effective Hamiltonians for these qubits and present strategies for fast, high-fidelity quantum gates.