  Quantum gates (unitary gates) on physical systems are usually implemented by
controlling the Hamiltonian dynamics. When full descriptions of the
Hamiltonians parameters is available, the set of implementable quantum gates is
easily characterised by quantum control theory. In many real systems, however,
the Hamiltonians may include unknown parameters due to the difficulty of
precise measurements or instability of the system. In this paper, we consider
the situation that some parameters of the Hamiltonian are unknown, but we still
want to perform a robust control of a quantum gate irrespectively to the
unknown parameters. The existence of such control was previously shown in
single-qubit systems, and a constructive method was developed for two-qubit
systems provided full single-qubit controls are available. We analytically
investigate the robust controllability of two-qubit systems, and apply Lie
algebraic approaches to handle the cases where only controlling one of the two
qubits is allowed. We also use numerical approaches for these problems since
our analytical approaches does not work in some systems.
