  The Hamiltonian control of n qubits requires precision control of both the
strength and timing of interactions. Compensation pulses relax the precision
requirements by reducing unknown but systematic errors. Using composite pulse
techniques designed for single qubits, we show that systematic errors for n
qubit systems can be corrected to arbitrary accuracy given either two
non-commuting control Hamiltonians with identical systematic errors or one
error-free control Hamiltonian. We also examine composite pulses in the context
of quantum computers controlled by two-qubit interactions. For quantum
computers based on the XY interaction, single-qubit composite pulse sequences
naturally correct systematic errors. For quantum computers based on the
Heisenberg or exchange interaction, the composite pulse sequences reduce the
logical single-qubit gate errors but increase the errors for logical two-qubit
gates.
