  We present a general systematic approach to design robust and high-fidelity
quantum logic gates with Raman qubits using the technique of composite pulses.
We use two mathematical tools -- the Morris-Shore and Majorana decompositions
-- to reduce the three-state Raman system to an equivalent two-state system.
They allow us to exploit the numerous composite pulses designed for two-state
systems by extending them to Raman qubits. We construct the NOT, Hadamard, and
rotation gates by means of the Morris-Shore transformation with the same
uniform approach: sequences of pulses with the same phases for each gate but
different ratios of Raman couplings. The phase gate is constructed by using the
Majorana decomposition. All composite Raman gates feature very high fidelity,
beyond the quantum computation benchmark values, and significant robustness to
experimental errors. All composite phases and pulse areas are given by
analytical formulas, which makes the method scalable to any desired accuracy
and robustness to errors.
