High-fidelity composite quantum gates for Raman qubits

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.