General off-resonance-error-robust symmetric composite pulses with three elementary operations

Accurate quantum control is a key technology for realizing quantum information processing, such as quantum communication and quantum computation. In reality, a quantum state under control suffers from undesirable effects caused by systematic errors. A composite pulse (CP) is used to eliminate the effects of systematic errors during control. One-qubit control, which is the most fundamental in quantum control, is typically affected by two errors: pulse length error and off-resonance error (ORE). In this paper, we focus on ORE-robust CPs and systematically construct symmetric ones comprising three elementary operations in order to understand their properties. We find an infinitely large number of ORE-robust CPs, including the well-known CORPSE family, and evaluate their performance according to gate infidelity and operation time, both of which are important for the realization of accurate quantum control.