Dynamically Optimized Nonadiabatic Holonomic Quantum Computation

Abstract: Nonadiabatic holonomic quantum computation (NHQC) is one of the promising approaches to realizing fault-tolerant quantum computation. However, due to the imperfect control in the experimental environments, the holonomic gate still needs to be further improved. Here, we propose a dynamically optimized NHQC (OPNHQC) scheme based on dynamically corrected gate technique. The scheme is implemented by carefully designing a sequence of elementary pulses to fulfill cyclic evolution, while the dynamical phase is not accumulated. In this way, the constructed holonomic gate is immune to the error. It is found that our scheme can correct the $X$ error up to fourth order. In addition, combining with the DFS encoding our scheme can be immune to both the $X$ and $Z$ errors. Therefore, our proposed scheme offers a prospective way to the realization of scalable fault-tolerant holonomic quantum computation.