Robustness Enhancement of Universal Noncyclic Geometric Gates via Evolution Optimization

Abstract: The concept of nonadiabatic noncyclic geometric quantum computation (NNGQC) breaks the constraint of cyclic conditions and allows the system to evolve on acyclic paths, which greatly extends the possibilities of quantum computation. By precisely controlling the evolution of quantum parameters along the acyclic path of the Bloch sphere, NNGQC is able to realize quantum logic gates under non-adiabatic conditions, which not only improves the speed of the operation, but also increases the path degrees of freedom, providing more operational flexibility and robustness for quantum computation. However, past work on NNGQC has not given a universal solution for different gate constructions, meanwhile due to the inability to optionally avoid some trajectory segments seriously affected by systematic errors, the performance of arbitrary geometric gate is still unsatisfactory. Here we give the general scheme of NNGQC, and also summarize the optimal gate construction corresponding to different schemes, and it is worth mentioning that we creatively introduce the universal robust control. Numerical simulations verifies that it is perfectly compatible with all types of noise terms and outperforms the transmission dynamic gates and quantum logic gates in the NGQC framework in terms of gate fidelity and robustness performance. Thus, our scheme can give the ideal quantum gate construction under noncyclic conditions, which sheds light on future large-scale quantum computation.