Nonadiabatic holonomic quantum computation based on a commutation relation

Abstract

Nonadiabatic holonomic quantum computation has received increasing attention\ndue to the merits of both robustness against control errors and high-speed\nimplementation. A crucial step in realizing nonadiabatic holonomic quantum\ncomputation is to remove the dynamical phase from the total phase. For this\nreason, previous schemes of nonadiabatic holonomic quantum computation have to\nresort to the parallel transport condition, i.e., requiring the instantaneous\ndynamical phase to be always zero. In this paper, we put forward a strategy to\ndesign nonadiabatic holonomic quantum computation, which is based on a\ncommutation relation rather than the parallel transport condition. Instead of\nrequiring the instantaneous dynamical phase to be always zero, the dynamical\npart of the total phase is separated from the geometric part and then removed\nby properly choosing evolution parameters. This strategy enhances the\nflexibility to realize nonadiabatic holonomic quantum computation as the\ncommutation relation is more relaxed than the parallel transport condition. It\nprovides more options for realizing nonadiabatic holonomic quantum computation\nand hence allows us to optimize realizations such as the evolution time and\nevolution paths.\n