Non-adiabatic holonomic quantum operations in continuous variable systems  

作　　者：Hao-Long Zhang Yi-Hao Kang Fan Wu Zhen-Biao Yang Shi-Biao Zheng 

机构地区：[1]Fujian Key Laboratory of Quantum Information and Quantum Optics,College of Physics and Information Engineering,Fuzhou University,Fuzhou 350116,China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2024年第6期12-19,共8页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grand Nos.12274080,and 11875108)。

摘　　要：Quantum operations by utilizing the underlying geometric phases produced in physical systems are favoured due to their potential robustness.When a system in a non-degenerate eigenstate undergoes an adiabatically cyclic evolution dominated by its Hamiltonian,it will get a geometric phase,referred to as the Berry Phase.While a non-adiabatically cyclic evolution produces an Aharonov-Anandan geometric phase.The two types of Abelian geometric phases are extended to the non-Abelian cases,where the phase factors become matrix-valued and the transformations associated with different loops are non-commutable.Abelian and non-Abelian(holonomic)operations are prevalent in discrete variable systems,whose limited(say,two)energy levels,form the qubit.While their developments in continuous systems have also been investigated,mainly due to that,bosonic modes(in,such as,cat states)with large Hilbert spaces,provide potential advantages in fault-tolerant quantum computation.Here we propose a feasible scheme to realize non-adiabatic holonomic quantum logic operations in continuous variable systems with cat codes.We construct arbitrary single-qubit(two-qubit)gates with the combination of single-and two-photon drivings applied to a Kerr Parametric Oscillator(KPO)(the coupled KPOs).Our scheme relaxes the requirements of the previously proposed quantum geometric operation strategies in continuous variable systems,providing an effective way for quantum control.

关 键 词：cat qubit continuous variable systems non-Abelian 

分 类 号：O413[理学—理论物理]