Nonadiabatic Geometric Quantum Computation

The computational capability of quantum computers is greater than that of classical computers.However,there are two main challenges for the realization of quantum computation.One is to correct the control errors induced by the inaccu-rate operation of quantum systems,the other is to suppress the decoherence cased by the interaction between the quantum system and its environment.Geometric phases are only dependent on evolution paths of quantum states but independen-t of evolution details so that quantum computation based on geometric phases is robust against control errors.Originally,adiabatic geometric phases were used to realize quantum computation,which is known as adiabatic geometric quantum computation.However,the realization of adiabatic geometric quantum compu-tation requires quantum systems to undergo long-run-time evolution.To resolve this problem,nonadiabatic geometric quantum computation based on nonadia.bat-ic Abelian geometric phases and nonadiabatic non-Abelian geometric phases was proposed.Nonadiabatic geometric quantum computation not only avoids the long-run-time evolution but also possesses the robustness against control errors.The realization of quantum computation relies on real physical systems so that building quantum computation on the realistic quantum systems is practical important for the realization of quantum computation.Thus,an important problem is how to realize nonadiabatic geometric quantum computation by using realistic physical systems.In this dissertation,we focus on this important problem.To start with,we propose two schemes of nona.diabatic geometric quantum computation with Rydberg atoms and superatoms.Then,we investigate the nonadiabatic geometric quantum computation in open system,where we propose an alternative protocol of nonadiabatic holonomic quantum computation in decoherence-free subspaces and a protocol of unconventional geometric quantum computation in decoherence-free subspaces.Finally,we propose an approach of realizing nonadiabatic holonomic multiqubit controlled gates.The following is the main results of this thesis.First,we propose Rvydberg-atom-based schemes of nonadiabatic geometric quan-tum computation computation.We propose a scheme of nonadiabatic geomet-ric quantum computation with Rydberg single atoms and furthermore propose a.scheme of nonadiabatic holonomic quantum computation with Rydberg superatoms Rydberg atoms have long-lived Rydberg states,which can be taken as well-defined qulbit states.Meanwhile,there is strong Rydberg-mediated interaction between t-wo Rydberg atoms,which allows the realization of fast two-qubit gates.Moreover.Rydberg superaoms are mesoscopic atomic ensembles,which are more operational than the microcosmic single atoms.Therefore,our scheme not only has the common merits of nonadiabatic geometric quantum computation such as the robustness and the speediness but also has the the merits of Rydberg atoms and superatoms.Second.we propose an alternative protocol of nona.diabatic holonomic quantum computation in decoherence-free subspaces.This protocol not only maintains all the merits of nonadiabatic holonomic quantum computation in decoherence-free subspaces,i.e.,robustness against both control errors and decoherence but also avoids the extra work of combining two gates to implement an arbitrary one-qubit gate.In addition,we propose a protocol of unconventional geometric quantum computation in decoherence-free subspaces,which allows us to realize nonadiabatic geometric quantum computation in decoherence-free subspaces without removing dynamical phasesThird,we propose an approach of realizing nonadiabatic holonomic multiqubit controlled gates,in which an(n+1)-qubit controlled-(n ·?)gate is realized by(2n-1)basic operations,while an(n + 1)-qubit controlled arbitrary gate can be obtained 1)y combining only two such controlled-(n · ?)gates.Comparing with the previous schemes of nonadiabatic holonomic computation,in which a multiqubit controlled gate is built by using a large number of universal element gat es,our scheme greatly reduces the operations of nonadiabatic holonomic quantum computation.