Physical Realization Of Nonadiabatic Holonomic Quantum Computation

Quantum computation has the potential to solve many problems faster than classical computation.The realization of quantum computation needs high-fidelity quantum gates,which requires that the quantum system used for the computation can be accurately controlled.Geometric phases are only dependent on evolution paths but independent of other evolution details so that the quantum gates based on geometric phases have the potential to be robust against control errors.In particular,the quantum gates based on nonadiabatic non-Abelian geometric phases,i.e.,nonadiabatic holonomic gates,have the features of be-ing purely geometric and implemented without the restriction of the adiabatic condition.Because of these features,we studied the realization of nonadiabatic holonomic quantum computation with practical quantum systems in this thesis,aiming to realize higher-fidelity quantum gates than before.In this thesis,we investigated the way to realize nonadiabatic holonomic quan-tum computation with atom-cavity systems and Rydberg atomic systems,respec-tively,and the main achievements are as follows.First,we realized a universal set of nonadiabatic holonomic gates with atom-cavity systems.Atom-cavity systems are important for realizing the interaction between laser fields and atoms.Based on such systems,we used the Stark shift generated by the off-resonant laser pulse to replace the detuning used in previous schemes.In this way,arbitrary single-qubit nonadiabatic holonomic gates can be realized in one step only.When realizing two-qubit nonadiabatic holonomic controlled gates,we used one cavity mode to couple two four-level atoms.With the control of laser pulses,the transition between the double-atom ground state and the double-atom auxiliary state can be realized by exchanging virtual photons through the common cavity mode.In this way,the double-atom transition is separated by the common cavity mode,making two-qubit nonadiabatic holonomic gates insensitive to the decay of the cavity mode.Second,we proposed a scheme of realizing three-qubit nonadiabatic holonomic gates with Rydberg atomic systems.Rydberg atoms have strong Rydberg interac-tions and long-lived Rydberg states,which benefit the realization of high-fidelity quantum gates.We based our scheme on three three-level Rydberg atoms that can be trapped in any desired shape,and the energy shift caused by the interac-tion between Rydberg atoms is compensated by imposed off-resonant laser pulses.As a result,the three-atom ground state and three-atom collective Rydberg state can be coupled to form a A type energy level structure.By appropriately setting the laser parameters,a three-qubit nonadiabatic holonomic controlled rotation gate can be realized by a one-shot implementation.Moreover,by sequentially im-plementing two such three-qubit quantum gates,an arbitrary three-qubit nona-diabatic holonomic controlled gate can be realizedThird,we proposed a scheme of realizing multiqubit nonadiabatic holonomic gates with Rydberg atomic systems.Multiqubit gates are an important family of quantum gates,which have been widely used in various quantum information processing tasks.In this scheme,we drove the quantum states in the computa-tional space into an auxiliary state space where only the controlled qubit can be operated by laser pulses,and then drove them back to the computational space at the end.In this scheme,one can realize an(n+1)-qubit nonadiabatic holo-nomic gate with only(2n-1)basic operations.Compared with the schemes of using the universal gates,our scheme significantly reduces the number of basic operations of realizing multiqubit gates.Besides,the effective coupling between two qubits is in the first-order strength of Rabi frequencies,which allows for the implementation of quantum gates within a shorter duration.