The Application Of Noncyclic Geometric Phase And Shortcut To Adiabaticity In Superconducting Qubits

The quantum computer has unique advantages over the classical computer.Its computing power increases exponentially with the increasing number of qubits,and it is more suitable for the simulation of quantum systems.Therefore quantum computing has become research focuses.There are many physical systems to realize quantum computing,such as superconducting qubits,ion trap,NV center and so on.The superconducting qubit,which is one of the potential schemes,is compatible with semiconductor technology and has strong expandability.In this thesis,we first introduce the principle of quantum computing,including quantum bits,quantum gates and quantum measurement.Then we explain the principle of superconducting quantum bits through circuit quantum electrodynamics,including the theory of quantum bits,the interaction between superconducting quantum bits and the cavity,and the theory of state measurement.Then we present our measurement system,the dilution refrigerator and the measuring circuit included.We use the system for the basic characterization of the sample.Finally,noncyclic geometric gate with shortcut to adiabaticity is performed on the transmon bits.In the experiment,the fidelity of the quantum gate is mainly limited by the decoherence time and the control errors.To overcome these effects,the fast and robust quantum gate is essential.The geometric phase gate has its instinct robustness,which has been proved in various experiments.However,either based on Abelian geometric phase gate,non-Abelian geometric phase gate or nonadiabatic non-Abelian geometric phase gate,geometric phase gates need cyclic evolution which limits the speed of small-angle gates.As small-angle gates play an important role in quantum control,schemes based on noncyclic geometric phase gates are proposed.Along with the noncyclic evolution,the small-angle gates are accelerated while remaining robust.We perform noncyclic geometric gates with shortcut to adiabaticity experimentally.After setting appropriate experimental parameters and calibrating single-qubit gates,the evolutionary trajectory of the quantum state is obtained by quantum state tomography.The fidelities of gates are over 99.5% characterized by randomized benchmarking.In comparison to the dynamic phase gates,we demonstrate the robustness of the noncyclic geometric phase gate by varying the control errors.Finally,we demonstrate that the operation time depends linearly on the rotation angle and the smaller rotation angle corresponds to the shorter operation time and the higher fidelity.This fast and robust scheme will have more applications in quantum control.