Optimal Control With Superconducting Qubits

As one of the most popular schemes to realize quantum computing,superconducting quantum system has developed rapidly in recent years.From the realization of quantum supremacy to the simulation of chemical reactions using quantum computers,superconducting quantum computing systems have made many milestones.Since entering graduate school,I have been learning the theoretical knowledge of superconducting quantum computing and experimental measurement and control methods.This paper will focus on the main theories and experimental techniques of Xmon-type superconducting qubits.The introduction section mainly introduces the history of quantum computing and related ba-sic knowledge.These basic knowledge include quantum state and density matrix of qubits,quan-tum superposition and quantum entanglement,single-qubit quantum gates and two-qubits quantum gates,and several different physical systems for quantum computing.In addition,the two main re-search directions of quantum computing,quantum error correction and quantum supremacy are briefly introduced.The second chapter mainly introduces the knowledge of circuit quantumization related to su-perconducting quantum computing.Starting from the quantumization of the circuit of the simplest LC resonant circuit,we introduce Josephson junction as a nonlinear element into the LC resonant circuit to obtain qubits.Then we show how to drive,how to achieve coupling between qubits,and how to readout qubit states and tune qubit frequency.Finally,the relevant knowledge of quantum decoherence is introduced.The third chapter mainly introduces the parameter calibration method of superconducting quantum chip,taking our laboratory as an example.These parameters include resonant frequency and quality factors for resonant cavities,qubits frequency and the driving amplitude,measurement of decoherence parameters,and calibration of the coupling strength between two qubits.The fourth chapter mainly introduces the GRAPE optimization algorithm which uses exper-imental measurement data as feedback.We propose one optimization scheme based on the evo-lution operator.Using these schemes,we have optimized the two-qubits CZ gate experimentally.The results show that the scheme enables rapid optimization of quantum gates,and the fidelity of the randomized benchmarcking measurement exceeds 98%.The fifth chapter mainly summarizes the thesis and makes a brief prospect in the field of superconducting quantum computing.