Simulating Topological Materials With Superconducting Qubits

With the rapid development in recent years,superconducting quantum computing based on superconducting quantum circuit has become the most promising scheme to realize quantum computer.The components of superconducting quantum circuit mainly include capacitance,inductance and Josephson junction.The combination of these components can be used to build superconducting artificial atom with specific energy level structure,namely superconducting qubit.This thesis mainly introduces the physical realization,measurement and control method of the superconducting quantum processor,as well as an important application of the superconducting quantum processor,namely,quantum simulation。The basic contents of this thesis include:(1)In the introduction part,the basic concepts of quantum computing are introduced,including qubit,quantum logic gate,decoherence theory and quantum measurement.(2)In the second chapter,we introduce the circuit model of the superconducting quantum processor.First,we take the resonant circuit as an example to illustrate the general method of quantization of mesoscopic circuit and the conditions for mesoscopic circuit to show quantum mechanical behavior.Next,by introducing the nonlinear inductance element,i.e.Josephson junction,we realize the quantum circuit with non-uniform energy level structure,and encode the lowest two energy levels as qubits through the two-level approximation.Finally,we introduce the manipulation,reading and coupling of qubits in turn.On this basis,we can design a superconducting quantum processor,which is also known as superconducting quantum chip.(3)The third chapter mainly introduces the measurement and control platform of superconducting quantum chip.We mainly explain the basic idea of establishing the measurement and control platform from four aspects: the realization and reading of single photon level incident power,the suppression of thermal noise and quantum noise of measurement and control circuit,the modulation of driving signal and the demodulation of reading signal,and the synchronization and delay of signals of microwave source,DC source and other equipment(4)In Chapter four,we mainly introduce the calibration of single qubit.We calibrate the basic parameters of qubit by using frequency-domain measurement and time-domain measurement,including reading resonance frequency,quality factor,dispersion displacement,qubit frequency,driving pulse length,etc.through the accurate calibration of these parameters,we get the high fidelity single qubit gate.(5)The chapter five introduces the application of superconducting qubits in the simulation of topological materials.By mapping the driving microwave parameter space of superconducting qubits with the quasi-momentum space of topological materials,i.e.the first Brillouin region,we have successfully simulated some topological materials that have not been prepared in the laboratory so far,and on this basis,we have studied some properties including topological protection and topological phase transition.