Research On Ergodic Phase And Localized Phase In Many-body Quantum Simulation And Two-dimensional Quantum Walk

With the development of semiconductor technology,the process of semiconductor chips has been reduced,from the 130 nm process in 2001 to the 22 nm process in 2012,and then to the 3 nm process trial-produced in 2021.The reduction in the transistor size has also greatly improved the computing power of classical semiconductor chips.But as the size of transistors gets closer to the atomic size,the performance of semiconductor chips gets disturbed by quantum mechanics,and Moore’s Law will fail.In order to avoid bottlenecks in the computing power,researchers are gradually turning their attention to quantum computing.After four decades of development,quantum computing has reached its first milestone,realizing the advantange of quantum computing.And thus we enter the noisy intermediate-scale quantum era.At present,there are two directions for quantum computing.One is to improve the integration and performance of processors,improve the ability of quantum error correction,and develop towards the universal fault-tolerant quantum computer;Another is to research the practical quantum algorithms running on the noisy intermediate-scale quantum processors,which is used to build the taskspecific quantum simulators.By correlating the Hamiltonian of the quantum system to be simulated with that of the quantum simulator,we can run a quantum simulation on the quantum simulator to rapidly simulate the dynamics of the quantum system to be simulated.The quantum simulation has the advantages of strong anti-noise ability,fewer qubits required,and wide range of applications.It becomes one of the most promising quantum algorithms for near-term applications.The author was mainly engaged in the experimental realization of quantum simulation in superconducting quantum computing system during the Ph.D.In order to fabricate the quantum processor,the core device of the superconducting quantum computing system,the author clarified the relationship between the parameters of the lumped circuit and the parameters of the qubit,and completed the design of the superconducting quantum processor.With the design of the quantum processor,a high-performance quantum processor was fabricated by the author through a fabrication process with an average energy relaxation time greater than 40 microseconds.Superconducting quantum computing systems was also consisted of measurement and control systems.According to the impact of the surrounding environment and signals,the author with members of the group had built a low-noise environment and a high-precision signal system for generation and transmission.In view of the functions of the measurement and control system and the principles of superconducting qubits,the author summarized a set of experimental methods for the calibration of superconducting quantum processors.And with these methods,it was determined whether the performance of the quantum processor meets the requirements of the quantum simulation.So far,the hardware requirements of the quantum simulation had been met.In addition,the author also needed to understand the dynamics of the quantum system to be simulated.To solve this problem,the author developed a classical program system to simulate the dynamics of small-scale many-body quantum systems.The program system provided both a theoretical reference and an error analysis tool for quantum simulation.The software program requirements of quantum simulation had also been met.The hardware and software requirements had been met,and the author performed the quantum simulation.In the research on ergodic phase and localized phase in manybody quantum simulation,the coupled system was encoded by a one-dimensional 12qubit quantum processor to simulate the dynamics of the coupled system.By measuring the time evolution of certain physical quantities,such as the number operator,the correlation function,and the localization length,it was clearly observed that the proximity effect destroyed the localization of the localized phase.It was the first time to observe the proximity effect in the driven system.In addition to the quantum simulation of the one-dimensional quantum system,a two-dimensional quantum walk was also performed on an 8 × 8 two-dimensional superconducting array.The author with collaborators not only simulated the dynamics of the two-dimensional quantum walk,but also defined the propagation paths of the walkers with the programmability of the quantum processor and observed the interference fringes of a Mach-Zehnder interferometer.The great results of the two experiments on the quantum simulation proves the reliability of our processor,the measurement and control system,calibration procedures,and the classical simulation system.It provides a solid theoretical and experimental foundation for subsequent quantum simulations about physical model,quantum chemical simulations,and material design,as well as the direction for future improvements in superconducting quantum computing systems.