Quantum Simulation Based On Superconducting Qubits

Quantum computing presents a new computational paradigm with the potential to outperform the classical computer.The quantum computer is based on quantum mechanics,and the properties of superposition and entanglement enable it to work exponentially faster than its classical counter-part.After the concept of quantum computing was first proposed by Richard Feynman in 1980s,there have been significant experimental efforts but the development of the quantum computer is still at its infancy up to now.The fundamental difficulty of building a quantum computer is re-lated to the quantum fragility,i.e.,any small disturbance from the environment can easily destroy a quantum state.Although it is extremely challenging,many countries,universities,and some no-table companies such as Google,Microsoft,and IBM have devoted a lot of resources to the research of the quantum computer considering the huge gain of quantum speedup.Although the current technology is far from realizing a universal quantum computer,there might be some reachable applications that exploit the power of quantum speedup,e.g.,quantum simulation of the small-scale quantum systems featuring interacting particles.When the number of the controllable qubits grows to more than 50,the quantum simulator can carry out certain simulation tasks which a supercomputer cannot handle.In this thesis we present the simulation experiments where we study two representative problems in condensed matter physics using the superconducting quantum simulator.In chapters 1 and 2,we give a brief introduction to the key concepts in quantum computing and an overview of our experimental system,respectively.In chap-ter 3,we describe our experiment of using the superconducting phase and Xmon qubits to simulate the fractional statistical behavior of anyons,which are exotic quasiparticles occurring in two di-mensions.We deterministically generate the multi-qubit graph state in the devices consisting of multiple qubits connected to a central resonator,based on which anyonic excitations and braiding operations are subsequently implemented with single-qubit rotations.The braiding robustness is witnessed by looping an anyonic excitation around another one along two distinct,but topologically equivalent paths,which constitutes the first experimental demonstration of the braiding robustness of anyons with solid-state systems.In chapter 4,we turn to another attractive topic in condensed matter physics,i.e.,the quantum phase transition in an atom-field interacting system.Quantum phase transitions are studied in a variety of naturally grown condensed matter materials such as conductors,superconductors and magnets.With the introduction of well-controlled quantum el-ements such as superconducting qubits,it becomes possible to engineer a quantum simulator to mimic and,more systematically and effectively,investigate the properties of complex interacting quantum materials.More specifically,in the experiment we use a superconducting circuit consist-ing of an Xmon qubit coupled to a resonator to simulate the critical behavior in a single particle-field interacting Jaynes-Cummings model.We observe a cusp-like feature around the critical point in the populations of both the qubit and the resonator,which indicates the occurrence of a phase transition.Chapter 5 is the summary.Our experiments demonstrate the potential of the superconducting quan-tum simulator as an alternative tool to investigate certain problems in condensed matter physics.As the number of controllable qubits continues to increase,the quantum simulator based on supercon-ducting circuits will become a truly powerful platform for studying novel phenomena in condensed matter physics.