Theorectical Research On High-dimensional Quantum State Transfer And Multi-qubit Logic Gates Implementation In Circuit QED

Qua.ntum state transfer and multi-qubit logic gates play important roles in quantum information processing and quantum computation.Many physical systems can be used to implement quantum state transfer and multi-qubit logic gates.Circuit quantum electrody-namics(circuit QED)has been considered as one of the promising physical platforms for realizing large-scale quantum information processing and quantum computation.Circuit QED consisting of microwave resonators and superconducting qubits,is an analogue of cav-ity QED and a well-established platform for the investigation of light-matter interaction at the quantum level.Hitherto,the quantum state transfer between two superconducting qubits and multiple superconducting qubits gates have been experimentally demonstrated in circuit QED.However,no experimental study has been reported for the quantum state transfer be-tween high-dimensional qubits or multi-qubit gates in a multi-resonator circuit QED system.This thesis will mainly focus on the high-dimensional quantum state transfer in circuit QED and multi-qubit logic gates implementation in a multi-resonator system.The thesis consists of eight chapters in which Chapters 3 to 7 cover the main research work performed during my doctoral study.In Chapter 1,we first introduce the research background of circuit QED and give the outline of this thesis.In Chapter 2.we introduce the basic theory and method used in our research works,which includes Josephson junction,superconducting qubits,circuit QED,etc.In Chapter 3,we propose a scheme to transfer an arbitrary quantum state between two flux qutrits coupled to two superconducting coplanar waveguide resonators.The quantum state transfer can be deterministically achieved without measurements.Because resonator photons are virtually excited during the operation time,the decoherences caused by the resonator decay and the unwanted inter-resonator crosstalk are greatly suppressed.In Chapter 4,we present a method to transfer arbitrary d-dimensional quantum states between two superconducting transmon qudits coupled to a single cavity.The state transfer can be performed by employing resonant interactions only.In addition,quantum states can be deterministically transferred without measurement.In chapter 5,we propose a scheme by utilizing the dispersive interaction in supercon-ducting quantum circuit to implement a hybrid Fredkin gate with a superconducting flux qubit as the control qubit and two separated quantum memories as the target qudits.The quantum memories considered here are prepared by the superconducting coplanar waveguide resonators or nitrogen-vacancy center ensembles.In particular,it is shown that this Frcdkin gate can be realized using a single-step operation and more importantly,each target qudit can be in an arbitrary state with arbitrary degrees of freedom.Furthermore,we show that this scheme has many potential applications in quantum information processing.In Chapter 6,we present a one-step method to achieve a multi-target-qubit controlled phase gate in a multi-resonator system,which possesses a common control qubit and multiple different target qubits distributed in their respective resonators.Noteworthily,the implemen-tation of this multi-qubit phase gate does not require classical pulses,and the gate operation time is independent of the number of qubits.In Chapter 7,we propose a method for realizing cross-Kerr nonlinearity interaction be-tween two superconducting coplanar waveguide resonators coupled by a three-level supercon-ducting flux qutrit(coupler).Because the resonator photons are virtually excited and the coupler is unexcited for the entire process,the effect of resonator decay and the coupler de-coherence are greatly minimized.More importantly,compared with the previous proposals,our proposal does not require classical pulses.Furthermore,due to use of only a three-level qutrit,the experimental setup is much simplified when compared with previous proposals requiring a four-level artificial atomic systems.The conclusion and the outlooks are given in Chapter 8.