Quantum Information Processing And Quantum Simulation With Superconducting Devices

Since1994Peter Shor proposed the first practical quantum algorithm, quantum computer with its powerful computational ability which is far beyond classical com-puter has attracts researchers’attentions in the past two decades. Although quantum computer has amazing computational ability, the system used to built it has to meet some rigorous technique requirements. We have to address every individual site and preform single-qubit and double-qubit operations with high fidelity; the system must have long enough coherent time, during which plenty quantum operation can be com-pleted; it also have to be scalable in order for possible practical applications. Quantum simulation with much lower technique requirements may have wide useful applications before the real quantum computer has been built up.In this dissertation, we mainly concentrate on quantum information processing and quantum simulation with superconducting devices. It contains,1. We give a brief review of basic concepts of quantum computation, such as qubit, universal quantum gates et.al; the idea of quantum simulation and various systems used for it. We also introduce the properties of two kinds of superconducting devices, Josephson junction and superconducting transmission line. We derive the Hamiltonian of various Josephson junction systems and put forward the Josephson qubits based on it. We quantized the superconducting transmission line and get interacting Hamiltonian when it couples to Josephson qubits.2. In the traditional quantum computation proposal with superconducting devices, the Josephson junction always behaves as a qubit and the transmission line works like a optical cavity as a qubit bus or a qubit state detector. The Josephson qubit has short coherent time due to its noisy surrounding environment, which means it cannot be used for scalable quantum computation. In another hand, the microwave photon in super-conducting transmission line has much longer coherent time because of relative pure environment. Here, we use the microwave photon in the transmission line as qubit, the qubit will have long life time as mentioned above. With carefully designed Joseph-son junction circuit, we can achieve the photon transfer operation between two differ-ent transmission lines with high fidelity, in other words we complete the high precise single-qubit gate. One disadvantage of photon qubits is that they can hardly interact with each other. Fortunately, in our system the photon interaction with large strength can be demonstrated using the intrinsic nonlinearity of Josephson junction. Due to that, the double-qubit gate can be realized with high precision. The Josephson junction sys-tem is only virtually excited during the proceeding of quantum gate operations, thus its rapid decay and decoherence rates have limited influences on the quantum gate. The Josephson junction and transmission line can be manufactured on the same supercon-ducting chip with micro-mechanical technologies and it can be extended to integrate more qubits on the chip. In principle, we proposed a scalable quantum computation scheme based on the superconducting devices on a chip, we demonstrate the feasibility of the scheme under realistic situations.3. In the field of quantum information processing, the Rabi model is the most widely used one. It describes the interacting Hamiltonian between a single-mode bosonic field and qubit, which can be used for quantum state transfer between these two systems. In the derivation of this Hamiltonian, the quadratic term of the vector potential of bosonic field has been dropped due to the weak interaction strength of traditional system. While in the superconducting system as the Josephson qubit inter-acting with microwave photon in transmission line, the coefficient of the quadratic term can be quite large which cannot be neglected. We analyzed the influences brought by it in various quantum information processing procedures, such as quantum state transfer, entangled state preparation and the collapse and revival dynamics of quantum states. The appearance of quadratic term can seriously affects the above quantum procedures, it can the previous scheme fails or bring some unique features. For example, it makes the quantum state collapse and revival dynamics have double-peak which can be ob-served by experiments.4. We investigate the large-capacitance coupled Joshpson junction array system and its applications in quantum simulation. With some mathematic techniques we solve the system Hamiltonian exactly and find there are appreciable non-adjacent in-teractions, thus can be used for frustrated phenomena simulation. However the system Hamiltonian is not exact the same as well known ANNNI model, we use the dynamical-decoupling technique to modulate the Hamiltonian by eliminating all the unwanted in-teractions. Then we use the TEBD algorithm to calculate the phase diagram of ANNNI model and find the evidences of its unique floating phase. For a realistic achievable finite-size Josephson junction system, we demonstrate that a six-site Josephson junc-tion array can reveal some essential properties of ANNNI model. Using the dynamical-decoupling control sequences, we also simulate the quantum phase transition process with high precision.