Theoretical Study of Quantum Feedback andQuantum Optimal Control for Superconducting Qubits

• Main Authors: Shang-Yu Huang, 黃上瑜
• Other Authors: Hsi-Sheng Goan
• Format: Others
• Language: en_US
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/73601137811516449853

博士 === 國立臺灣大學 === 物理研究所 === 102 === An essential prerequisite for quantum information processing (QIP) is precise coherent control of the dynamics of quantum systems or quantum bits (qubits). This thesis is devoted to the study of quantum control and manipulation of superconducting qubits that are promising candidates for scalable solid-state quantum computing. We study two different types of superconducting qubits and architectures: Circuit cavity quantum electrodynamics (QED) and coupled flux qubit systems. In the first part, we present a simple and promising quantum feedback control scheme for deterministic generation and stabilization of a three-qubit entangled W state in the superconducting circuit QED system. We simulate the dynamics of the proposed quantum feedback control scheme using the quantum trajectory approach with an effective stochastic maser equation obtained by a polaron-type transformation method and demonstrate that in the presence of moderate environmental decoherence, the average state fidelity higher than 0.9 can be achieved and maintained for a considerably long time (much longer than the single-qubit decoherence time). This control scheme is also shown to be robust against measurement inefficiency and individual qubit decay rate differences. Finally, the comparison of the polaron-type transformation method to the commonly used adiabatic elimination method to eliminate the cavity mode is presented. In the second part, we apply the quantum optimal control theory based on the Krotov method to implement single-qubit X and Z gates and two-qubit CNOT gates for inductively coupled superconducting flux qubits with fixed qubit transition frequencies and fixed off-diagonal qubit-qubit coupling. The qubits in our scheme are operated at the optimal coherence points and the gate operation times (single-qubit gates <1 ns; CNOT gates 2 ns) are much shorter than the corresponding qubit decoherence time. A CNOT gate or other general quantum gates can be implemented in a ingle run of pulse sequence rather than being decomposed into several single-qubit and some entangled two-qubit operations in series by composite pulse sequences. Quantum gates constructed via our scheme are all with very high delity (very low error) as our optimal control scheme takes into account the fixed qubit detuning and fixed two- qubit interaction as well as all other time-dependent magnetic-eld-induced single- qubit interactions and two-qubit ouplings. In addition, we also investigate the effects of inefficient measurement and additional decoherence on the problems of nonadiabatic elimination of an auxiliary mode coupled to the system of interest in continuous quantum measurements. In contrast to the adiabatic elimination method, the eveloped nonadiabatic elimination approach is particularly important when the eliminated auxiliary mode evolves at a time scale larger than or comparable to the typical system evolution or decay time scale as, in this case, the auxiliary mode has finite memory, and the resultant dynamics of the system alone becomes non-Markovian. We investigate an exactly solvable model of an optomechanical system with a linear interaction with an auxiliary cavity mode to illustrate our approach.