Optimal Control of CNOT Gate Operation with Leakagestates and Non-Markovian Environments

• Main Authors: Tsun-Yi Yang, 楊存毅
• Other Authors: 管希聖
• Format: Others
• Language: en_US
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/41258403533969586769

碩士 === 國立臺灣大學 === 應用物理所 === 101 === When building a quantum computer, high precision gate operations are needed. In particular, the controlled-not (CNOT) operation regarded as a crucial universal two-qubit gate is a very important quantum gate to implement. However, real world contains a lot of problems and causes the difference between experimental results and theoretical simulations. In this thesis, we investigate CNOT gate operation using quantum optimal control theory for superconducting charge qubit system taking into account the effects of leakage states and a non-Markovian environment. First, we give a brief introduction to superconducting qubits and decide the Hamiltonian of a simple one-qubit model. Then we describe the noise power spectrum of environments, which gives the relation between the relaxation rate and the bath correlation function through the Fermi golden rule . After that, we describe the non-Markovian master equation approach and apply it to our model together with the quantum optimal control theory. The Krotov optimal control method that we used in this thesis can minimize the error of gate operations and find the corresponding optimal control pulses to realize the gate operations. Considering the non-local memory effect in non-Markovian open quantum systems. We also discuss the effect of different shapes and behaviors in the bath correlation function on the optimal control gate fidelity. We find that it is possible to implement high-fidelity CNOT gates with error about 1e-4~1e-5 in superconducting charge qubit system with environment parameters extracted from the realistic noise power spectrum of experiments.