Optimal Control of Quantum Gates for a Non-Markovian OpenQuantum Qubit System

• Main Authors: Bin Hwang, 黃斌
• Other Authors: Hsi-Sheng Goan
• Format: Others
• Language: en_US
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/65587038244690737057

碩士 === 國立臺灣大學 === 物理研究所 === 99 === One of the fundamental criteria for physical implementation of a practi- cal quantum computer is to design a reliable universal set of quantum gates. A promising class of candidates for realization of scalable quantum com- puters are solid-state quantum devices based on superconducting Josephson- junction qubits. Typically, a central challenge to overcome in this enterprise is decoherence and dissipation induced by the coupling to the its environ- ment. It is thus important to find strategies to alleviate the problems and to to build a high-fidelity quantum gates meeting the error threshold of about 10− 3 ∼ 10− 4 . Optimal control method is one of the powerful tools already applied to the problem of dynamical decoupling from the environment and to finding the control sequence for high-fidelity quantum gates. Furthermore, optimal control technique has recently been applied to Markovian open quan- tum systems in which the approximation of the bath correlation function be- ing delta-correlated in time is assumed. H owever, in some real experiments, we need to consider the non-local memory effects of the bath on the dynamics of the qubits. Especially, the bath memory effects are typically non-negligible in solid state devices. Thus it is desirable to apply optimal control technique to quantum gate operations in the non-Markovian open quantum systems. In this thesis, we first review some basic elements of superconducting quan- tum circuit and introduce the quantum qubit devices. We then introduce the Krotov optimization method which is one of the most effective and univer- sal computation methods for solving optimal control problems. Then the quantum master equation approach for non-Markovian open quantum sys- tems with time-dependent external control are presented. The Krotov based optimal method is then used to implement quantum logical gates for a single qubit in a non-Markovian environment. It is possible to achieve high-fidelity Z-gate with error less than 10^−5 for the non-Markovian open qubit system. The control-dissipation correlation and the memory effect of the bath are cru- cial in achieving the high-fidelity gates.