Pulse modulation for enhanced control in NMR-based Quantum Devices
In this work an oversight on qubit control methods in NMR quantum computing is provided. Significant emphasis is placed on the utilization of modulated pulses to enhance qubit control and logic gate fidelity, discussing how various aspects of qubit control can be optimized: mitigation of the detrimental effects of noise such as inhomogeneities in the magnetic field, calibration errors, and compensation of the spectral width of RF pulses. Special attention is given to the employment of Fourier series analysis in the design of modulated pulses to overcome certain effects, such as the Dilation Property and the Gibbs Phenomenon. Through simulation of NMR qubits and optimization methods, the best numeric pulses for both homonuclear and heteronuclear systems are identified. Although numerically, high fidelity is achieved by the pulses, their experimental results, as tested on Chloroform in a 500MHz Varian spectrometer, are found to be satisfactory on average.
Moreover, a discussion on quantum open systems and Choi matrices is provided. A deterministic algorithm for Quantum Process Tomography was developed to access the typical noise for qubits in the spectrometer. Experimental Choi matrices were then identified, and the corresponding noise is now incorporated in the optimization of the pulses. Reruns of the pulses with the incorporated noise robustness were not tested in the spectrometer due to time limitations, and are left for future research.