Control techniques in spin based quantum computation

nuclear magnetic resonance;quantum computation;optimal control

Katiyar, Hemantaffiliation1:Faculty of Applied Health Sciences ; advisor:Laflamme, Raymond ; Laflamme, Raymond ;

University of Waterloo

关键词: optimal control;    nuclear magnetic resonance;    Doctoral Thesis;    quantum computation;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/14795/1/Katiyar_Hemant.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

Working on quantum systems entail different interests, for example, working on fundamentalunderstanding of quantum systems also lay foundation for better quantum computationtechniques. A test for whether a system is behaving quantum mechanically orclassically is devised by Leggett and Garg in form of inequalities, called Leggett-Garg Inequalities(LGI). Such Inequalities are violated by a system whose evolution is governedby quantum mechanics. A precise experiment to violate LGIs require a guarantee that themeasurement does not affect the system or its future dynamics. These Inequalities wereproposed for dichotomic systems,systems which can have two outcomes. Here we presentan LG experiment on a three-level quantum system, which theoretically have larger quantumupper bound than that of a two-level quantum system. This larger violation alsoprovides a bigger buffer to taking in account of the various experimental imperfections.Performing a quantum computing task requires precise level of control to initialize,perform and measure the quantum system. With increasing size of the quantum processorthe challenge is to maintain optimal control. Nuclear Magnetic Resonance (NMR) hasalways been a very faithful test-bed for quantum processing ideas. In NMR, we performRadio Frequency (RF) pulses to control and steer the system to the desired state. Mostused method to derive the exact frequency and amplitude of these pulses for a giventask is based on gradient. Although systematic, one have to simulate these pulses ona classical computer first, which makes the task very inefficient. We report a a way ofperforming optimization with a hybrid quantum-classical scheme. This scheme helps usperform classically harder computational tasks on the quantum processor. We optimizepulses which drive our system from 7-coherence state to 12-coherence state on a 12-qubitNMR processor.Electron Spin Resonance (ESR) employs the same techniques as of NMR but havingadvantage in larger polarization compared to later. Although this does not imply bettercontrol, cause the frequency at which pulses are required to control an ESR system fall intomicrowave region. Microwave frequency are harder to control electronically, thus makingit harder for performing ESR quantum computing. The hybrid scheme used in NMRexperiment relies on some ideal pulses which are needed to be optimized classically. Wealleviate this requirement by using finite difference method of calculating gradient. Wecompare these methods with the earlier methods to show the superiority of such a scheme.State-to-state transfer pulses are sufficient for most of the quantum computing task,but, an universal quantum information implementation requires state independent pulses.The techniques used in optimizing state-to-state pulses can be modified to optimize for astate independent pulse. We show that this methods scale polynomially with the numberof qubits and is general in terms of its implementation. We further reduce the resourcerequirement by using a NMR related implementation.