發(fā)布時間：2018-06-22 13:16

  本文選題：量子控制 + 核磁共振　； 參考：《清華大學(xué)》2016年博士論文

【摘要】：對量子系統(tǒng)實現(xiàn)精準(zhǔn)操控是量子信息處理中的重要環(huán)節(jié),而實現(xiàn)這一目標(biāo)面臨諸多難題。首先,量子系統(tǒng)會與環(huán)境發(fā)生耦合,導(dǎo)致系統(tǒng)出現(xiàn)退相干現(xiàn)象;其次,控制操作本身會存在各種誤差,使量子系統(tǒng)演化偏離目標(biāo)演化。目前用于實現(xiàn)量子精準(zhǔn)操控的技術(shù)主要分為兩類:閉環(huán)量子控制與開環(huán)量子控制。開環(huán)量子控制技術(shù)通過對量子系統(tǒng)引入外部控制操作來調(diào)制系統(tǒng)哈密頓量,使系統(tǒng)有效哈密頓量的演化趨近于目標(biāo)演化。在這個過程中我們不必測量系統(tǒng)量子態(tài)和獲知噪聲環(huán)境的信息。本文圍繞開環(huán)量子控制中的三個重要技術(shù):濾波函數(shù)、動力學(xué)解耦以及組合脈沖,在核磁共振量子系統(tǒng)中開展了以下研究:一、動力學(xué)解耦技術(shù)可以延長量子態(tài)的相干時間,解耦序列可以看作在頻域內(nèi)對特定噪聲的高通濾波器。我們研究了包含兩種脈沖的復(fù)雜動力學(xué)解耦序列的濾波函數(shù),給出了其在布洛赫球空間中的三維表示。借助濾波函數(shù),我們討論了三種序列針對縱向弛豫噪聲和橫向弛豫噪聲的解耦能力差異,指出在使用脈沖資源相同的情況下,解耦序列的表現(xiàn)為序列結(jié)構(gòu)和特定脈沖數(shù)目兩種因素相互競爭的結(jié)果。二、我們在核磁共振系統(tǒng)中驗證了復(fù)雜動力學(xué)解耦序列在混合噪聲環(huán)境中的解耦表現(xiàn),第一次在實驗中觀測到二次解耦序列的解耦優(yōu)勢。為了得到具有縱向弛豫和橫向弛豫效應(yīng)的噪聲環(huán)境,我們完善了噪聲模擬理論體系,首次提出利用控制場同時模擬兩種弛豫效應(yīng)的方法。計算解耦序列的濾波函數(shù)可以得出該序列在噪聲環(huán)境中的演化保真度,實驗結(jié)果精準(zhǔn)的符合了濾波函數(shù)的理論預(yù)測。三、我們在核磁共振系統(tǒng)中驗證了級聯(lián)組合脈沖在兩種時變誤差同時存在時的魯棒性表現(xiàn)。這些原本用于消除靜態(tài)或準(zhǔn)靜態(tài)誤差的組合脈沖,被證明在動態(tài)非馬爾科夫噪聲環(huán)境中同樣具有魯棒性,而級聯(lián)組合脈沖可以同時消除原始脈沖中存在的脈沖長度誤差和脈沖失諧誤差。通過計算級聯(lián)組合脈沖的濾波函數(shù),我們能夠得到該組合脈沖對兩種誤差抑制能力的差異,并找到脈沖能保持魯棒性的噪聲截止頻率閾值。我們在實驗中證實了級聯(lián)組合脈沖的解耦表現(xiàn),實驗數(shù)據(jù)和濾波函數(shù)預(yù)測一致。
[Abstract]:Accurate manipulation of quantum systems is an important part of quantum information processing. First, the quantum system will be coupled with the environment, resulting in the system decoherence; secondly, there will be a variety of errors in the control operation itself, which makes the evolution of the quantum system deviate from the target evolution. At present, there are two kinds of quantum control techniques: closed loop quantum control and open loop quantum control. The open-loop quantum control technology modulates the Hamiltonian by introducing external control operations to the quantum system, which makes the evolution of the effective Hamiltonian approach to the target evolution. In this process, we do not have to measure the quantum state of the system and get information about the noise environment. This paper focuses on three important techniques in open-loop quantum control: filtering function, dynamic decoupling and combinatorial pulses. The following studies have been carried out in the NMR quantum system: firstly, the dynamic decoupling technique can prolong the coherent time of quantum states. Decoupling sequences can be regarded as high-pass filters for certain noises in frequency domain. In this paper, we study the filtering function of complex dynamical decoupling sequences containing two impulses, and give their three dimensional representation in Bloch sphere space. With the help of filtering function, we discuss the decoupling ability of three sequences for longitudinal relaxation noise and transverse relaxation noise, and point out that when the pulse resource is the same, Decoupling sequences are represented by competing results of sequence structure and number of specific pulses. Secondly, we have verified the decoupling performance of the complex dynamic decoupling sequences in the nuclear magnetic resonance system. The decoupling advantages of the quadratic decoupling sequences have been observed in experiments for the first time. In order to obtain the noise environment with longitudinal and transverse relaxation effects, we have perfected the theoretical system of noise simulation and proposed for the first time a method to simulate the two relaxation effects simultaneously by using the control field. The evolution fidelity of the decoupled sequence in noise environment can be obtained by calculating the filtering function of the decoupled sequence. The experimental results are accurate in line with the theoretical prediction of the filtering function. Thirdly, we verify the robustness of the cascaded combined pulses in the presence of two time-varying errors in the nuclear magnetic resonance (NMR) system. These combined pulses, which were originally used to eliminate static or quasi-static errors, have been proved to be equally robust in dynamic non-Markov noise environments. The cascade combined pulse can eliminate both the pulse length error and the detuning error in the original pulse at the same time. By calculating the filtering function of the cascaded combined pulse, we can obtain the difference of the combined pulse's ability to suppress the two kinds of errors, and find the threshold of the noise cutoff frequency which can keep the robustness of the pulse. We have verified the decoupling performance of cascaded combined pulses in experiments, and the experimental data are consistent with the filter function prediction.
【學(xué)位授予單位】：清華大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：O413

【相似文獻】

相關(guān)期刊論文 前5條

1 曹曙天;;有源濾波器濾波函數(shù)的一種逼近方法[J];西安建筑科技大學(xué)學(xué)報(自然科學(xué)版);1987年04期

2 劉立人;雙濾波產(chǎn)生相位體的等位線條紋[J];光學(xué)學(xué)報;1986年02期

3 李立;田逢春;劉賽;邱宇;;4f光學(xué)系統(tǒng)中濾波函數(shù)角位移補償?shù)难芯縖J];光學(xué)技術(shù);2009年04期

4 徐茂林,邱鈞,范惠榮,張兆田,李興東;用一種新濾波函數(shù)作CT圖像局部重建[J];計算物理;2004年03期

5 陳盛祖;模型試驗研究 SPECT 濾波函數(shù)的最佳選擇[J];核電子學(xué)與探測技術(shù);1998年05期

相關(guān)會議論文 前1條

1 許峰;胡小方;繆泓;曲洪巖;袁清習(xí);;基于新濾波函數(shù)的SR-CT反投影算法研究[A];第十二屆全國實驗力學(xué)學(xué)術(shù)會議論文摘要集[C];2009年

相關(guān)博士學(xué)位論文 前2條

1 甄興龍;量子系統(tǒng)噪聲的動力學(xué)抑制[D];清華大學(xué);2016年

2 徐茂林;透射及散射斷層成像中若干反演算法的研究[D];浙江大學(xué);2004年

，

本文編號：2052954