基于核磁共振系統(tǒng)的拓?fù)湎嗔孔幽M和拓?fù)淞孔佑?jì)算實(shí)驗(yàn)研究
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本文關(guān)鍵詞：基于核磁共振系統(tǒng)的拓?fù)湎嗔孔幽M和拓?fù)淞孔佑?jì)算實(shí)驗(yàn)研究 出處：《中國(guó)科學(xué)技術(shù)大學(xué)》2016年博士論文 論文類型：學(xué)位論文
更多相關(guān)文章： 量子計(jì)算 量子模擬 核磁共振 拓?fù)湎?/b> 拓?fù)淞孔佑?jì)算
【摘要】：基于量子力學(xué)原理構(gòu)建的量子計(jì)算機(jī)具有經(jīng)典計(jì)算機(jī)不可比擬的計(jì)算能力。然而,噪聲和退相干是實(shí)現(xiàn)量子計(jì)算機(jī)的主要障礙之一。噪聲來(lái)源于量子比特上操作的不完美；退相干起源于量子系統(tǒng)與環(huán)境間不可避免的相互作用。噪聲和退相干會(huì)導(dǎo)致編碼信息的部分丟失甚至完全錯(cuò)誤。解決方案之一是量子糾錯(cuò)。但這需要額外引進(jìn)輔助比特消耗過(guò)多的資源,而且糾錯(cuò)過(guò)程本身也是有噪聲的。另一種策略是拓?fù)淞孔佑?jì)算。與主動(dòng)的量子糾錯(cuò)方式不同,拓?fù)淞孔佑?jì)算是被動(dòng)的,即無(wú)需作任何的嘗試或操作讓系統(tǒng)無(wú)噪聲,因?yàn)橄到y(tǒng)本身具有魯棒性的自糾錯(cuò)功能。這與系統(tǒng)的整體拓?fù)湫再|(zhì)有關(guān)。拓?fù)淞孔佑?jì)算是目前已知容錯(cuò)率最高的量子計(jì)算方案。拓?fù)淞孔佑?jì)算方案依賴于拓?fù)湎嗟拇嬖�。拓�(fù)湎嗍且活惒荒苡山?jīng)典朗道對(duì)稱破缺理論描述的奇特的物質(zhì)態(tài)。這種態(tài)具有一些有趣的性質(zhì),如依賴于拓?fù)淞餍蔚幕鶓B(tài)簡(jiǎn)并度,準(zhǔn)粒子分?jǐn)?shù)統(tǒng)計(jì)和拓?fù)浼m纏熵等。一類特殊的拓?fù)湮镔|(zhì)態(tài)稱為拓?fù)湫?可描述為有能隙且具有不受微擾影響的長(zhǎng)程糾纏模式。已知的例子是分?jǐn)?shù)量子霍爾態(tài),是首次在真實(shí)體系下觀測(cè)到拓?fù)湫�。另外在一些二維晶格模型中也存在拓?fù)湫颉Ｍ負(fù)湫虿粌H為容錯(cuò)量子計(jì)算提供了天然的無(wú)噪聲介質(zhì),同時(shí)在凝聚態(tài)物理中作為基礎(chǔ)科學(xué)研究如拓?fù)湫再|(zhì),拓?fù)湎嘧円约靶滦筒牧系陌l(fā)現(xiàn)等也具有重要意義。在真實(shí)系統(tǒng)中觀測(cè)拓?fù)湎嗪蛯?shí)現(xiàn)拓?fù)淞孔佑?jì)算極具挑戰(zhàn),主要受限于目前的實(shí)驗(yàn)方法和控制技術(shù)。例如,存在拓?fù)湫虻亩S晶格模型常涉及多體相互作用(如toric code模型具有四體相互作用),并且構(gòu)建一個(gè)晶格往往需要較多的量子比特。實(shí)驗(yàn)驅(qū)動(dòng)和控制這樣復(fù)雜的多量子比特系統(tǒng)不是一件容易的事情。也正因?yàn)榇?拓?fù)淞孔佑?jì)算的研究依然停留在理論中,無(wú)任何相關(guān)的實(shí)驗(yàn)報(bào)道。量子模擬用一個(gè)可控的量子系統(tǒng)模擬復(fù)雜的或難以觀測(cè)的物理現(xiàn)象,在凝聚態(tài)物理,高能物理和量子化學(xué)等鄰域有著許多成功的應(yīng)用。量子模擬為我們提供了一個(gè)有力的手段去探索拓?fù)湎嗪屯負(fù)淞孔佑?jì)算。另一方面,作為量子模擬的物理實(shí)現(xiàn)平臺(tái)之一,核磁共振體系在多量子比特實(shí)驗(yàn)中具有成熟的控制技術(shù)和精確的測(cè)量手段,是一個(gè)很好的測(cè)試平臺(tái)。本人在攻讀博士學(xué)位期間基于核磁共振系統(tǒng)對(duì)拓?fù)湎嗔孔幽M和拓?fù)淞孔佑?jì)算方向展開(kāi)了系列理論和實(shí)驗(yàn)研究,主要?jiǎng)?chuàng)新性成果有：1.利用核磁共振系統(tǒng)對(duì)拓?fù)湎噙M(jìn)行了系列的量子模擬實(shí)驗(yàn)研究： (i)國(guó)際上首次實(shí)驗(yàn)實(shí)現(xiàn)了不同拓?fù)湫蜷g的絕熱躍遷。實(shí)驗(yàn)中我們模擬的Wen-plaquette自旋晶格模型存在兩種不同的拓?fù)湫颉Ｓ捎诓煌耐負(fù)湫蚓哂邢嗤膶?duì)稱性,這是不能由經(jīng)典的朗道對(duì)稱破缺理論描述的一種新型相變現(xiàn)象。該工作為研究當(dāng)前有著廣泛興趣的拓?fù)湎到y(tǒng)上邁出了新的重要一步。內(nèi)容詳見(jiàn)3.1節(jié)。 (ii)實(shí)驗(yàn)觀測(cè)了二、三、四自旋量子系統(tǒng)中的動(dòng)力學(xué)量子霍爾效應(yīng)。通過(guò)非絕熱響應(yīng)直接測(cè)量Berry曲率和Chern數(shù),清晰地觀測(cè)到不同的量子化平臺(tái)即拓?fù)湎嘧兊陌l(fā)生,是目前在最大系統(tǒng)上的非平庸演示。同時(shí),得到的Chern數(shù)揭示了哈密頓量的幾何結(jié)構(gòu)。類似于傳統(tǒng)的量子霍爾效應(yīng),精確的量化平臺(tái)可以用于量子精密測(cè)量。內(nèi)容詳見(jiàn)3.2節(jié)。 (iii)首次通過(guò)測(cè)量非阿貝爾幾何相實(shí)驗(yàn)識(shí)別拓?fù)湫�。區(qū)分多體相互作用量子體系中出現(xiàn)的拓?fù)溆行驊B(tài)是凝聚態(tài)理論最重要的任務(wù)之一。然而直到目前為止還沒(méi)有相關(guān)的實(shí)驗(yàn)報(bào)道,主要?dú)w結(jié)于實(shí)驗(yàn)測(cè)量本身的極大困難。我們通過(guò)測(cè)量拓?fù)浜?jiǎn)并基態(tài)下的非阿貝爾幾何相識(shí)別出給定某模型的拓?fù)湫?并得到了其準(zhǔn)粒子維度和分?jǐn)?shù)統(tǒng)計(jì)等信息。與傳統(tǒng)的拓?fù)浼m纏熵相比,非阿貝爾幾何相提供了更完備的關(guān)于拓?fù)湫虻男畔ⅰ＿@對(duì)實(shí)驗(yàn)分類不同的拓?fù)湫蚓哂兄匾饬x。內(nèi)容詳見(jiàn)3.3節(jié)。2.從量子態(tài)制備和存儲(chǔ)的角度對(duì)拓?fù)淞孔佑?jì)算進(jìn)行了系列研究： (i)實(shí)驗(yàn)制備拓?fù)湫�。我們通過(guò)絕熱驅(qū)動(dòng)含時(shí)的多體哈密頓量成功地制備出四重簡(jiǎn)并的拓?fù)湫颉＿@不僅為進(jìn)一步研究拓?fù)湫虻男再|(zhì)提供了可能。同時(shí),基于基態(tài)的拓?fù)浜?jiǎn)并和長(zhǎng)程糾纏,也為構(gòu)建具有魯棒性的量子存儲(chǔ)做好了鋪墊。內(nèi)容詳見(jiàn)4.1節(jié)。 (ii)理論計(jì)算和分析拓?fù)淞孔哟鎯?chǔ)。我們以Wen-plaquette模型為例,從熱噪聲和退相干兩個(gè)角度理論分析了拓?fù)淞孔哟鎯?chǔ)的物理機(jī)制。并以一個(gè)具體的例子來(lái)進(jìn)一步考慮實(shí)驗(yàn)演示的可能性。內(nèi)容詳見(jiàn)4.2節(jié)。3.開(kāi)發(fā)新的四量子比特核磁樣品和脈沖生成自動(dòng)化程序,不僅提高了實(shí)驗(yàn)控制的精確度,也降低了脈沖設(shè)計(jì)的復(fù)雜性。該樣品及相關(guān)程序已為實(shí)驗(yàn)室大量使用,在實(shí)驗(yàn)技術(shù)改進(jìn)和提升上有著重要意義。內(nèi)容詳見(jiàn)附錄A和B。
[Abstract]:The quantum computer based on the principle of quantum mechanics has the incomparable computing power of the classical computer. However, noise and decoherence are one of the main obstacles to the realization of quantum computers. Noise originates from the imperfect operation of quantum bits; decoherence originates from the inevitable interaction between quantum systems and the environment. Noise and decoherence can cause partial loss or even complete error of the encoding information. One of the solutions is quantum error correction. But this requires additional auxiliary bits to consume too much resources, and the error correction itself is also noisy. Another strategy is topological quantum computing. Unlike active quantum error correction, topological quantum computation is passive, that is, no attempt or operation is required to make the system without noise, because the system itself has a robust self correcting function. This is related to the overall topological properties of the system. Topological quantum computing is a quantum computing scheme with the highest known fault tolerance at present. The topological quantum computing scheme depends on the existence of the topological phase. The topological phase is a kind of strange material state that can not be described by the classical Landau symmetry breaking theory. This state has some interesting properties, such as the base state degeneracy of the topological manifolds, the quasi particle fraction statistics and topological entanglement entropy. A kind of special topological physical state is called topological order, which can be described as a long range entanglement mode with energy gap and has no perturbation effect. The known example is the fractional quantum Holzer state, which is the first time to observe the topological order in a real system. In addition, there is a topological order in some two-dimensional lattice models. Topological ordering not only provides natural noise free media for fault-tolerant quantum computation, but also plays an important role in condensed matter physics as basic scientific research, such as topological properties, topological transformation and discovery of new materials. It is very challenging to observe topology and realize topological quantum computation in a real system, which is mainly limited by the current experimental methods and control techniques. For example, a two-dimensional lattice model is the topological order often involves many body interactions (such as the toric code model with four body interactions), and construct a quantum bit lattice often need more. It is not an easy task to drive and control such a complex multi qubit system. Because of this, the research of topological quantum computing remains in the theory, without any related experimental reports. Quantum simulation, using a controllable quantum system to simulate complex or difficult physical phenomena, has many successful applications in condensed matter physics, high-energy physics and quantum chemistry. Quantum simulation provides us with a powerful means to explore topological and topological quantum computing. On the other hand, as one of the physical implementation platforms of quantum simulation, nuclear magnetic resonance system has mature control technology and precise measurement method in multi qubit experiment, which is a good test platform. During my PhD in nuclear magnetic resonance system of topological quantum simulation and topological quantum computation based on the direction of the theory and a series of experimental studies, the main innovative results are as follows: 1. the use of nuclear magnetic resonance system of topological phase on the quantum simulation: (I) the experimental realization of the adiabatic transition of different topology the order. In the experiment, there are two different topological orders in our simulated Wen-plaquette spin lattice model. Because the different topological order has the same symmetry, it is a new phase transformation phenomenon which can not be described by the classical Landau symmetry breaking theory. The work has taken a new and important step to study the current topology system with wide interest. The content is detailed in Section 3.1. (II) the kinetic quantum Holzer effect in the two or three and four spin quantum systems was experimentally observed. By measuring the Berry curvature and Chern number directly through the adiabatic response, we can clearly observe the occurrence of the different quantization platform, namely the topological transformation, which is a non mediocre demonstration on the largest system at present. At the same time, the obtained Chern number reveals the geometric structure of Hamiltonian. Similar to the traditional quantum Holzer effect, an accurate quantization platform can be used for quantum precision measurement. The content is detailed in Section 3.2. (III) to identify the topological order by measuring the non Abel geometric phase for the first time. It is one of the most important tasks of the condensed state theory to distinguish the topological ordered states appearing in the quantum system of multibody interaction. However, there have been no related experimental reports until now, mainly due to the great difficulty of the experimental measurement itself. We measure the topological order of a given model by measuring the non Abel geometry recognition under topological degenerate ground state, and get the information of quasi particle dimension and fractional statistics. Compared with the traditional topological entanglement entropy, the non Abel geometry provides a more complete information about the topological order. This is of great significance to the classification of different topological order in the experiment. The content is detailed in Section 3.3. 2. from the perspective of quantum state preparation and storage, a series of studies on topological quantum computation are carried out: (I) experimental preparation of topological order. We have successfully prepared four degenerate topological order by adiabatic drive time - containing multibody Hamiltonian. This not only provides a possibility for further study of the properties of the topological order. At the same time, the topology degenerate and long range entanglement based on the ground state also pave the way for the construction of robust quantum storage. The content is detailed in Section 4.1. (II) theoretical calculation and analysis of topological quantum storage. We take the Wen-plaquette model as an example to analyze the physical mechanism of topological quantum storage from two angles of thermal noise and decoherence. And a specific example is given to further consider the possibility of an experimental demonstration. The content is detailed in Section 4.2. 3. the development of new four qubit NMR samples and pulse generation automation program not only improves the precision of experimental control.
【學(xué)位授予單位】：中國(guó)科學(xué)技術(shù)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O413.1;O482.532
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