敲開圖靈之門：量子計算與機器學習

{"type":"doc","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"italic"},{"type":"strong"}],"text":"本文最初發表於 The Gradient ，經原作者 Ather Fawaz 授權，由InfoQ 中文站翻譯並分享。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"零和一。零零碎碎。陰與陽。最重要的是，開關，有些是開，有些是關。人們已經習慣於看到和使用現代計算機。每年，像英特爾、AMD、ARM 和英偉達這樣的行業巨擘，都會發布他們的下一代頂級芯片，不斷地互相競爭，並將其推向極限。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"當我們仔細評估這些新的多核 CPU、 GPU 和雲端託管的大型計算集羣時，我們很快意識到更快的處理器不一定能提高計算能力。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"的確，計算速度在過去的幾十年中呈指數級增長，但是我們能夠處理的數據量也在增長。我們可以在互聯網上存儲和分析"},{"type":"link","attrs":{"href":"https:\/\/www.bernardmarr.com\/default.asp?contentID=1846","title":"","type":null},"content":[{"type":"text","text":"艾字節"}]},{"type":"text","text":"（譯註：艾字節：ExaByte，EB，一種信息計量單位，現今通常在標示網絡硬盤總容量，或具有大容量的保存媒介之保存容量時使用。1EB=1024PB==2⁶⁰字節）數據，用來訓練像"},{"type":"link","attrs":{"href":"https:\/\/openai.com\/blog\/openai-api\/","title":"","type":null},"content":[{"type":"text","text":"OpenAI 的 GPT-3"}]},{"type":"text","text":"這樣的深度學習模型，以及實現在圍棋和國際象棋等複雜遊戲中"},{"type":"link","attrs":{"href":"https:\/\/www.neowin.net\/news\/one-of-the-biggest-go-players-retires-due-to-the-rise-of-invincible-ai-players","title":"","type":null},"content":[{"type":"text","text":"擊敗冠軍"}]},{"type":"text","text":"和"},{"type":"link","attrs":{"href":"https:\/\/www.wired.com\/story\/defeated-chess-champ-garry-kasparov-made-peace-ai\/","title":"","type":null},"content":[{"type":"text","text":"特級大師"}]},{"type":"text","text":"所需的計算能力。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"但是，所有這些技術進步是否已經從根本上擴大了我們能用計算機做的事情，超出了我們最初使用計算機的範圍呢？或者簡單地說，我們是否改變了我們經典的計算模式？"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"現代計算機是按照馮·諾依曼結構（von Neumann architecture）的原理運行的（Ogban 等人，2007 年）。馮·諾依曼結構利用輸入和輸出到處理器的邏輯函數，根據一組指令對輸入進行操作。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https:\/\/static001.infoq.cn\/resource\/image\/99\/5c\/99eac59f8232eee909e382a832403d5c.jpg","alt":null,"title":"","style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":"","fromPaste":false,"pastePass":false}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":"center","origin":null},"content":[{"type":"text","text":"馮·諾依曼結構"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"儘管馮·諾依曼結構有助於實際解決問題，但是它們並不能描述計算過程本身。爲此，我們需要圖靈機（De Mol 等人，2018 年）。圖靈機提供了當今計算機的抽象模型。圖靈機按一套規則操縱磁帶上的符號。接着磁帶會根據機器的當前狀態繼續或停止。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"衆所周知，經典計算機現在能夠進行的所有計算，都可以在圖靈機上完成。精明的讀者會將這一結果與丘奇 - 圖靈論題（Church-Turing thesis）聯繫起來，後者指出，“任何現實世界的計算都可以通過 λ 演算（λ-calculus）來完成，這相當於使用一般遞歸函數”（Rabin，2012 年）。然而，在實踐中，對於任何實際的、合理大小的問題來說，圖靈機實際上都太慢了。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https:\/\/static001.infoq.cn\/resource\/image\/37\/b9\/3728d3yy7aa14fe1ab78944b82a6dab9.jpg","alt":null,"title":"","style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":"","fromPaste":false,"pastePass":false}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":"center","origin":null},"content":[{"type":"text","text":"圖靈機的圖解表示"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"正如丘奇 - 圖靈論題所證明的那樣，圖靈機提供的可計算性是我們尚未突破的玻璃天花板。正如我們稍後要討論的那樣，儘管我們的計算設備以圖靈機爲基礎，開啓了計算的可能性，但是這個模型本身也有一些固有的缺陷，令人望而卻步。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"但這並不意味着，一切都已經結束了。馬丁·路德·金（Martin Luther King Jr.）曾說過：“我們必須接受失望，因爲它是有限的，但千萬不可失去希望，因爲它是無窮的。”（"},{"type":"text","marks":[{"type":"italic"}],"text":"We must accept finite disappointment, but never lose infinite hope."},{"type":"text","text":"）要打破這一玻璃天花板，需要的不僅僅是在計算機芯片上裝上大量的晶體管。它需要從根本上對計算機進行徹底的重新思考；從最基本的單元——比特開始。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"heading","attrs":{"align":null,"level":2},"content":[{"type":"text","text":"進入量子領域"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在過去的 120 年裏，也許是物理學史上最偉大的進步。愛因斯坦的狹義相對論和廣義相對論改變了我們對時間、空間和引力的認識，而狄拉克、泡利、費曼、薛定諤、海森堡和普朗克關於量子力學的公式則從根本上徹底改變了我們關於電子、質子和中子這個無窮小世界的理解。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https:\/\/static001.infoq.cn\/resource\/image\/5d\/75\/5d879293e0c1d85cdb48f3918a5ef675.jpg","alt":null,"title":"","style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":"","fromPaste":false,"pastePass":false}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":"center","origin":null},"content":[{"type":"text","text":"1927 年索爾維國際會議（Solvay International Conference）被視爲現代物理學的轉折點"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"量子力學是這些進步中的最後一個，它與尋求強大的新計算模型有着最直接的聯繫。20 世紀 80 年代初，理查德·費曼設想，量子計算機能夠提供一種解決當代（或經典）計算機難以指數化解決的問題的方法（費曼，1986 年）。量子計算機要求我們採用一個完全不同的比特概念，這是有可能的。在深入研究這種計算模式之前，我們首先必須定義量子計算機的含義。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"與經典計算機不同的是，經典計算機的比特在任何時刻都可以存在於 0 或 1 的狀態，而量子計算機中的量子比特（或簡稱量子位，qubit）可以存在於額外的狀態。它可以作爲離散狀態（0 或 1）存在，也可以作爲兩種狀態的疊加存在。這是量子比特的一個固有屬性，它爲其定域性賦予了一個概率分佈。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":"center","origin":null},"content":[{"type":"text","text":"經典比特與量子比特"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"本文目的不是解釋量子計算機背後的量子偏心。然而，有必要回顧量子物理學的兩個基本概念：波粒二象性和糾纏。我們在後面將會看到，正是這兩個概念構成了量子計算機的基石。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"heading","attrs":{"align":null,"level":2},"content":[{"type":"text","text":"量子力學插曲"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"量子比特的狀態可以表示爲列向量。不同的狀態由不同的列向量表示，其中每個列向量與其餘列向量正交。一個量子比特對應的狀態是由可能的狀態的線性組合給出的，這些可能的狀態用複數加權。這相當於說，在任何給定的時刻，量子比特處於這些基態的疊加，或者說處於概率波中。測量所有這些可能位置中某一精確位置的行爲將導致這種概率波，或波函數塌縮，從而揭示出單一狀態。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"這就是波粒二象性的關鍵之處：一個粒子既表現出類似波的行爲，又表現出類似粒子的行爲。在我們明確地觀察到一個粒子之前，我們永遠無法說出它處於什麼狀態；哥本哈根解釋正式提出了一個關於測量前粒子位置的問題（Faye，2002 年）。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https:\/\/static001.infoq.cn\/resource\/image\/18\/0f\/18451251cc22e578b221d169354da20f.jpg","alt":null,"title":"","style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":"","fromPaste":false,"pastePass":false}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":"center","origin":null},"content":[{"type":"text","text":"波粒二象性"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"第二個需要理解的重要原理是量子糾纏。以粒子系統爲例，每個粒子都有自己的波函數。一個多粒子的系統被定義爲狀態空間的"},{"type":"link","attrs":{"href":"https:\/\/www.math3ma.com\/blog\/the-tensor-product-demystified","title":"","type":null},"content":[{"type":"text","text":"張量積"}]},{"type":"text","text":"。這個由 k 個粒子組成的張量積，每個粒子由一個 n 維的列向量表示，稱爲具有 nᵏ維。這種狀態空間的表示方法稱爲狀態的集合。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"爲了說明這一點，讓我們把我們的初始系統中的 k 個粒子簡化成只有兩個，每個粒子都處於 a 和 b 兩種狀態的疊加中（爲簡單起見，也可以是圓形或正方形）。假如一種粒子的狀態知識不能揭示另一種粒子的狀態，那麼我們可以說這兩種粒子是獨立的。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https:\/\/static001.infoq.cn\/resource\/image\/82\/70\/82e0cd6524fa52cc564982cd9d160770.jpg","alt":null,"title":"","style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":"","fromPaste":false,"pastePass":false}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":"center","origin":null},"content":[{"type":"text","text":"獨立粒子"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"但是，如果知道一個粒子的狀態，就能立即得到另一個粒子狀態的信息，那麼我們就可以說這兩個粒子是糾纏的。最令人困惑的實驗結果之一是：無論兩個糾纏粒子之間的距離有多遠，測量一個粒子的狀態都能在瞬間揭示出另一個粒子的信息，而這正是我們能夠迅速得到的。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"這意味着如果"},{"type":"link","attrs":{"href":"https:\/\/www.forbes.com\/sites\/chadorzel\/2017\/02\/28\/how-do-you-create-quantum-entanglement\/","title":"","type":null},"content":[{"type":"text","text":"產生兩個糾纏的粒子"}]},{"type":"text","text":"，把它們帶到太陽系的相對兩端，一個粒子的波函數坍縮，另一個粒子的波函數也會立即坍縮。兩個粒子之間的這種通訊速度比光速還快，因此愛因斯坦將"},{"type":"link","attrs":{"href":"https:\/\/www.sciencemag.org\/news\/2018\/04\/einstein-s-spooky-action-distance-spotted-objects-almost-big-enough-see","title":"","type":null},"content":[{"type":"text","text":"這種奇特現象"}]},{"type":"text","text":"稱爲“鬼魅般的超距作用”（"},{"type":"text","marks":[{"type":"italic"}],"text":"spooky action at a distance"},{"type":"text","text":".）。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https:\/\/static001.infoq.cn\/resource\/image\/18\/cf\/18ede69c1a61aa38d7d868c04c24f9cf.jpg","alt":null,"title":"","style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":"","fromPaste":false,"pastePass":false}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":"center","origin":null},"content":[{"type":"text","text":"處於糾纏態的量子"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"沉迷於糾纏的更深指導，需要一些嚴格的數學公式，故本文不再贅述。此外，儘管糾纏以比光速更快的速度傳輸信息，但它並沒有違反定域性。但有關這方面的更多細節，請參閱該指南（Wilczek，2016 年）。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在實踐中，由於系統間的相互作用會導致糾纏，因此很少會遇到獨立的粒子，而粒子之間的相關性是由連接波函數和具體概率的基本數學原理引入的（Joos，2009 年）。對於波粒二象性和量子糾纏的概念，讓我們看看量子計算機如何巧妙地利用這些現象進行計算。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"heading","attrs":{"align":null,"level":2},"content":[{"type":"text","text":"完全不同的計算模型"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"就像在經典計算機中晶體管代表 1 比特的信息一樣，硅或磷等半導體材料的核自旋代表一個量子比特的信息。這些半導體硅或磷原子通過電場和磁場進行操縱和讀取（Vogel，N.D.，Physics World 期刊，2019 年）。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如前所述，量子比特是量子計算機的基本單元。由於量子比特可以以更多的狀態存在，而不僅僅是一個經典比特的 0 和 1，因此我們可以使用它們來編碼更多的信息。實際上，使用量子比特編碼經典比特是可能的，但反之則不然。量子比特的信息不能在經典晶體管中被編碼。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"對於比特，n 個晶體管可以用來編碼 n 分量系統；封裝一個 8 位經典系統只需要 8 個存儲位。若 n 分量系統是量子的，則需要 2ⁿ 個複數來編碼它（Kopczyk，2018 年）。推而廣之，編碼一臺 8 量子比特的量子計算機需要 256 個複數。而要在經典機器上模擬 64 個量子比特，則需要 2⁶⁴=18,446,744,073,709,551,616 個複數。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"因此，相對於經典計算機，量子計算提供了一個更大的勢態空間；儘管量子比特是一個更大的計算對象，但它需要更少的量子比特來表示困難的計算問題。顯然，經典計算機很難模仿這樣的表示。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"就像經典門（如 AND、OR、XOR）是對比特進行任何操作的麪包和黃油一樣，量子門也是通過相應的量子門來修改量子比特的狀態。然而，量子計算機有一組特殊的門，這些門是特定於量子比特操作的。其中包括"},{"type":"link","attrs":{"href":"https:\/\/www.sciencedirect.com\/topics\/mathematics\/hadamard-gate","title":"","type":null},"content":[{"type":"text","text":"Hadamard 門"}]},{"type":"text","text":"和"},{"type":"link","attrs":{"href":"https:\/\/www.quantiki.org\/wiki\/cnot","title":"","type":null},"content":[{"type":"text","text":"CNOT 門"}]},{"type":"text","text":"（Djordjevic，2012 年）。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"Hadamard 門可用於創建狀態的疊加（Qiskit\/IBM，未標明日期），而 CNOT 門可以用來糾纏量子比特（Qiskit\/IBM，未標明日期）。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https:\/\/static001.infoq.cn\/resource\/image\/42\/e4\/427cda87a1097e864946344f0f596ae4.jpg","alt":null,"title":"","style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":"","fromPaste":false,"pastePass":false}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":"center","origin":null},"content":[{"type":"text","text":"量子電路"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"通過使用量子門，量子計算將從接收輸入的某個初始狀態開始。從那裏，它向最終狀態過渡，然後可以對其進行測量以檢索特定信息。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https:\/\/static001.infoq.cn\/resource\/image\/7f\/70\/7fb69fyyd420a0afca74225e1f628470.jpg","alt":null,"title":"","style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":"","fromPaste":false,"pastePass":false}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":"center","origin":null},"content":[{"type":"text","text":"應用在量子比特上的可能變換可以用布洛赫球面（Bloch sphere）的旋轉來表示"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"量子計算機巧妙地利用了疊加和糾纏的原理，從而能夠同時計算來自多個量子比特的結果（Kopczyk，2018 年）。舉例來說，假設我們的量子計算需要對一組輸入進行轉換或者使用函數，我們可以把這個函數應用到多個輸入端，同時得到它們的結果。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"相反，對於經典計算機的相同操作需要按照每個輸入順序執行，或按照單個經典電路執行。舉例說明，由於經典比特沒有糾纏，也沒有疊加，所以要從中提取信息，需要分別測量和計算。對於量子計算機來說，糾纏和疊加使我們可以在同一時間內同時計算有關多個量子比特的信息。實質上，這個計算模型讓我們可以探索不同的路徑，並同時進行數學運算。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"這是量子計算機的一大優點。固有的並行性相當強大，因此我們稱之爲“指數計算能力”。要"},{"type":"link","attrs":{"href":"https:\/\/www.microsoft.com\/en-us\/research\/video\/quantum-computing-computer-scientists\/","title":"","type":null},"content":[{"type":"text","text":"使這種能力翻倍"}]},{"type":"text","text":"，我們只需在電路中再增加一個量子比特。這一發現導致了導致了量子算法的發展，量子算法利用量子計算機所提供的並行性，在某些問題的求解速度比經典最佳解快得多。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https:\/\/static001.infoq.cn\/resource\/image\/4f\/d0\/4fef493a7c744002e583608e8aaa89d0.jpg","alt":null,"title":"","style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":"","fromPaste":false,"pastePass":false}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":"center","origin":null},"content":[{"type":"text","text":"量子計算機的詳細概述"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在 2019 年，量子計算機超越經典計算機的首次有形展示首次亮相。谷歌的研究人員使用 53 位量子計算機 Sycamore 在 200 秒內解決了一個問題。相反，這個同樣的問題，現有的一臺經典超級計算機大約需要 1 萬年才能解決。Sycamore 的研究結果被官方稱爲“量子霸權”的展示，這是一個顯而易見的例子，表明量子計算範式顯然比經典計算範式更爲強大（Arute 與 Arya，2019 年，第 505~510 頁）。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https:\/\/static001.infoq.cn\/resource\/image\/2b\/b7\/2b8e0688d69b0e58d510f6cfea7808b7.jpg","alt":null,"title":"","style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":"","fromPaste":false,"pastePass":false}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":"center","origin":null},"content":[{"type":"text","text":"谷歌的量子計算機 Sycamore，擁有 53 位量子比特"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"雖然 IBM 很快用自己的後續論文（Pednault 等人，2019 年）"},{"type":"link","attrs":{"href":"https:\/\/www.ibm.com\/blogs\/research\/2019\/10\/on-quantum-supremacy\/","title":"","type":null},"content":[{"type":"text","text":"對谷歌的說法提出了質疑"}]},{"type":"text","text":"，但谷歌的研究成果（《使用可編程超導處理器的量子霸權》（"},{"type":"text","marks":[{"type":"italic"}],"text":"Quantum supremacy using a programmable superconducting processor"},{"type":"text","text":"））被普遍視爲量子計算機發展的突破性時刻。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"heading","attrs":{"align":null,"level":2},"content":[{"type":"text","text":"量子計算世界未非想象般美好"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"迄今爲止，我們只討論了量子計算機的積極方面。但是它的實現和發展並不是一帆風順的。事實證明，在疊加狀態下懸浮量子比特非常困難。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"爲了實現穩定性，量子計算機需要被保存在冰箱中，冰箱將量子比特要冷卻到接近絕對零度（0 K）的溫度。這意味着量子計算機僅限於小衆研究領域和昂貴的實驗室，至少現在是這樣。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https:\/\/static001.infoq.cn\/resource\/image\/8b\/40\/8b1439986c352fd6e25783cb21d5a040.jpg","alt":null,"title":"","style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":"","fromPaste":false,"pastePass":false}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":"center","origin":null},"content":[{"type":"text","text":"一個典型的 NISQ 時代的量子計算機環境"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"此外，量子比特容易受到噪聲的影響（這種現象被稱爲退相干（decoherence）），這意味着它們在相互作用的粒子環境中失去了概率量子行爲和存儲的信息。這是因爲在量子層面上，任何觀察或相互作用都無法溫和地從一個系統同時獲取信息，但卻可以保持其原始的不受干擾狀態。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"這種交互作用有效地將量子定域化，導致有利的狀態疊加消失（Bacciagaluppi,2020年），這也是爲什麼我們沒能實現量子計算機的全部潛力（Kopczyk，2018 年）。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https:\/\/static001.infoq.cn\/resource\/image\/d0\/b6\/d0ac13e0159bc89e41b2552a3acff8b6.jpg","alt":null,"title":"","style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":"","fromPaste":false,"pastePass":false}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":"center","origin":null},"content":[{"type":"text","text":"關於連貫性的問題"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"考慮到它們的侷限性，我們正處於研究人員所說的“嘈雜中型量子”（Noisy Intermediate-Scale Quantum，NISQ）時代。現有的量子計算機的能力還不足以產生容錯結果。退相干還會影響量子算法的有效性，破壞其加速優勢。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"同時，由於"},{"type":"link","attrs":{"href":"https:\/\/qiskit.org\/textbook\/ch-algorithms\/shor.html","title":"","type":null},"content":[{"type":"text","text":"Shor 算法"}]},{"type":"text","text":"能夠在多項式時間內對大量數據進行質因式處理，因而有可能破壞我們現有的加密標準，但它仍是一種理論上的進展。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"最重要的是，量子計算機並不是每種計算類型的上乘選擇。它們不會更快的完成兩個數字的基本運算，也不會輕鬆地訓練神經網絡，當然也不會更快地運行日常程序。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"像 IBM 這樣的公司甚至聲稱，量子計算機“永遠不會在經典計算機中佔據‘霸權’地位，而是會與它們協同工作，因爲每種計算機都有其獨特的優勢。”（Pednault 與 Gunnels，2019 年）"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"然而，量子計算機在某些問題上有過人之處，這是值得討論的。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"heading","attrs":{"align":null,"level":2},"content":[{"type":"text","text":"量子機器學習"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"近年來的研究表明，量子計算的真正潛力在於建立一個由經典段和量子段共同組成的管道。對於科學應用，我們必須計算粒子的基態。這一問題在研究化學反應和平衡時往往很重要。基態被定義爲粒子處於最低能級的狀態，因而也是最穩定的狀態。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"傳統上，要獲得基態，需要從粒子態的本徵向量中計算出最小本徵值，這些本徵向量由稱爲"},{"type":"link","attrs":{"href":"http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/quantum\/hamil.html","title":"","type":null},"content":[{"type":"text","text":"哈密頓"}]},{"type":"text","text":"（Hamiltonian）量的矩陣來表示。對於小型系統，經典計算機在求解時並不會很費力，但對含有大量粒子的大系統來說，這一簡單的任務將以指數方式增長，很快就會破壞可用的計算資源。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"但是，如果我們使用混合的量子機器學習算法，這種搜索空間的增加就變得容易處理。"},{"type":"link","attrs":{"href":"https:\/\/pennylane.ai\/qml\/demos\/tutorial_vqe.html","title":"","type":null},"content":[{"type":"text","text":"變分量子本徵求解器"}]},{"type":"text","text":"（Variational-Quantum-Eigensolver ，VQE）利用經典算法和量子算法來估計哈密頓量的最低本徵值。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"簡而言之，它的量子部分叫做 ansatz，可以智能地搜索出粒子的所有可能狀態的空間。經典部分通過梯度下降來調整 ansatz 參數，使其接近最優解。這一組合表明，量子計算機在這類粒子模擬任務中特別有用。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https:\/\/static001.infoq.cn\/resource\/image\/94\/77\/94c6d5010f96967509f17d294ff5bb77.jpg","alt":null,"title":"","style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":"","fromPaste":false,"pastePass":false}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":"center","origin":null},"content":[{"type":"text","text":"VQE 算法示意圖"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在過去的幾年裏，其他各種量子機器學習算法也得到了發展。用於經典 k- 均值聚類的最著名的量子算法優化了向量之間的 Lloyd 經典距離計算子程序（Rebollo-Monedero 與 Girod，2009 年），以將經典"},{"type":"codeinline","content":[{"type":"text","text":"O(NkM)"}]},{"type":"text","text":"計算複雜度呈指數級地降低到"},{"type":"codeinline","content":[{"type":"text","text":"O(Mklog(N))"}]},{"type":"text","text":"，其中"},{"type":"codeinline","content":[{"type":"text","text":"k"}]},{"type":"text","text":"是聚類的數量，"},{"type":"codeinline","content":[{"type":"text","text":"M"}]},{"type":"text","text":"是訓練樣本的數量，並且"},{"type":"codeinline","content":[{"type":"text","text":"N"}]},{"type":"text","text":"是特徵計數（Biamonte 與 Wittek，2017 年，第 195~202 頁）。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"研究人員還研究了量子計算機在運行神經網絡方面的能力。儘管神經網絡的穩健表達在量子領域仍然任重道遠（Schuld 與 Sinayskiy，2014 年），但學者們已經提出了各種方法來用量子電路來表示經典的神經網絡。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"例如，來自蘇黎世的瑞士聯邦理工學院和 IBM Q 的研究人員就經典神經網絡和量子神經網絡的維數、可最優性和訓練性進行了比較。（Abbas 等人，2020 年）"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https:\/\/static001.infoq.cn\/resource\/image\/by\/43\/byy2aed978bb3437480ea7c0273e9443.jpg","alt":null,"title":"","style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":"","fromPaste":false,"pastePass":false}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":"center","origin":null},"content":[{"type":"text","text":"量子神經網絡研究"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"Abbas 等人利用模型的維數來比較不同神經網絡的能力。研究結果表明，量子神經網絡結合了良好的特徵圖（對數據進行編碼），使其有效維數高於經典神經網絡。此外，與經典神經網絡不同的是，量子神經網絡提供了更好的"},{"type":"link","attrs":{"href":"https:\/\/web.stanford.edu\/class\/stats311\/Lectures\/lec-09.pdf","title":"","type":null},"content":[{"type":"text","text":"Fisher 信息矩陣"}]},{"type":"text","text":"，並且特徵值更均勻，不爲零。這種量子神經網絡在 IBM 的 27 位量子比特機器上的"},{"type":"link","attrs":{"href":"https:\/\/archive.ics.uci.edu\/ml\/datasets\/iris","title":"","type":null},"content":[{"type":"text","text":"Iris 數據集"}]},{"type":"text","text":"上，於經典神經網絡相比，訓練和收斂速度更快。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https:\/\/static001.infoq.cn\/resource\/image\/30\/04\/305f621ee3809efd9411fd0b1fa4c704.jpg","alt":null,"title":"","style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":"","fromPaste":false,"pastePass":false}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":"center","origin":null},"content":[{"type":"text","text":"與經典神經網絡相比，量子神經網絡訓練得更好"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"這些結果表明，具有三段（特徵映射、變異和測量）的健壯量子神經網絡具有高容量和快速訓練性等優勢。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"heading","attrs":{"align":null,"level":2},"content":[{"type":"text","text":"NP 困難問題、搜索和蒙特卡洛模擬"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"量子計算機還擅長於解決優化問題。優化問題利用一種特定的啓發式解決方案，從一組有效的解決方案中找到最佳可能的解決方案。爲了理解優化如何在量子計算環境下運行，研究人員設計了"},{"type":"link","attrs":{"href":"https:\/\/stackoverflow.com\/questions\/1857244\/what-are-the-differences-between-np-np-complete-and-np-hard","title":"","type":null},"content":[{"type":"text","text":"NP 困難問題"}]},{"type":"text","text":"的量子算法。舉個例子，旅行商問題（Traveling-Salesman-Problem，TSP）中使用的量子算法，它爲許多城市提供了比經典蠻力方法更高的二次加速（Srinivasan 等人，2018 年）。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"其他利用量子計算機並行性的算法也取得了很有希望的結果。Grovers 算法是目前搜索具有 N 個條目的未排序數據庫的最快的量子算法。在經典計算機上，這項任務所需的時間與 N 成正比，但量子計算機顯示出平方根加速，並在"},{"type":"codeinline","content":[{"type":"text","text":"O(sqrt(N))"}]},{"type":"text","text":"內完成任務。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"類似地，量子計算機可以在 N 個數據點上進行傅里葉變換，反演稀疏 N*N 矩陣，並在時間上求出它們的本徵值和本徵向量，與 "},{"type":"codeinline","content":[{"type":"text","text":"log(N)"}]},{"type":"text","text":" 中的一個多項式成正比。對於這些任務，已知的最優經典算法所需的時間與 "},{"type":"codeinline","content":[{"type":"text","text":"N log(N)"}]},{"type":"text","text":" 成正比，也就是說，在這種情況下，量子計算機也表現出指數級的加速（Biamonte 與 Wittek，2017 年，第 195~202 頁）。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"金融行業也正在爲量子計算機的潛在應用做準備。分析股票市場及其相關指標的任務可以轉化爲一個優化問題。有鑑於此，量子計算機的直接實際應用有可能在金融領域紮根。去年7月，西班牙 BBVA 銀行發佈了一項研究報告，結果發現量子計算機能夠提高信用評分，現貨套利機會，以及加速蒙特卡洛模擬（The Economist 期刊，2020 年）。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"同樣，摩根大通（JPMorgan Chase & Co.）研究部門負責人 Marco Pistoia 也希望量子計算機可以通過加速資產定價，挖掘表現更好的投資組合以及改進現有的機器學習算法來提高利潤。就連高盛（Goldman Sachs）量子研究主管 William Zeng 也大膽宣稱，量子計算機能夠革新銀行業和金融業（The Economist 期刊，2020 年）。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"heading","attrs":{"align":null,"level":2},"content":[{"type":"text","text":"糾纏的未來"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"量子計算機揭示了一種很有前途的計算和解決問題的新方法。對棘手問題的指數加速比和多項式時間解都是量子比特的量子力學性質的自然後果。這使得計算模型更接近於"},{"type":"link","attrs":{"href":"https:\/\/cs.stackexchange.com\/questions\/125\/how-to-define-quantum-turing-machines","title":"","type":null},"content":[{"type":"text","text":"量子圖靈機"}]},{"type":"text","text":"的抽象模型。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"回到我們最初對圖靈機的討論，量子圖靈機是經典圖靈機的泛化或量子化，其中磁頭和磁帶是疊加的。形式上，機器的狀態是希爾伯特空間（Hilbert space）中的量子態。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"量子圖靈機的磁帶是一個無限長的單邊磁帶，它代表了疊加的比特。在這種情況下，量子計算是一種幺正變換（unitary transformation），由量子測量決定結果，它將相干疊加中的“單邊磁帶”簡化爲經典的“雙邊磁帶”，其具有可分離的正交本徵態（Moschovakis，2003 年）。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https:\/\/static001.infoq.cn\/resource\/image\/37\/b9\/3728d3yy7aa14fe1ab78944b82a6dab9.jpg","alt":null,"title":"","style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":"","fromPaste":false,"pastePass":false}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":"center","origin":null},"content":[{"type":"text","text":"量子圖靈機的圖解表示"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"將這種計算模型與使能硬件結合起來，谷歌展現出的量子霸權被研究界很多人認爲違反了丘奇 - 圖靈論題的擴展，後者認爲這種計算模型應該有效地用經典圖靈機建模。事實上，（Bernstein 與 Vazirani，1993 年）論文表明，量子圖靈機與傳統圖靈機有着本質上的不同，它可以解決某些在經典圖靈機上需要超多項式時間的問題。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在化學、金融和優化問題中的具體應用，也爲量子計算機在現實世界的應用提供了一條途徑。此外，量子神經網絡令人印象深刻的可訓練性和維度爲利用量子計算機進行機器學習和深度學習的研究提供了令人興奮的新途徑。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"IBM、英特爾、 Zapata、亞馬遜和霍尼韋爾等科技公司認識到了量子計算機的潛力，紛紛加大了對其商業應用的投資。用於量子計算機編程的高級語言、框架和庫，如 Q#、Qiskit、TensorFlow Quantum 和 Cirq 等，也在穩步增長。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"這些框架及其教程已經降低了量子計算開發的入門門檻，如果這一趨勢能夠持續下去，我們將會在這十年裏看到一系列令人振奮的量子計算進展。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"儘管取得了這些進展，我們仍需要批判性地思考量子計算機的現狀。量子比特對退相干的偏好，加上其高昂的低溫要求，給我們現有的硬件帶來了極大的限制。所以量子計算機能否真正在實際應用中佔據霸權地位，在這個時候提出這個問題可能並不是正確的。更爲緊迫的問題是，我們能否克服 NISQ 時代的不切實際之處。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"現在看來，這是一個大衛與歌利亞之間的史詩級戰鬥故事，只是現在宣佈這場戰爭還爲時過早。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong"}],"text":"作者介紹："}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"Ather Fawaz，是巴基斯坦拉合爾的 FAST 大學本科生，現上大四，主修計算機科學，但對物理和數學也有濃厚的興趣。他的畢業項目是關於使用生成對抗網絡的高保真語音合成。他定期爲 Neowin 撰寫關於量子計算、人工智能和太空旅行的最新進展。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong"}],"text":"原文鏈接："}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"https:\/\/thegradient.pub\/knocking-on-turings-door-quantum-computing-and-machine-learning\/"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}}]}