諾獎得主Wilczek：量子奇普_風聞

撰文 | Frank Wilczek

翻譯 | 胡風、梁丁當

中文版

古印加人用來結繩記事的奇普，為現代物理學和量子計算提供了一個令人驚訝的模型

存儲複雜信息的方式有很多。在現代技術中，主要有三種方式：人類的語言文字、計算機的二進制代碼以及遺傳學的DNA和RNA序列。然而，還有一種美麗又古老的存儲和處理信息的方法，它不僅集合了這三種方式的元素，還添加了一些獨特的東西：拓撲學，一門關於穩定的形狀與結構的科學。

奇普 (qiupu) 的意思是“結”。誕生於安第斯山脈中的古印加文明曾用奇普來記錄信息。形式略微不同的結也曾盛行在中國和日本。在秘魯的一些偏遠村莊中，至今仍在使用奇普，成為了一種文化遺產。對大多數人來説，它不過是件稀奇的民俗文物。但對一些物理學家來説，它正在成為一種創造力的靈感來源。

奇普文的“字母”是用繩編成的結。通常一個奇普有一根主繩，上面繫着很多副繩，在副繩上結着幾種不同樣式的結。結的排列順序和間距代表了不同的含義，而繩索的顏色也用來指代不同的範疇。比如，藍繩上的兩個結可能代表“戰士”和“羔羊”，而紅繩上的兩個同樣的繩結則代表“1000”和“10”。這和分化細胞在DNA的4個鹼基上表達表觀遺傳變異可謂異曲同工。

奇普文字有很多優點。它不需要紙。與其他方式的符號相比，這些繩結不易被弄髒、抹除或者錯誤複製，並且輕便易攜。

傳統奇普中的每根繩都是獨立的（雖然它們的順序是確定的）。它們可以互相纏繞，形成辮子。辮子的拓撲結構——即一條繩是從另一根繩的上方或是下方穿過——可以產生豐富的代碼。結的間隔則可以代表空，或者説零。一位哈佛大學的人類學家認為，印加人使用奇普進行二進制編碼，比計算機早了幾個世紀。

最近，一種奇異的新奇普——量子奇普——經常成為物理前沿的頭條新聞。為了説明什麼是量子奇普，我必須先解釋構成它們的奇異的繩子——這不是古印加人用的繩子。

幾十年來，物理學家一直用“世界線”這個概念來形象地描述粒子的運動。為了簡單起見，我們假設粒子在一個水平面上移動，而用垂直這個水平面的縱軸來標記時間。於是，粒子在不同時間的運動軌跡形成了一條上升的曲線，即它的世界線。當同時有幾個粒子時，它們的世界線可以打結，或者更準確地説，它們可以編成辮子。有一種被稱為任意子的粒子，它們的量子行為記錄下了由其世界線形成的辮子。任意子的世界線形成了一個量子奇普。

任意子這個名字是我在40年前提出的，取自“一切都會發生”的含義。當時我還預言了任意子的一些關鍵屬性。兩年前，兩個實驗團隊各自在實驗中證明了任意子的存在。在這些開創性實驗中實現的量子奇普還比較簡單，存不了太多信息。但上個月，微軟的研究人員宣佈實現了功能更強的任意子。在此基礎上，有可能構造出令人印象深刻的量子奇普。

這個量子奇普中的辮子有幾個優點：當引入更多的線並將其拉長時，存儲的信息會指數式增加，即使受到外界擾動，它們的基本結構也能保持不變——因為其拓撲結構沒變。跟隨着古印加文明賦予的靈感指引，我們有可能製造出一台拓撲量子計算機，它可以挑戰對其他計算機來説甚是棘手的計算。

英文版

The Inca system of quipu-tying a series of knots to record information-is providing a surprising model to modern physics and quantum computing.

Complex information can be stored in many ways. Three methods-written human language, the binary code of computers and the DNA and RNA sequences of genetics- dominate today’s technologies. But there is a beautiful, ancient method of storing and processing information that incorporates elements of all three and adds something unique: topology, the science of stable shapes and structures.

Quipu-meaning “knot”-served the Incan civilizations of the Andes well for centuries. In a slightly different form, it also flourished in China and Japan. Though quipu is still used in remote Peruvian villages and valued as a cultural heritage, it is mostly regarded as a historical curiosity. For some physicists, however, it is becoming a creative inspiration.

The basic letters of quipu are knots made in strings. Typically, many strings are hung from a common cord. Several different kinds of knots are used, and their order and spacing is meaningful. Different colors of string get used, too, to set a context. Thus, on a blue string, two knots might represent “warrior” and “lamb,” while those knots on a red string represent “1,000” and “10”-a trick similar to how differentiated cells apply epigenetic variation to the four-letter codes of DNA.

Quipu has a lot going for it. It does not require the production of paper. The knots are less prone to getting smudged, erased or miscopied than other kinds of signals. The strings are lightweight and portable.

In traditional quipu, each string is independent (though they come in a definite order). They can be wound around one another, producing braids. The topological pattern of a braid-which strand passes over or under another-can be used to enrich the code. The knots can also encode spaces, or zeros, through their separation. A Harvard anthropologist has argued that the Inca used them as binary representations, centuries before computers.

Now, an exotic new form of quipu-quantum quipu-is making headlines at the frontier of physics. To explain this ferment, I must describe the weird strings it is based on. These are not our ancestors’ strings.

For decades, physicists have used the concept of “world-lines” to visualize the motion of particles. To keep things simple, let’s suppose that our particles move on a horizontal plane and that we use the vertical direction to label time. That way, the history of how a particle moves becomes an ascending curve: its world- line. When we have several particles, their world-lines can get knotted up-or more precisely, they can form braids. There are certain particles, called anyons, whose quantum behavior keeps track of the braid that their world-lines form. The anyon world-lines form a quantum quipu.

I first named and analyzed some key properties of anyons about 40 years ago (the name was meant to suggest that “anything goes.”) Then, just two years ago, the existence of anyons was demonstrated experimentally by two different teams. The simple quantum quipus that were produced in those pioneering experiments can’t store much information. But last month Microsoft researchers announced that they have engineered much more capable anyons. These could be the building blocks for an impressive quantum quipu.

Braids have several advantages in this work: They store exponentially more information as they bring in more strands and lengthen, and their essential structure stays intact even if jostled-the intertwined strings’ topology doesn’t change. The result could be a topological quantum computer ready to take on otherwise intractable computational challenges, while evoking how the Inca recorded what they knew.

Frank Wilczek

弗蘭克·維爾切克是麻省理工學院物理學教授、量子色動力學的奠基人之一。因發現了量子色動力學的漸近自由現象，他在2004年獲得了諾貝爾物理學獎。

本文經授權轉載自微信公眾號“蔻享學術”。

特 別 提 示

1. 進入『返樸』微信公眾號底部菜單“精品專欄“，可查閲不同主題系列科普文章。

2. 『返樸』提供按月檢索文章功能。關注公眾號，回覆四位數組成的年份+月份，如“1903”，可獲取2019年3月的文章索引，以此類推。