撰文 | Frank Wilczek

翻译 | 胡风、梁丁当

中文版
 

古印加人用来结绳记事的奇普，为现代物理学和量子计算提供了一个令人惊讶的模型
 

存储复杂信息的方式有很多。在现代技术中，主要有三种方式：人类的语言文字、计算机的二进制代码以及遗传学的DNA和RNA序列。然而，还有一种美丽又古老的存储和处理信息的方法，它不仅集合了这三种方式的元素，还添加了一些独特的东西：拓扑学，一门关于稳定的形状与结构的科学。

奇普 (qiupu) 的意思是“结”。诞生于安第斯山脉中的古印加文明曾用奇普来记录信息。形式略微不同的结也曾盛行在中国和日本。在秘鲁的一些偏远村庄中，至今仍在使用奇普，成为了一种文化遗产。对大多数人来说，它不过是件稀奇的民俗文物。但对一些物理学家来说，它正在成为一种创造力的灵感来源。

奇普文的“字母”是用绳编成的结。通常一个奇普有一根主绳，上面系着很多副绳，在副绳上结着几种不同样式的结。结的排列顺序和间距代表了不同的含义，而绳索的颜色也用来指代不同的范畴。比如，蓝绳上的两个结可能代表“战士”和“羔羊”，而红绳上的两个同样的绳结则代表“1000”和“10”。这和分化细胞在DNA的4个碱基上表达表观遗传变异可谓异曲同工。

奇普文字有很多优点。它不需要纸。与其他方式的符号相比，这些绳结不易被弄脏、抹除或者错误复制，并且轻便易携。

传统奇普中的每根绳都是独立的（虽然它们的顺序是确定的）。它们可以互相缠绕，形成辫子。辫子的拓扑结构——即一条绳是从另一根绳的上方或是下方穿过——可以产生丰富的代码。结的间隔则可以代表空，或者说零。一位哈佛大学的人类学家认为，印加人使用奇普进行二进制编码，比计算机早了几个世纪。

最近，一种奇异的新奇普——量子奇普——经常成为物理前沿的头条新闻。为了说明什么是量子奇普，我必须先解释构成它们的奇异的绳子——这不是古印加人用的绳子。

几十年来，物理学家一直用“世界线”这个概念来形象地描述粒子的运动。为了简单起见，我们假设粒子在一个水平面上移动，而用垂直这个水平面的纵轴来标记时间。于是，粒子在不同时间的运动轨迹形成了一条上升的曲线，即它的世界线。当同时有几个粒子时，它们的世界线可以打结，或者更准确地说，它们可以编成辫子。有一种被称为任意子的粒子，它们的量子行为记录下了由其世界线形成的辫子。任意子的世界线形成了一个量子奇普。

任意子这个名字是我在40年前提出的，取自“一切都会发生”的含义。当时我还预言了任意子的一些关键属性。两年前，两个实验团队各自在实验中证明了任意子的存在。在这些开创性实验中实现的量子奇普还比较简单，存不了太多信息。但上个月，微软的研究人员宣布实现了功能更强的任意子。在此基础上，有可能构造出令人印象深刻的量子奇普。

这个量子奇普中的辫子有几个优点：当引入更多的线并将其拉长时，存储的信息会指数式增加，即使受到外界扰动，它们的基本结构也能保持不变——因为其拓扑结构没变。跟随着古印加文明赋予的灵感指引，我们有可能制造出一台拓扑量子计算机，它可以挑战对其他计算机来说甚是棘手的计算。

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

弗兰克·维尔切克是麻省理工学院物理学教授、量子色动力学的奠基人之一。因发现了量子色动力学的渐近自由现象，他在2004年获得了诺贝尔物理学奖。

本文经授权转载自微信公众号“蔻享学术”。