【诺奖得主Wilczek科普专栏】量子奇普
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Frank Wilczek
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.
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编辑:黄琦
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