【诺奖得主Wilczek科普专栏】用“CT”看量子世界
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Frank Wilczek
作者 | Frank Wilczek
翻译 | 胡风、梁丁当
中文版
最新实验表明，借助CT扫描的原理，我们可以“看到”亚原子粒子与波
几周前，我惊喜地在一个物理网站上看到一则新闻报道，题为“量子重叠层析成像的实验实现”。众所周知，对量子系统进行成像极其困难。2020年，我和乔丹·科特勒提出了一项量子重叠层析成像技术，以获得量子世界的清晰图像。南洋理工大学的Zhengning Yang团队在一项突破性实验中，实现了量子重叠层析成像技术。
量子重叠层析成像的英文是Quantum Overlapping Tomography (QTO)。我们可以通过拆解与分析这三个单词，来理解什么是QTO、以及它为什么重要。
先来看Q。要描绘一个量子体系，哪怕它很小，也需要一张很大的画布。比如，一个只有两到五个电子的量子系统，它的波函数有六到十五的空间维度。这让物理学家陷入了一个困境：我们知道描述系统的方程是什么，可是即使用目前最先进的超级计算机，我们也只能非常粗糙地求解系统的波函数。多电子量子体系的波函数包含了我们需要的所有信息。如果我们能够更加准确地求解它，以更好地理解真实的量子世界，我们将能够把化学和材料科学，包括药物和催化剂的设计，提升到一个全新的高度。
为了解决这一挑战，科学家们开发了量子模拟器和量子计算机。在理想的情况下，量子模拟器和量子计算机可以在模型层面实现我们所希望了解的系统的波函数。可到此为止，问题只解决了一半。我们还需要从波函数中读取它所包含的信息。而这一步很难：量子力学告诉我们，对波函数进行测量会使其“塌缩”，破坏了对它的进一步使用。
这时候就需要发挥T（断层扫描）的作用了。“断层扫描”源自希腊语“tomos”，意思是“切片或切片”。它也是CT扫描（计算机辅助断层扫描）中的T。在CT扫描中，通过对许多二维X射线的信息进行汇总重组，可以准确地构建出身体内部的三维图。QOT的思想是在更广阔的量子领域中做类似的事情。
如何从量子波函数中获得它蕴含的信息？这个问题有点像我们在玩Wordle填字游戏或益智棋盘游戏（Mastermind）时碰到的难题。在这些游戏中，我们可以进行多次查询（类似于测量）。从每个查询中，我们只能得到部分信息。我们可以把从波函数中获取信息想象成在玩一个大型的填字游戏，其中包含了上千个字符；又或者是一个大规模的益智棋盘游戏，其中包含了上千个钉子和数十种颜色。难度可想而知。
这就引出了第三个字母，表示重叠的O。为了解决量子测量问题，一个好的策略是以不同的分辨率对波函数进行采样，以获得交叠的图像信息。把这些图像编织在一起，就能够形成一幅更加完整的画。南洋理工大学的研究人员们在实验中测试了科特勒博士和我提出的算法。他们展示了这种方法确实能够把测试图像准确、有效地重构出来。
实验成功的好消息勾起了我的一个美好回忆。几年前的一个夏天，在斯德哥尔摩外的波罗的海海边，科特勒博士和我有一次漫长的散步。当时，为了应对中国的杰出物理学家潘建伟提出的挑战，我们想出了一个办法，使波函数的测量变得比较实用。
颇有点浪漫的是，好消息传来时，我正在从胆囊手术中恢复，而恰恰是CT扫描确诊了我的病况。CT扫描为手术消除了许多不确定因素。量子技术也终将对生物化学产生同样的作用。或许有那么一天，借助强效新药，人们甚至不需要手术就能够康复。
英文版
A recent experiment suggests that the principle behind CT scans can also be used to view elusive subatomic particles and waves
A couple of weeks ago I got a nice surprise from a news story on a physics website headlined “The Experimental Realization of Quantum Overlapping Tomography.” It reported on breakthrough work by Zhengning Yang and colleagues at Nanyang Technical University, who implemented a technique suggested by Jordan Cotler and me in 2020. This line of work aims to get a clear image of the notoriously hard-to-view quantum world.
Each of the three words in Quantum Overlapping Tomography (QTO) can use some unpacking to understand what is and why it matters.
Let’s look at the Q first. A good quantum picture needs a very large canvas, even when it’s depicting something very small. For example, the wave functions for systems of two to five electrons exist in spaces ranging from six to 15 dimensions. This puts physicists in a peculiar situation. We know what the relevant equations are, but using current supercomputers we can only solve them very approximately. If we could do a better job of understanding quantum reality, we would be able to take chemistry and materials science, including the design of drugs and catalysts, to new levels. Wave functions of multi-electron systems contain all the needed information.
Quantum simulators and quantum computers are meant to rise to this challenge. Ideally, they can embody the complete quantum-mechanical wave function of the system you’re hoping to understand, as a sort of scale model. But with that, the problem will only be half-solved. The thing is, it’s not easy to read the information that wave functions contain. In quantum mechanics, infamously, measuring a wave function “collapses” it and spoils it for further use.
That’s where the T, for tomography, comes in. “Tomography” derives from the Greek “tomos” meaning “slice, or section.” It is also the T in CT scan (Computer-assisted Tomography). CT scans assemble the information from many 2-D X-rays into an accurate 3-D rendering of the body’s interior. The idea with QOT is to do something similar in the vaster quantum realm.
The problem of reading quantum wave function information is something like the challenge posed by games like Wordle and Mastermind. In those games, you make multiple queries (akin to measurements) and get back only partial information from each one. But now imagine that the Wordle contains thousands of characters or the Mastermind template thousands of pegs and dozens of colors.
That brings us to the third letter, O for overlapping. A good strategy for the quantum measurement problem is making measurements that sample the wave function with different resolutions. This gives you overlapping images that you can weave together into a fuller picture. The Nanyang researchers tested the algorithms that Dr. Cotler and I came up with by showing that they gave back a complicated test image accurately and efficiently.
The good news from the Nanyang experiment brought back pleasant memories of the long summer walk by the Baltic Sea, outside Stockholm, that Dr. Cotler and I took a few years ago. There, responding to a challenge from the brilliant Chinese physicist Jian- Wei Pan, we cracked the problem of making wave function measurement reasonably practical.
The news came just as I was recovering from gallbladder surgery. That was weirdly poetic, since it was a CT scan that had nailed my diagnosis. That technology has taken a lot of the guesswork out of surgery. Quantum technology will eventually do the same for biochemistry. Eventually, by supplying potent new medicines, it might even take the surgery out of treatment.
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编辑：黄琦
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