用“CT”看量子世界丨諾獎得主Wilczek專欄_風聞

在CT掃描中，通過對許多二維X射線的信息進行彙總重組，可以準確地構建出身體內部的三維圖。QOT的思想是在更廣闊的量子領域中做類似的事情。

撰文 | Frank Wilczek

翻譯 | 胡風、梁丁當

中文版

最新實驗表明，藉助CT掃描的原理，我們可以“看到”亞原子粒子與波

幾周前，我驚喜地在一個物理網站上看到一則新聞報道，題為“量子重疊層析成像的實驗實現”。眾所周知，對量子系統進行成像極其困難。2020年，我和喬丹·科特勒提出了一項量子重疊層析成像技術，以獲得量子世界的清晰圖像。南洋理工大學的Zhengning Yang團隊在一項突破性實驗中，實現了量子重疊層析成像技術。

量子重疊層析成像的英文是Quantum Overlapping Tomography (QTO)。我們可以通過拆解與分析這三個單詞，來理解什麼是QTO、以及它為什麼重要。

先來看Q。要描繪一個量子體系，哪怕它很小，也需要一張很大的畫布。比如，一個只有兩到五個電子的量子系統，它的波函數有六到十五的空間維度。這讓物理學家陷入了一個困境：我們知道描述系統的方程是什麼，可是即使用目前最先進的超級計算機，我們也只能非常粗糙地求解系統的波函數。多電子量子體系的波函數包含了我們需要的所有信息。如果我們能夠更加準確地求解它，以更好地理解真實的量子世界，我們將能夠把化學和材料科學，包括藥物和催化劑的設計，提升到一個全新的高度。

為了解決這一挑戰，科學家們開發了量子模擬器和量子計算機。在理想的情況下，量子模擬器和量子計算機可以在模型層面實現我們所希望瞭解的系統的波函數。可到此為止，問題只解決了一半。我們還需要從波函數中讀取它所包含的信息。而這一步很難：量子力學告訴我們，對波函數進行測量會使其“塌縮”，破壞了對它的進一步使用。

這時候就需要發揮T（斷層掃描）的作用了。“斷層掃描”源自希臘語“tomos”，意思是“切片或切片”。它也是CT掃描（計算機輔助斷層掃描）中的T。在CT掃描中，通過對許多二維X射線的信息進行彙總重組，可以準確地構建出身體內部的三維圖。QOT的思想是在更廣闊的量子領域中做類似的事情。

如何從量子波函數中獲得它藴含的信息？這個問題有點像我們在玩Wordle填字遊戲或益智棋盤遊戲（Mastermind）時碰到的難題。在這些遊戲中，我們可以進行多次查詢（類似於測量）。從每個查詢中，我們只能得到部分信息。我們可以把從波函數中獲取信息想象成在玩一個大型的填字遊戲，其中包含了上千個字符；又或者是一個大規模的益智棋盤遊戲，其中包含了上千個釘子和數十種顏色。難度可想而知。

這就引出了第三個字母，表示重疊的O。為了解決量子測量問題，一個好的策略是以不同的分辨率對波函數進行採樣，以獲得交疊的圖像信息。把這些圖像編織在一起，就能夠形成一幅更加完整的畫。南洋理工大學的研究人員們在實驗中測試了科特勒博士和我提出的算法。他們展示了這種方法確實能夠把測試圖像準確、有效地重構出來。

實驗成功的好消息勾起了我的一個美好回憶。幾年前的一個夏天，在斯德哥爾摩外的波羅的海海邊，科特勒博士和我有一次漫長的散步。當時，為了應對中國的傑出物理學家潘建偉提出的挑戰，我們想出了一個辦法，使波函數的測量變得比較實用。

頗有點浪漫的是，好消息傳來時，我正在從膽囊手術中恢復，而恰恰是CT掃描確診了我的病況。CT掃描為手術消除了許多不確定因素。量子技術也終將對生物化學產生同樣的作用。或許有那麼一天，藉助強效新藥，人們甚至不需要手術就能夠康復。

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.

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。

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