一把茶壺揭真相 量子優勢成笑談

一把茶壺揭真相  量子優勢成笑談

作者：徐令予

上圖中的那位老先生是理查德·博徹茲（Richard Borcherds），他是英國著名數學家，目前從事量子場論研究。博徹茲教授以其在格、群論和無限維代數方麵的工作而聞名，他因此於 1998 年獲得菲爾茲獎—等同於數學界的諾貝尓獎。

上圖是一段視頻的截屏，該視頻是博徹茲教授為美國著名大學所作線上教程的一部分，視頻中的他手握茶壺侃侃而談，道盡了“量子優勢”之荒唐，這段視頻非常值得觀看。

由於博徹茲這位老先生操一口英式英語，不太容易聽懂，特把一些重要段落轉成文字、附上時間節點和中文翻譯，供讀者們對照參考。

02:53 視頻時間點

為了評估計算設備，需要選擇某個計算問題。我非常感興趣的計算問題稱之為茶壺問題，茶壺問題是要計算當茶壺從空中掉落地麵後會分解為幾塊。

茶壺問題對於經典數字計算機是一個極難求解的問題，因為一把茶壺是由百萬百萬百萬百萬個原子組成，對如此複雜的係統使用量子力學的薛定諤方程求解已經遠遠超出了世上任何超級數字計算機的能力。

但是茶壺問題可以讓茶壺落地在一秒鍾內解決，在這個特定問題上茶壺可以擊敗任何數字計算機。但是由此而宣稱“茶壺優勢”就實在太愚蠢了！

“茶壺優勢”錯在何處？錯誤首先就是在比較茶壺和數字計算機的計算能力時選擇了一個毫無意義的問題，茶壺碎成幾片沒人會關心。錯誤更主要是在評估計算能力時高度偏向茶壺，它特意選擇了一個茶壺很擅長解決但數字計算機無法解決的問題。

In order to test computational devices, you need to choose a problem. And the problem i'm really interested in is known as the teapot problem, and the teapot problem is the following, so as you take a teapot and you drop it on the floor the teapot problem asks calculate how many pieces does the teapot break into.

And if you think about this is an incredibly difficult problem for a digital computer to solve, because you need to simulate a teapot and a teapot has several million million million million atoms, and you need to solve a Schrodinger equation for that and so on and it's it's just way beyond the ability of any current digital computer to solve.

This problem however the teapot can solve in one second, well yeah, well since there's a borrowed teapot i don't think i wish to actually do that, but you can imagine it falling down. So the teapot can beat any digital computer at this problem. However it does undoubtedly occur to you that claiming a teapot is an advanced computational device is really really stupid. 

So what is wrong with my argument? Well the problem with the argument i gave about teapots being advanced computational devices is the first of all the problem i chose is completely and utterly pointless. I mean who cares how many pieces a teapot breaks into. But the major problem is it is highly biased towards teapots it was specially selected to be a problem that teapots are very good at solving but digital computers can't solve.

04:34 視頻時間點

通過選擇特定的問題，可以讓任何事物顯得比其他事物更具優勢。要證明食蟻獸比愛因斯坦更聰明也是小菜一碟，可以為食蟻獸與愛因斯坦設計特殊的智能競賽：看一分鍾內誰能抓住更多的螞蟻。所以隻要掌握比賽規則的決定權，取得某種所謂的優勢就易如反掌。

So by selecting a problem you can make anything look better than almost anything else. You know suppose I want to prove that an anteater is smarter than Einstein. Well that's easy, I just administer an intelligence test the anteater and to Einstein and see who does better, and the intelligence test I choose is how many ants can you catch in one minute okay yeah so if you choose the test you can make anything look good.

05:43 視頻時間點

首先創造了“量子優勢“這樣一個詞組，然後宣傳量子計算機取得了量子優勢。這聽上去很高大上，那麽是否意味著量子計算機優於經典數字計算機呢？答案是否定的，因為按量子優勢的定義，隻能說明量子計算機在某個特定問題上優於數字計算機。這其實毫無意義，因為你總可以找到特定的問題讓任何東西優於經典數字計算機。

茶壺可以對經典計算機取得茶壺優勢，因為在求解一個特定問題上茶壺可以勝過經典計算機。所以量子優勢具有很大的誤導性，它並不表示量子計算機在實用意義上有什麽優越性，量子計算機和茶壺可能很難用經典計算機模擬，但這並不能說明它們是有實際價值的計算工具。

First of all we have this phrase quantum supremacy, and you know quantum computers have achieved quantum supremacy. It sounds really impressive that means does that mean they're better than classical computers? Well, no it doesn't, because if you look at the definition of quantum supremacy, it turns out to mean that there is some problem at which quantum computers are better than classical ones. Well as we've just seen this is sort of useless you can always find some problem which things are better than classical computers. 

My teapot for example has attained teapot supremacy over classical computers, because there's a problem it can solve better than classical computers. So quantum supremacy is a kind of really misleading term. It doesn't actually mean that quantum computers are better at anything useful the point is um quantum computers or for that matter teapots may be really hard to simulate on a classical computer that doesn't mean they're useful at computation.

視頻鏈接  https://youtu.be/sFhhQRxWTIM

博徹茲教授對“量子優勢”的質疑集中在“計算”的真正含義上，在這個問題上相信沒有什麽人會比這位菲爾茲獎得主更專業更權威，他對“量子優勢”的否定極具說服力。該視頻獲得過萬的觀看，500+點讚，4個反對，人心向背 一目了然。YouTube 視頻下麵的62條評論也值得一讀。

中科大的“九章”光學實驗裝置就是一把價值千萬的高擋茶壺，它和茶壺一樣根本不具備任何有實質意義的計算能力。“九章”剛麵世時，一幫吹鼓手們在大眾媒體上企圖把“九章”與求解矩陣的“積和式”勾連起來。但是經反複質疑後，人們方才明白“九章”與求解“積和式”風馬牛不相及。現在他們又用所謂的 Torontonian（多倫多人）函數來打扮粉飾“九章”。

請注意：

• Torontonian函數絕不是一個古老的數學問題，它產生於2018年的年底；
• Torontonian函數是為某種特殊高斯玻色釆樣獲取量子優勢而特意定製的；
• Torontonian函數並不能解決什麽實際問題。

中科大的“九章”恰恰就是用作那種特殊高斯玻色釆樣的實驗裝置，而Torontonian函數就是為“九章”而生的一個數學問題。所以“九章”根本就不是用來解決已有的數學問題，“九章”把自己定義為了一個數學問題。

更為詭異的是，“九章”通過200秒的光子采樣實驗，其實也不可能給出任何有意義的 Torontonian矩陣的函數值 [2]，它隻能反複強調“九章”的實驗得到了一大堆的光子的分布數據，超級計算機通過計算Torontonian 函數得到相同的釆樣分布數據需要化費多少億萬年。這和茶壺實驗何其相似？所謂的茶壺優勢也不是茶壺的碎裂真能求解什麽數學問題，而是強調模擬茶壺碎裂過程需要對複雜係統求解薛定諤方程，而這遠遠超出了超級計算機的計算能力，所以茶壺對超級計算機具有計算優勢。茶壺和“九章”基於完全相同的邏輯，顛倒黑白莫此為甚！

需要注意的是，博徹茲教授質疑和反對的隻是“量子優勢”，並不是量子計算，他在視頻中多次指出研究 Shor量子算法破解公鑰密碼還是有實際意義的，因為茶壺對破解公鑰密碼完全無能為力。他還認為不同的量子計算機之間作比較也無可厚非，但是用一些似是而非的問題對量子計算機和經典計算機作比較會誤導公眾。

[1] 九章光學實驗解讀（中）數據不支持九章取得量子優勢

[2] 亞倫森教授博客對茶壺視頻的反應

      評論區可能更有價值

1. chorasimilarity Says: 
   Comment #129  May 1st, 2021 at 3:26 am

Came here to say that the problem of how an elastic brittle teapot cracks into pieces is mathematically well defined, but hard numerically. There is a whole mathematical and numerics field around smashing teapots. All starts from the Mumford-Shah functional (where Mumford is the great David Mumford), 

https://en.wikipedia.org/wiki/Mumford%E2%80%93Shah_functional

I know this because a long, long time ago it was a part of my phd thesis, for example the article Energy Minimizing Brittle Crack Propagation, J. of Elasticity, 52, 3 (1999) (submitted in 1997), pp 201-238
free pdf here: http://imar.ro/~mbuliga/brittle.pdf