一把茶壶揭真相 量子优势成笑谈

一把茶壶揭真相  量子优势成笑谈

作者：徐令予

上图中的那位老先生是理查德·博彻兹（Richard Borcherds），他是英国著名数学家，目前从事量子场论研究。博彻兹教授以其在格、群论和无限维代数方面的工作而闻名，他因此于 1998 年获得菲尔兹奖—等同于数学界的诺贝尓奖。

上图是一段视频的截屏，该视频是博彻兹教授为美国著名大学所作线上教程的一部分，视频中的他手握茶壶侃侃而谈，道尽了“量子优势”之荒唐，这段视频非常值得观看。

由于博彻兹这位老先生操一口英式英语，不太容易听懂，特把一些重要段落转成文字、附上时间节点和中文翻译，供读者们对照参考。

02:53 视频时间点

为了评估计算设备，需要选择某个计算问题。我非常感兴趣的计算问题称之为茶壶问题，茶壶问题是要计算当茶壶从空中掉落地面后会分解为几块。

茶壶问题对于经典数字计算机是一个极难求解的问题，因为一把茶壶是由百万百万百万百万个原子组成，对如此复杂的系统使用量子力学的薛定谔方程求解已经远远超出了世上任何超级数字计算机的能力。

但是茶壶问题可以让茶壶落地在一秒钟内解决，在这个特定问题上茶壶可以击败任何数字计算机。但是由此而宣称“茶壶优势”就实在太愚蠢了！

“茶壶优势”错在何处？错误首先就是在比较茶壶和数字计算机的计算能力时选择了一个毫无意义的问题，茶壶碎成几片没人会关心。错误更主要是在评估计算能力时高度偏向茶壶，它特意选择了一个茶壶很擅长解决但数字计算机无法解决的问题。

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 视频时间点

通过选择特定的问题，可以让任何事物显得比其他事物更具优势。要证明食蚁兽比爱因斯坦更聪明也是小菜一碟，可以为食蚁兽与爱因斯坦设计特殊的智能竞赛：看一分钟内谁能抓住更多的蚂蚁。所以只要掌握比赛规则的决定权，取得某种所谓的优势就易如反掌。

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 视频时间点

首先创造了“量子优势“这样一个词组，然后宣传量子计算机取得了量子优势。这听上去很高大上，那么是否意味着量子计算机优于经典数字计算机呢？答案是否定的，因为按量子优势的定义，只能说明量子计算机在某个特定问题上优于数字计算机。这其实毫无意义，因为你总可以找到特定的问题让任何东西优于经典数字计算机。

茶壶可以对经典计算机取得茶壶优势，因为在求解一个特定问题上茶壶可以胜过经典计算机。所以量子优势具有很大的误导性，它并不表示量子计算机在实用意义上有什么优越性，量子计算机和茶壶可能很难用经典计算机模拟，但这并不能说明它们是有实际价值的计算工具。

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.

视频链接  https://youtu.be/sFhhQRxWTIM

博彻兹教授对“量子优势”的质疑集中在“计算”的真正含义上，在这个问题上相信没有什么人会比这位菲尔兹奖得主更专业更权威，他对“量子优势”的否定极具说服力。该视频获得过万的观看，500+点赞，4个反对，人心向背 一目了然。YouTube 视频下面的62条评论也值得一读。

中科大的“九章”光学实验装置就是一把价值千万的高挡茶壶，它和茶壶一样根本不具备任何有实质意义的计算能力。“九章”刚面世时，一帮吹鼓手们在大众媒体上企图把“九章”与求解矩阵的“积和式”勾连起来。但是经反复质疑后，人们方才明白“九章”与求解“积和式”风马牛不相及。现在他们又用所谓的 Torontonian（多伦多人）函数来打扮粉饰“九章”。

请注意：

• Torontonian函数绝不是一个古老的数学问题，它产生于2018年的年底；
• Torontonian函数是为某种特殊高斯玻色釆样获取量子优势而特意定制的；
• Torontonian函数并不能解决什么实际问题。

中科大的“九章”恰恰就是用作那种特殊高斯玻色釆样的实验装置，而Torontonian函数就是为“九章”而生的一个数学问题。所以“九章”根本就不是用来解决已有的数学问题，“九章”把自己定义为了一个数学问题。

更为诡异的是，“九章”通过200秒的光子采样实验，其实也不可能给出任何有意义的 Torontonian矩阵的函数值 [2]，它只能反复强调“九章”的实验得到了一大堆的光子的分布数据，超级计算机通过计算Torontonian 函数得到相同的釆样分布数据需要化费多少亿万年。这和茶壶实验何其相似？所谓的茶壶优势也不是茶壶的碎裂真能求解什么数学问题，而是强调模拟茶壶碎裂过程需要对复杂系统求解薛定谔方程，而这远远超出了超级计算机的计算能力，所以茶壶对超级计算机具有计算优势。茶壶和“九章”基于完全相同的逻辑，颠倒黑白莫此为甚！

需要注意的是，博彻兹教授质疑和反对的只是“量子优势”，并不是量子计算，他在视频中多次指出研究 Shor量子算法破解公钥密码还是有实际意义的，因为茶壶对破解公钥密码完全无能为力。他还认为不同的量子计算机之间作比较也无可厚非，但是用一些似是而非的问题对量子计算机和经典计算机作比较会误导公众。

[1] 九章光学实验解读（中）数据不支持九章取得量子优势

[2] 亚伦森教授博客对茶壶视频的反应

      评论区可能更有价值

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