「墨子沙龙」怎样控制量子计算机的量子态｜David·Wineland（上）
视 频
Quantum Computers——诺贝尔物理学奖获得者David·Wineland_腾讯视频
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Thanks all of you for coming and I'm sorry there isn't more room for you here. But... Anyway so I'm gonna try to give you a little idea about quantum qubit computers, ah... and the second part of the title is some kind of what's called the thought experiment in physics, it's the idea of Schroedinger's Cat if you haven't heard about it before, I'll describe briefly, but it's it's one of the mysteries that still exist that should be possible, anyway I'll get started.
感谢大家来听报告，抱歉位子不够了。我会给大家简单介绍一下量子比特计算机，第二部分的标题是所谓的物理思想实验，也就是薛定谔的猫，如果你们没听过的话，我简单介绍下。这个谜（薛定谔的猫）一直都存在，而且也应该是可能的。我开始报告。
So to just summarize, I think many of you know how the basics... how your PCs and your iPads work and... why do you need... what's interesting about quantum mechanics for computers. It has to do with some very weird properties that we can realize them in quantum systems, and one is called superposition. I'll talk about that briefly and then, I'm gonna say how we can manipulate quantum states for the computers, and at the end I'll come back to how quantum computers relate to Schrodinger's cat which I'll describe along the way.
我先做个概述，想必大家都知道你们的计算机和iPad如何工作的，那么量子力学对计算机又有什么有意思的影响呢。这跟量子系统中可以实现的一些奇异的性质有关，其中一种性质就是叠加态，我马上会简要介绍。我会讲一下怎样控制量子计算机的量子态，最后回到量子计算机和薛定谔的猫有什么关系。
So one example that I like to try to give an idea about superposition is. From this image up here, You see this line drawing of a cube, some instance of time the front surface will be the square on the left, and at other times you might this this square being in the foreground. So there is kind of this ambiguity about which image you see. If you look at the upper right hand square for a while, you can sometime see one picture. I like this example, because the image up here has both properties simultaneously. This is very much like what we talked about superposition states in quantum mechanics. For example our quantum bits can possess both properties at once, and I'll say a little about that in a minute. The only thing I like about this example is if we have a two-state system in the case whether this image looks like this or like that. When you tend to see in one orientation than the other, that's very much like quantum measurement that is. That is in this image of in the right-hand corner you see both the properties, but when you tend to see one figure or another, that's very much like projecting.
我想举个例子说明一下叠加态的意思。在上面这个图片中大家看到线段画成的立方体，有时候是左边的这个正方形在前面，有时候你又会看到这个正方形在最前面，所以你看到哪个面有某种不确定性。如果你看一会儿右上角的正方形，有时候可以看到一个图片。我喜欢这个例子，因为这个图片同时有两个属性，这非常像我们在量子力学中所说的叠加态。比如量子比特就可以同时有两种性质，我待会儿还要再讲一下。我喜欢这个例子的是如果我们有一个两个态的系统，就像这里的图片看起来像这样或者是那样，当你试图从一个方向到另一个方向看时就非常类似量子测量，也就是在右手边的角上你可以同时看到两面，但是当你倾向看一个或者另一个图片的时候就非常像（测量）投影。
So some examples of small superpositions, what I'm gonna talk about are quantum bits, are atoms that are within their containers what we call traps. So you can think like a marble in a bowl and then Marvel can go back and forth in this bowl, one example of superposition we can realize with our atoms in this bowl. Is that we can realize this situation, where at some instance of time the atom is both at the left side of bowl and in the right side of the ball at the same time. This makes no sense in our ordinary daily experience, but this is the kind of thing (things) that we can realize in these quantum systems. So that we called superposition in this example here, it's... at some instance of time it's a superposition of the atom being (on the) most on the left side of the right side at the same time. What we are gonna be interested in, for making trying to make a quantum computer using these ideas of superposition, is that we are gonna use the internal energy levels, so the states of the electron in the atom to make a quantum bit. And so for example we can take the very lowest energy state which I'm labeling 0 here, and we can take the next higher energy state and we can label it as one, and in this quantum systems we could make up ordinary quantum bit in this way by just using these different energy states. But we can also we can also make these superposition states, where it's both at 0 and 1 at the same time. I'll say just a little bit about what these coefficients mean in a minute.
还有一些小系统的叠加态的例子，我要讲到的是量子比特，是处于势阱中的原子，你可以把它想象成碗里的弹珠，弹珠可以在碗里来回地滚动，我们通过“碗里”的原子就可以实现一种叠加态。这种条件下,有时候原子同时处在“碗”的左边和右边，而这在我们的日常经验中讲不通，但是在量子系统中就可以实现。这就是叠加态的一个例子，有时候原子可以同时处在左边和右边的叠加态。对于利用叠加态来做量子计算机，我们感兴趣的是利用原子的电子内态作为量子比特。比如可以把最低能太标记为|0>，把相邻的较高能态标记为|1>，这样利用这些不同的能态就可以在量子系统中组成普通的量子比特。但是我们也可以用它们的叠加态，也就是同时处在 |0>和|1>态。我马上就说一下这些系数的意义。
So I'm not sure I'm gonna explain quantum computing to you, but I hope I can give you an idea why this looks interesting. And so again what we're gonna can talk about is a system where we can. In our classical computers we know a bit can be either 0 or 1, but in our quantum bits or qubits we call it, this bit can be both 0 and 1 at the same time, so one reason you can get an idea why this is interesting is how memory could scale in a in a quantum register. So here's a simple example where we have a 3 bit memory register, and for our normal classical computers this will store one 3-bit binary number, for example 101, but in a superposition sense, our quantum register will store 000, 001 up to 111, all of these 8 possibilities at the same time. So what I want you to take away from this is that there is this property that we can have a massive parallel memory, that is we can store all of these at once.
我可能不会给你们详细解释量子计算，但是我希望可以让你们理解它为什么有意思。我们要讨论这样一个系统...... 大家知道经典计算机里一个比特可以是0或1，但是量子比特中，它可以同时是0和1，所以量子计算机有意思的一方面是量子寄存器是如何按比例增加的。比如这个3比特的内存寄存器，通常的经典计算机中可以存储一个3比特的二进制数，比如101，但是如果是叠加态，量子寄存器就可以同时存储从000，001一直到111，也就是所有的8中可能存的数。所以我希望你们能从中学到的是量子比特的这种大量并行内存，可以同时存储所有这些数。
So then why this is interesting, this example I gave with 3 bits in our quantum register, we can store all 8 possible 3-binary numbers at once, that number of 8 is 2 to the 3, it's the number of states of a bit to the power of number of bits we have. And why this is potentially interesting is that if we have 300 quantum bits, that can store 2 to the 300 numbers at once, that's about 10 to the 90, that's more than all the elementary particles in the Universe. In some sense our quantum memory with just 300 bits , quantum bits, could store more memory than if we made a classical memory based on all the matter in the universe, that sounds pretty interesting. So then the thing is that, you notice I've used these different coefficients, I'll explain, that's a little bit mathematical... but it explains these coefficients have so different values. They are meant to represent the, you know... the probability of the state being in the |000> versus |111>, that's to distinguish these probabilities. So the other issue is that when we do one operation on this quantum register, we just flip the first bit, in general it changes all these coefficients in front of this quantum register at once. I am writing it like this, this is sort of standard notation for how we write wave functions in quantum mechanics. The quantum computers are very good that we don't have this one, it's ok, so anyway the idea is that we could do massive parallel processing.
所以有意思的就是从我刚才举例的3比特量子寄存器中，可以同时存储所有8个3比特二进制数，8等于2的3次方，也就是每个比特的态数目的幂，幂次是比特数目。有意思的是，如果可能，假设有300个量子比特，那就可以同时存储2的300次方个数，也就是大概10的90次方个数，这比宇宙中所有基本粒子的数目还要多，某种意义上讲，300个量子比特的内存，可以存储的容量比所有宇宙中物质制作的经典内存还要多，听起来就很有意思。然后我来解释一下这些不同的系数是什么意思。有点数学，但是是这样的，这些系数的值一般不同，它们是用来表示处在|000>、|111>之类的态上的概率，用来区别这些概率。另外就是当我们对量子比特做一次操作时，只要翻转第一个比特，通常这样会马上改变所有这些量子寄存器前面的系数。这样的写法是量子力学里面写波函数的标准写法，量子计算机非常优秀，这种问题不存在的，好的，想法就是去做这种大量的并行处理。
Ok, but there is something we have to realize in quantum mechanics, So when you first take quantum mechanics, you realize you can think about making these superposition states, when you actually go on and measure the system, the quantum states which are represented here, collapses down into one state. In other word, this register that has 8 numbers binary numbers, when we measure it, it will collapse down to one of the binary numbers in a sense independent of the number of bits. So if you have a 300-quantum-bit machine, when we measure the register, it will collapse down to a 300-bit binary number. So that sounds like a severe restriction. But in 1995 or 1994, Peter Shora computer theorist, came up with a computer algorithm, that said if we can make this quantum computer which I'll briefly describe to you, we can efficiently factorize large numbers. That means... Factorization is if we have a large number, if it's the product of two smaller numbers. We can find those factors, and for very large numbers, say 300 digit numbers decimal numbers, that becomes a very hard problem. But he, Peter Shor figured out an efficient way to do that. And I should have said that, one of the reasons I think many of you know why that is interesting if you factorize large numbers, basically that, almost all encryption that's used to provide privacy for you.
但是还得用量子力学来实现一些前提，首先考虑到量子力学时，你会想到可以制成这些量子叠加态，但是当你真正继续测量量子系统时，这里的量子叠加态就会坍缩到一个态上去。换句话说，这个存储8个二进制数的寄存器，当我们测量它的时候，无论有多少个比特，都会坍缩成为其中的一个二进制数，所以当你测量一个300量子比特的计算机，它会坍缩成“一个”300比特的二进制数，这听起来是严重的限制。但是1995年或1994年，计算机理论学家Peter Shor提出了一个计算机算法，说假如可以制成量子计算机就可以有效的进行大数分解。大数分解也就是，如果一个非常大的数，可以表示成两个更小的数的乘积，我们可以找到这两个小的因子，对于非常大的数，比如300位的十进制数，这是非常困难的问题。但是Peter Shor得到了大数分解的非常有效的方法。我要说，你们很多人应该知道，这有意思的理由是如果可以分解大数，基本上几乎所有提供隐私的加密。
For example when you buy something with credit card, you gain security, you have privacy because the inability to factorize large numbers. And so if this machine could be made, it will obviously have important applications not only for credit card but also for national secret things. Anyway what I want to say here, this will get a little bit mathematical. But I want to say what we think about when we talk about programming our quantum computer if we compared it to a classical computer. It turn out it may not be the most efficient way to make a classical computer. Basically you can do what's called universal computation, you can do any computation if you just combine two gates. One is a bit flip, and the other is some nontrivial 2-bit logic gate, this gate is a 2-bit “AND” gate. Now there is an analogy with our quantum bits that rather than just doing simple bit flip, what we talk about is rotation. And the idea here is we can represent our quantum bits by a vector, so the vector could be pointing either up or down, But in the quantum world we can make this vector point in any direction. And so we want this a bit more general property than a bit flip, in fact I write one example of a 2-bit logic gate in the quantum world. These two tables for this (gate), (I mean) it looks like it does nothing except we pick up a minus sign in front of this for this particular phase gate, we pick up a minus sign in front of this state.
比如你买东西时用信用卡，你获得的安全和隐私是因为大数难以分解，如果可以制成这样一个机器，它毫无疑问不仅可以用在信用卡上，还对国家机密有用。这里想解释的，还是有点数学。当讲到编程，相对于经典计算机，量子计算机又是什么样的呢，结果发现，可能制作一台经典计算机并不是最有效的。基本上的做法是我们称为通用计算的方法，只需将两个门结合起来用就可以做任何一种计算，一个是比特翻转门，另一个是一种非平凡的2比特逻辑门，这里这个门是2比特的“与门”。量子比特中也类似，这里（单比特操作）不只是简单的比特翻转，而是（相位）“旋转”，基本想法是用向量表示量子比特，（经典计算中）向量方向可以朝上或朝下。但是量子世界中，向量可以朝向任何方向，我们还想让这个比特有比比特翻转更通用的性质，比如这里这个2比特l量子逻辑门，这个相位门的两边的列表中，看起来除了在特定的位置提取出一个负号什么都没做。
And so why is that interesting? The reason it's interesting is that if we have two quantum bits and let's say they are both in equal superposition of |0> and |1>, Then if we apply this phase gate operator, we get a wave function that looks like this. And what I write here expresses the idea that, initially the initial states, the states of the bits are independent of each other, but it turns out when we make this phase gate, we can no longer write a wave function that's where the properties of the two bits are separate. This is what we call entanglement, if we measure one of the bits it affects the value of the other bit.
所以它为什么有意思呢？有意思的地方在于，如果有两个量子比特都处于|0>和|1>的叠加态，然后做这个相位门操作，得到的波函数是这样的。这个波函数表示，这两个在量子比特的初态时是相互独立的，但是通过这个相位门发现，这两个量子比特不能再写成性质相互独立的波函数了，我们把这叫做纠缠，（纠缠态下）如果测量一个比特，会影响另外一个比特的值。
So anyway, here is a picture of Peter Shor at the time he invented this algorithm, there were some earlier ideas by other theorists who I mention here, but Peter Shor's algorithm has such implications particularly for security. That starts things on fire, you know the governments got interested so there's a lot of interest in founding this kind of research. I think you know even today this interest continues to grow, in China here they spend a huge flux of interest trying to make quantum computers and related devices. So the interest continues to grow.
这是一张Peter Shor发明Shor算法的时候的照片，在他之前还有一些其他理论学家提出的想法，就是这些人。但是Peter Shor的算法影响到了安全，这样就使这个方向火了起来，政府开始感兴趣，并且非常想资助这类研究。相比大家都知道，直到今天这种兴趣还持续增长，在中国，大家花了很大的兴趣来制造量子计算机和相关的器件，所以这类兴趣一直在增长。
I can't remember whether you're gonna see, Peter Shor's lecture, he's giving it in Shanghai, and there was supposed to be video link I'm not sure whether it's gonna happen. So anyway I may embarrassed myself and in front of Peter Shor here, but just to give you an idea that it's not too mystical, it's not so much different from the way we do classical programming. And the very crude explanation how this works is, if you're gonna factorize big numbers you need to stick in a superposition state, that has all the numbers up to the one you're trying to factorize and some additional numbers, you know work space to do the computations. But basically it's not so much different than line programming in our classical computers. The idea of the algorithm is that basically you have these inputs which could be equal superposition of all these possible numbers, and then you just apply a series of these both 2-bit logic gates and a single-bit rotations, we say where change the direction of the vector. Anyway that would provide us a very simple explanation all the way how the algorithm works, so in fact in a way it's not mysterious.
不知道你们会不会看得到，Peter Shor会在上海做讲座，应该有视频连接的，不知道还有没有，我就在Peter Shor面前班门弄斧了。但是告诉你们，其实也不是特别神秘，跟我们做经典编程的方法区别并不很大，这个算法工作的一个非常简单的解释是加入要分解大数，需要插入一个叠加态，这个态包含直到需要分解的大数的所有数，以及用来做计算需要的一些额外的比特数，但是基本上跟经典计算机里的线路编程没有很大的不同，这个算法的思想就是输入相当于所有这些可能数值的叠加态，然后运用一系列的2比特逻辑门和单比特的旋转操作，改变向量的方向，这样就可以简单地解释算法怎么运行的，所以其实一定程度上并不是很神秘。
I think many of you have see this in your beginning of physics classes, maybe you performed an experiment where you have this water wave experiment. So the idea here in this a simple demonstration about waves that you have a wave coming and pinching on this barrier. There will be some little opening series of this barrier, then some of the wave propagate through. And in fact they pass this barrier, the waves interfere, so you get constructive interference and destructive interference, and in fact what we do in our quantum systems. One way to think about it, it's obviously a much more complicated kind of interference experiment, but it's essentially the same idea where you are interfering these different waves from our quantum bits.
我想你们很多人刚上物理课的时候就看到这个图了，有水波实验的甚至可能做过实验了。这里这个波动的示意图的内涵是如果一个波冲向这个障碍物，障碍物上有一系列小的开口，就会有一些波传过。事实上这些波通过障碍物并干涉，就会得到相长干涉和相消干涉，量子系统中我们的做法其实（类似），可以把量子系统一定程度上看作复杂得多的干涉实验，但是本质上同样都是把量子比特相互干涉。
So anyway there is are a lot of details, but anyway the idea is then you perform the algorithm that Peter Shor described, then you finally measure your quantum register. In his algorithm, if everything works perfectly, you still, when you measure make some probabilities, several possible states, but it turns out, he showed that in his algorithm, that anyone of those states could be used as a classical number theory algorithm to give you the factors. So just give you an idea of, you know, the difficulty and where we are now. So just for example to factorize a 150-digit decimal number, it takes about 10 to the 9 operations like this to do it, and so far in our experiments it's still pretty crude. Now at the point, we can do several hundred operations without an error, but beyond that we can't get anywhere near 10 to the 9, so we have a long way to go. There's another whole subject which is in part invented by Peter Shor, that is, he showed that in fact you can correct for errors in the quantum mechanics, so but that's a whole subaspect course in college and I'm not gonna talk about that.
反正其中有很多的细节，按照Peter Shor的想法做算法操作，然后最后得到量子寄存器，在他的算法中，如果一切完美的话，当你测量概率的时候，仍然有一些态，但结果是，他在算法中证明，这些态中的任意一个都可以用经典数论算法给出因子。然后让大家了解一下我们面临的困难和目前的处境，比如分解一个150位的十进制数，需要大约10的9次方次操作完成分解。而我们目前的实验仍然非常简单，目前，我们可以做几百次操作不出现错误，但是超过几百次，就很难做到10的9次方次操作了，所有还有很长的路要走。还有另外一个完整的研究方向，Peter Shor部分参与了开拓，他证明量子力学中其实可以进行纠错，但那是大学里一整个的子分支方向，我就不多说了。
（未完待续）
关于“墨子沙龙”
墨子沙龙是由中国科学技术大学上海研究院主办、上海市浦东新区科学技术协会及中国科大新创校友基金会协办的公益性大型科普论坛。沙龙的科普对象为对科学有浓厚兴趣、热爱科普的普通民众，力图打造具有中学生学力便可以了解当下全球最尖端科学资讯的科普讲坛。