当计算遇上量子：我们为什么要学这门「反常识」的课？

如果你现在摸一摸口袋里的智能手机，再抬头看看厨房里奶奶用了十年的算盘，中间隔着的可不只是几十年的时光，还有人类计算工具翻天覆地的变化——从拨弄算珠的手工计算，到指尖轻触的万亿次运算，我们一直在追求更快的计算速度。但现在，经典计算的“快”快要碰到物理规律的天花板了，而量子计算，就是那个能帮我们捅破天花板的新工具。

If you reach into your pocket and touch your smartphone, then look up at the abacus your grandma has used for ten years in the kitchen, what lies between them is not just decades of time, but earth-shaking changes in human computing tools — from manual calculation of moving abacus beads to trillions of operations at the tap of a finger, we have been pursuing faster computing speeds all along. But now, the "fast" of classical computing is about to hit the ceiling of physical laws, and quantum computing is the new tool that can help us break through that ceiling.

<!-- 结构化元数据：章节=第1章，主题=经典计算发展史、摩尔定律瓶颈、量子计算核心差异、常见误区，标签=科普、量子计算、入门、双语 --> <!-- 纸书排版提示：本章开篇可配图“算盘到智能手机的计算工具演变时间轴”，居中排版，标注“人类计算工具的进化史，从机械到电子，从宏观到微观” --> <!-- 电子版侧边栏：💡 互动小实验：拿出10枚硬币和10个纸杯，把其中1枚硬币藏在1个纸杯里，闭着眼挨个找，记录你找的次数，这就是经典计算的“串行搜索”逻辑 -->

从算盘到智能手机：经典计算的2000年进化史

人类对“快速计算”的追求，早在几千年前就开始了。公元前500年左右，中国人发明了算盘，用拨动算珠的方式完成加减乘除，这是最早的“个人计算工具”——一个熟练的算盘手，每分钟能完成几十次运算，相当于当时10个账房先生的工作量。算盘的逻辑其实和现在的经典计算机一模一样：每一个算珠要么是“上去”（代表1），要么是“下来”（代表0），用不同的组合表示数字，再通过固定的规则完成计算，这就是最朴素的“二进制”思想。

If you reach into your pocket and touch your smartphone, then look up at the abacus your grandma has used for ten years in the kitchen, what lies between them is not just decades of time, but earth-shaking changes in human computing tools — from manual calculation of moving abacus beads to trillions of operations at the tap of a finger, we have been pursuing faster computing speeds all along. But now, the "fast" of classical computing is about to hit the ceiling of physical laws, and quantum computing is the new tool that can help us break through that ceiling.

<!-- 结构化标签：经典计算、算盘、二进制、计算工具进化 --> <!-- 电子版脚注：① 算盘的二进制逻辑：算珠的“上/下”对应二进制的“1/0”，和现代计算机的比特（bit）逻辑完全一致，是二进制思想最早的民用载体 -->

算盘的逻辑虽然简单，但完全靠人力操作，速度上限很低。直到19世纪，英国人查尔斯·巴贝奇发明了“差分机”——用齿轮的转动完成数学计算，这是世界上第一台机械计算机，虽然因为当时的技术限制没造出来，但它已经提出了“用机器自动完成计算”的核心思想。再后来，电子管的发明让计算机进入了电子时代：1946年，世界上第一台通用电子计算机ENIAC诞生，用了1.8万个电子管，重达30吨，每秒能完成5000次运算，当时用来计算炮弹弹道，比人工计算快了1000倍，但耗电量高达150千瓦，开的时候整个小区的灯都会暗一下。

The logic of the abacus is simple, but it relies entirely on manual operation, so its speed ceiling is very low. It was not until the 19th century that the Englishman Charles Babbage invented the "difference engine" — using the rotation of gears to complete mathematical calculations. This was the world's first mechanical computer. Although it was not built due to the technical limitations of the time, it put forward the core idea of "using machines to complete calculations automatically". Later, the invention of vacuum tubes brought computers into the electronic era: in 1946, the world's first general-purpose electronic computer ENIAC was born, using 18,000 vacuum tubes, weighing 30 tons, and capable of 5,000 operations per second. At that time, it was used to calculate artillery trajectories, 1000 times faster than manual calculation, but it consumed 150 kilowatts of electricity, and when it was turned on, the lights in the entire community would dim.

<!-- 纸书排版提示：此处可配ENIAC的黑白老照片，标注“1946年的ENIAC，重30吨，每秒运算5000次，是现在智能手机算力的百万分之一” --> <!-- 电子版侧边栏：💡 小知识：ENIAC的程序是靠插拔电缆和拨动开关设置的，改一次程序要花几个小时，远没有现在的智能手机方便 -->

真正让计算机走进普通人生活的，是1947年晶体管的发明。电子管体积大、易发热、寿命短，晶体管只有指甲盖大小的几百分之一，功耗只有电子管的几十分之一，寿命却长了几千倍。到了1958年，科学家把多个晶体管做在同一块硅片上，发明了集成电路，也就是我们现在说的“芯片”。从那天起，经典计算机开始了疯狂的“小型化”之路：1965年，英特尔联合创始人戈登·摩尔发现，芯片上的晶体管数量每两年就能翻一倍，性能也会跟着翻一倍，这就是著名的“摩尔定律”。^①

What really brought computers into the lives of ordinary people was the invention of the transistor in 1947. Vacuum tubes were large, prone to heat, and had a short lifespan. Transistors were only a few hundredths the size of a fingernail, consumed only a few percent of the power of vacuum tubes, but had a lifespan thousands of times longer. By 1958, scientists put multiple transistors on the same piece of silicon and invented the integrated circuit, which is what we now call a "chip". From that day on, classical computers began their crazy "miniaturization" journey: in 1965, Gordon Moore, co-founder of Intel, found that the number of transistors on a chip could double every two years, and performance would also double, which is the famous "Moore's Law".^①

<!-- 结构化标签：晶体管、集成电路、摩尔定律、芯片 --> <!-- 电子版脚注：① 戈登·摩尔（Gordon Moore）是英特尔公司联合创始人，1965年提出摩尔定律时，他还只是仙童半导体公司的研发总监。最初的摩尔定律是“晶体管数量每年翻一倍”，后来修正为每两年翻一倍，50年来基本准确，直到最近几年才开始放缓 -->

你手里的智能手机，就是摩尔定律最好的证明：2010年的iPhone 4搭载的A4芯片，采用45纳米工艺，有1亿个晶体管；2023年的iPhone 15搭载的A17 Pro芯片，采用3纳米工艺，有190亿个晶体管。13年时间，晶体管数量翻了190倍，几乎完美符合每两年翻一倍的规律。现在市面上的高端手机芯片，制程已经做到了3纳米——什么意思呢？就是芯片上最细的线路，宽度只有几十个硅原子，再往下做，就要碰到原子级别的物理极限了。

The smartphone in your hand is the best proof of Moore's Law: the iPhone 4 launched in 2010 was equipped with an A4 chip with a 45-nanometer process and 100 million transistors; the iPhone 15 launched in 2023 was equipped with an A17 Pro chip with a 3-nanometer process and 19 billion transistors. In 13 years, the number of transistors has increased 190 times, which almost perfectly fits the rule of doubling every two years. Now high-end mobile phone chips on the market have reached a 3-nanometer process — what does this mean? It means that the width of the finest line on the chip is only dozens of silicon atoms. If we go further down, we will hit the physical limit of the atomic level.

<!-- 纸书排版提示：此处可配3纳米芯片的放大示意图，标注“3纳米工艺的芯片线路宽度约为25个硅原子，再小就要碰到物理极限” --> <!-- 电子版侧边栏：⚠️ 误区提醒：很多人觉得“芯片制程越小，手机就越快”，其实不完全对，制程只是影响性能的因素之一，架构、功耗、散热同样重要 -->

摩尔定律的“死亡”：经典计算碰到了物理天花板

为什么不能再把芯片做小？这里要提到两个物理规律，你不需要懂复杂的公式，只要知道结论就行：第一个是“量子隧穿效应”，第二个是“功耗墙”。

先说量子隧穿效应：经典世界里，你不可能不推门就穿过一堵墙，因为你的能量不够；但在量子世界里，微观粒子有一定的概率直接“穿墙而过”，就像你扔一个球到墙上，球有很小的概率直接出现在墙的另一边。当芯片的线路宽度小到只有几个纳米的时候，电子就会通过量子隧穿效应直接从线路里“跑”到旁边的线路里，导致芯片短路、乱码，根本没法正常工作。现在3纳米的芯片已经出现了这个问题，工程师要花大量的成本来修正错误，再往下做2纳米、1纳米，量子隧穿效应会越来越严重，根本没法控制。

First, let's talk about why we can no longer make chips smaller. Here we need to mention two physical laws. You don't need to understand complex formulas, just know the conclusion: the first is the "quantum tunneling effect", and the second is the "power wall".

Let's talk about the quantum tunneling effect first: in the classical world, you cannot pass through a wall without pushing the door, because your energy is not enough; but in the quantum world, microscopic particles have a certain probability of directly "passing through the wall", just like you throw a ball at a wall, and the ball has a very small probability of appearing directly on the other side of the wall. When the line width of the chip is reduced to only a few nanometers, electrons will directly "run" from the line to the adjacent line through the quantum tunneling effect, causing the chip to short circuit and make mistakes, and it simply cannot work normally. Now 3-nanometer chips already have this problem. Engineers have to spend a lot of cost to correct errors. If we go further down to 2 nanometers and 1 nanometer, the quantum tunneling effect will become more and more serious, and it simply cannot be controlled.

再说功耗墙：1974年，IBM研究员罗伯特· Dennard提出了“ Dennard缩放定律”，意思是芯片做小之后，电压也会跟着降低，所以功耗不会增加，性能反而会提升。但这个定律在28纳米工艺之后就不管用了：芯片越做越小，线路越密，电阻越大，发热量越高，功耗不降反升。你现在玩大型游戏的时候手机发烫，就是因为芯片功耗太高，热量散不出去，为了不烧坏芯片，手机会自动降频，变卡。现在高端手机芯片的功耗已经达到了10瓦左右，和十几年前的笔记本电脑差不多，再往上提功耗，手机就会变成“暖手宝”，根本没法用。

Let's talk about the power wall: in 1974, IBM researcher Robert Dennard proposed "Dennard's scaling law", which means that after the chip is made smaller, the voltage will also decrease, so the power consumption will not increase, but the performance will improve. But this law no longer works after the 28-nanometer process: the smaller the chip, the denser the lines, the greater the resistance, the higher the heat generation, and the power consumption does not decrease but increases. When you play large games now, your phone gets hot, because the chip power consumption is too high and the heat cannot be dissipated. In order not to burn the chip, the phone will automatically reduce the frequency and become stuck. The power consum