Why do we need quantum computing?

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In accordance with the friend's appointment, I wanted to write a science popular video draft about quantum computing. As a result, I accidentally wrote too much. It is considered to be in the public, so he cheekily send the whole draft here. In fact, there are a lot of popular science articles about quantum computing. I have also written it, but the perspective of this article is still slightly different: why do we need quantum computing? Why did it attract so much attention in recent years? If you can answer these questions, it may be relieved: quantum computing is not a madness of scientists, but a product of this era. Just as quantum mechanics and relativity are the glorious marks left by humans in the 20th century. Quantum computing may also become another eternal mark left by humans in the 21st century.

Written article | No Evil

We live in the era of calculation

Human desire for computing power is endless. Since the note of the rope, the improvement of computing power is closely related to the progress of civilization. The Pydagoras school in ancient Greece even regarded it as the truth. Today, we are too used to the benefits of computing, so that most people ignore its greatness. When we slide on the screen, enter a keyword, and the search engine pops up the results we want. These operations can be completed within a few seconds. How many people know how many "calculations" have experienced behind this? When we are happy to brush the small video with Harazi, how many people know that the machine is desperately calculating the next video for you? At the moment when the epidemic situation is severe, each of us cooperates with the code scanning and checking acid. How many people can perceive the great achievements of "calculation" in resistance? Today, our computing power has reached its peak, and machines have overcome the last intellectual fortress that humans are proud of -Go. Next, the machine also tries to conquer autonomous driving and conquer the Yuan universe. It can be said that we live in an era of calculation.

Inca civilization of the knot of civilization: Qipu

Today's super computing power, thanks to a non -linear element called "crystal tube", is made of the most ordinary material in nature -silicon, but condenses the top wisdom of human beings. It is full of every corner of us, but it was born in the cleanest dustless factory. It changes our lives so quickly, but now we Chinese have found that they are subject to others. This is the chip.

Among the top -level silicon semiconductor chips, tens of billions of crystal pipes follow this binary logic called "Boolean number". This logic is not efficient, but it is very flexible and universal, so that after more than 50 years, it has increased by the index level of Moore's law, which has destroyed all opponents and has almost become the only calculation tool.

Moore's Law has been proposed for more than 50 years, and it is still valid to this day, and the corresponding computing power has also increased its index level. As the size of the transistor is getting smaller and smaller, approaching the nano level, Moore's Law will be terminated sooner or later. This is actually a common talk. What I want to say is that in today's Internet era, even if Moore's Law is effective for a long time, the development of computing power is far from keeping up with the speed of data expansion on the Internet. Through calculation of the amount of information excavated from the Internet, we will be poor compared to the actual amount of information contained in the Internet. If we imagine data as a mine and imagine the computing power as a mining machine, the mining machine will become increasingly small in front of the mines. In this case, human beings need to go beyond the current paradigm's new computing power. In this context, we can also understand companies like Google, why we pay so much attention to quantum computing and do not hesitate to launch water in person. Because it has that mine. Imagine the feeling of sitting on the gold mine without a tool!

Moore's Law for 50 years

Quantum calculation photos into reality

Having said so much, the topic finally caused quantum computing. Many people are easily associated with the mysterious phenomenon when they hear quantums. What are both waves and particles, what instant moves, etc., are actually not necessary. When I talked to others about quantum, I was most afraid of being in discussions such as nihilism and cognitive theory, because I was actually an experiment, not a philosophy. I like to look at quantum from the perspective of pragmatism: it accurately describes the behavior mode of the bottom layer of the material; it is still very accurate now. Well, let's look at what extraordinary things can we do under the rules of quantum? Use quantum to calculate, which is definitely the most bold idea of ​​the last century, because in that era, the ability to control the quantum world was very different from the present, so that the first few important quantum algorithms, including the SHOR algorithm, The GroVer algorithm, in fact, was done by mathematicians -they were studying this as a mathematical toy and never thought about it.

Entering the 21st century, the situation is very different. The 2012 Nobel Prize in Physics was awarded Serge Haroche and David J. Wineland to recognize their "progressive progress of breakthroughs in measurement and controlling independent quantum systems." For the first time, they captured atoms and used the interaction between light and atoms to achieve the control and measurement of atomic quantum -this is actually the beginning of ion trap quantum computing. This work opened the door to the manipulation and read quantum state, and also ignited the fire of hope for physical realization. Since then, quantum bits, quantum doors, and quantum calculations have not only stayed at the stage of mathematics and theoretical. 2012 Nobel Prize in Physics Award

There is also a very important breakthrough in the intercourse of the century. For the first time, the Cai Zhaoshen Research Team of the Institute of Physics and Chemical Research found the quantum oscillation phenomenon on a superconducting "island". The biggest difference between Haroche and Wineland is that the quantum system at this time is a "macro -subfuter system" -Chide electrons in macroweas participating in the entire quantum process. This "superconducting Curob's box" is the predecessor of superconductant quantum computing one of the most watched quantum computing candidates today. The macro -subsystem is easy to control and easy to read, and its production process and semiconductor chip are largely compatible, which has led to a strong vitality of this system in the following ten years. (For more introductions about superconductant quantum bites, please refer to "When Quantum Calculation Meets Super Guide: A Beautiful Encounter")

Macro quantum Bit: Cooper against the box 丨 Source: Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent Control of Macroscopic Quantum States in A Single-Pair Box. Nature 398, 786–788.

Early superconductant quantum bits, including the "Cooper pair box" mentioned above, and magnetic flux quantum bits and phase quantum bits, solved many technical problems related to handling, coupling, and reading, but they have been trapped in a one Important indicators -Anti -time time (quantum "life"). Available time refers to the characteristic time of a system quantum disappearance and tendency to the classic system. We know that no system can be completely isolated, otherwise this system does not exist. As a quantum bit that can be "calculated", it is even more unlocked. It must interact with the outside world. Otherwise How to control it and measure it? And interaction will inevitably lead to the loss of quantum information. The particles of nature, such as atoms, can have a long life span, they only have very weak interactions with photons, which also becomes a double -edged sword: because of weak interaction, there is strong quantum nature; at the same time Because of the weak interaction, it is difficult for us to control and measure it. In this way, some understanding why Haroche and Wineland work can win the Nobel Prize -it is really difficult.

The situation of superconductant quantum bites is exactly the opposite. The super fine energy level that constitutes the quantum bit is caused by the collective behavior of the macro quantity Cooper. It is in a more macro solid system. The situation is much worse. From where the photon, the remaining electrons, and the changes in magnetic fields caused by the disturbance of the external electromagnetic field disturbance will affect the quantum bites. In addition, it is a macro degree of freedom, so the coupling strength of these external freedoms is also very strong, resulting in the loss of quantum bites in a very short period of time. But because of this, we can also manipulate and read them through the electromagnetic field regulation, and we can also manipulate and read them in a very short period of time. Breaking through 500 microseconds -although it is the moment of the world, it is extraordinary ")

Agreeing time, the transfer was ushered in in 2007. At that time, scientists in the field had noticed the role of increasing capacitance in suppressing charge noise, while Yale University's KOCH et al., my country ’s You Jianqiang was almost at the same time, in the cowper's box and magnetic flux quantum system, systematically studied the increase of the next side. The improvement of road capacitors on the time to retreat, the former is the currently popular Transmon quantum quantum bit. From then on, the time of superconductant quantum bits quickly boarded 10 microseconds to 100 microseconds. Compared with the control time of 10 -nan seconds, this is a very long time. Following it, the Martinis group of the University of California Santa Barbara quickly proposed the TRANSMON quantum -based scalability solution and system electronic solution, which laid the foundation for superconductant quantum computing. The latter story is that this group adds Google, and creates a "Sycamore" chip for Google, creating a milestone of the sensation of quantum hegemony. This story can be opened for a single period, and you can press it first. (See IBM to refute Google, quantum hegemony vs quantum advantage, how far is quantum computing is from us? "

In short, Google's Sycamore chip (Source: Wikipedia.org), to this day, quantum computing has gradually transformed from the idea of ​​toys and theoretical physicists of mathematicians to reality. Among them, the efforts of a large number of experimental physicists and engineers are hard to be outsider. In any case, with these experiments and technical progress and accumulation, we are qualified to talk about the future of quantum computing, and we have the confidence to brag about how to crush the traditional calculation. Next, start blowing!

The God of the Quantum Calculation

The concept of Bit is derived from the information theory of Kannon. Some information shows that this concept was created by mathematicians in the early 1940s. It is used to represent the minimum information unit under the logic of binary generation. In traditional computers, the information is coded, processed, transmitted, and obtained in the unit. In the quantum world, the smallest unit of information has become a quantum bit. It is also an unit for information coding, processing, transmission, and acquisition, but it is now conducted in the field of quantum. Logically, it is a two -state system that can be superimposed; physically, it is a distinguished (quasi -) two -energy system. Multiple quantum bits can form a composite system. If they can be entangled between them, it is the moment of witnessing miracles.

Claude Xiangnon, founder of information theory 丨 Source: Network

The entanglement is unique to the quantum world. It hides very deep physics and cannot understand it so far, but we have confirmed its existence through a lot of experiments. Taking the composite system formed by two quantum bits as an example: This system can be in a certain quantum state. At this time, the system is considered as a whole. Quantum. In other words, the composite system can only be used as a whole, and it cannot get information from its subsystem. Mathematically, the entanglement system opens a larger direct accumulation space, and the dimension of this direct accumulation space increases with the comparison number index. List several horrible numbers here: when n = 50, the dimension of this space is about the number of calculations of the most advanced supercomputer in one second; when n = 300 The general atomic (about 1023 atoms in a cup of water).

The expansion of this horror dimension brought by entanglement provides a huge encoding space for the calculation problem, so that some problems can seek more efficient solutions on a higher dimension. After more than 100 years of development, traditional computers and theories have been able to solve many problems efficiently, but there are still many problems that cannot be solved, such as weather forecast, stock price, cancer drugs ... If these problems can be accurately calculated, then our world can It will become particularly beautiful, and maybe it is also particularly boring. For example, we can accurately calculate the football team in the next game. Unfortunately, quantum computing cannot solve these problems. Okay, why are we doing so much? Intersection Don't worry, we have found that some problems can be solved by amazing efficiency under the quantum computing framework, and these problems are of great significance.

One of them is the famous SHOR algorithm. On the Internet today, we browse the web and enter the user name and password. How can we guarantee that they are not peeped by others? How can our bank card password prevent others from stealing? Some people say that covering some. In fact, on the Internet, if there is no protection of the encryption system, this information is almost transparent. Another characteristic of the Internet is that information can be transmitted to any corner of the earth in an instant: those who peek at your password, perhaps at this time, they hold their feet and drink coconut juice with their feet. Traditional point -to -point encryption is not suitable for the Internet. As the number of nodes increases, the light storage password will be a disaster. An asymmetric encryption system -the RSA password effectively solves this problem. The so -called non -symmetry refers to the different keys used for encryption and decryption: a private key, which is used to decrypt; a public key is used to encrypt. The public key is public, and anyone can get it. If Li Si wants to pass a described information to Zhang San, he needs to encrypt with the public key released by Zhang San. After Zhang San received it, he could enjoy it with a private key. At this time, if a Wang Wu secretly stabbed these materials in secret, sorry, although he could get the public key in his hands, it would not be able to open without any private key. Since anyone wants to share a public key with Zhang Santong, this encryption system greatly saves the required key resources.

This encryption system has escorted the Internet for many years and rarely made mistakes. The principle of encryption is derived from a mathematical discovery: the large number of large numbers cannot be divided. The two known large numbers are multiplied to get a larger number, and a careful junior high school student can calculate the results. But in turn, I tell you the result of the multiplier and ask which two quality numbers you have brought together? Top mathematicians have to be dumbfounded. At present, the most proud record of human beings is the cracked of RSA-768. Please see:

1

1230186684530117755130494958384962720772853569595334792197322452151726400507263657518745202199786469389956474942774063845925192557326303453731548268507917026122142913461670429214311602221240479274737794080665351419597459856902143413=

334780716989568878784169848212608177047983768912431388883793876147174737379994899

×

36746043666679959042824633796279526327916434342283815739666662333339680927987363089177

At present, RSA-1024 and RSA-2048 are generally adopted. The latter figures are index. Because the difficulty of cracking this problem increases with the size index of the problem, modern computers can only stop mountains and be over.

Thanks to the acceleration of the index level of the quantum Fourier transformation, the SHOR algorithm can solve the above problems under the difficulty of the quasi -polynomial difficulty. It originally needed a million -year crack time to reduce it directly to second -dimensional -dimensional reduction. The SHOR algorithm is terrifying, but it will not become a problem in the twentieth century: I want to achieve the SHOR algorithm. From the technical point of view at the time, it is more difficult than Deng Mars.

The situation is different now, and it has passed before. Everyone is scared, because in the password industry, the most troublesome problem is: you will never be sure if your password has been broken. In addition, the password that cannot be broken now can be preserved. Even if it is broken after twenty years, the lethality is sufficient. Therefore, the emergence of the SHOR algorithm, especially the possibility of technology implementation, forced people to actively find new encryption forms. China is biased towards quantum communications. In this regard, the world leads the world, while Americans are accepted after quantum cryptography. Europeans do not want to let it go ... In short, this is a problem that is urgent to solve. Break instantly, the consequences are unimaginable.

Another useful quantum algorithm is the Grover algorithm: searching for targets in no structure array, faster than the classic algorithm N times, N is the length of the array. This acceleration ability is more useful than the SHOR algorithm, but maybe this algorithm is more useful, because searching problems is the basis for solving many problems and an important means of digging information. When N is very large, the benefits of this algorithm are very significant. Is the large amount of data generated on the Internet that does not correspond to this N is very big?

Long Road Manfo

After the cowhide is blowing, it also needs to face the reality: the above two algorithms, and their derivative algorithms, the requirements of the control and reading error rate are almost high, and the quantum bit is perfect, and it will not make mistakes. The problem is that any physical system will make mistakes. Any practical operation is accurate. We can achieve error correction by creating a certain redundant redundant, which is also an important theme in the early traditional computer research process. Interestingly, the probability of errors in semiconductor chips is so low that the error correction becomes completely unnecessary. When these error correction theoretical heritage is lost, quantum computing runs inheritance.

Quantum error correction is a major challenge to achieve quantum computing. It is difficult to achieve in the short term. Even if we find the topology code correction technology such as surface coding, the requirements of error correction can be reduced to today's technology acceptable level. This is a very complicated science and engineering cross -problem. Only when the ratio reaches 1,000, it is simultaneously progressing at the same time of control, isolation, and reading. At that time, we may really face this problem. (See "The Next Super Challenge of Quantum Calculation")

During this period, should we be patiently waiting for the breakthrough of quantum correction? In fact, everyone does not do this. At present, scientists and engineers in the entire field put more energy on the "Nisq) of the" Misty Simplicate Quantum Calculation (Nisq) ". This idea is based on the level of the current quantum hardware, allowing the existence of noise, and a targeted search for quantum algorithm or quantum simulation method with practical application value. Therefore, the current research hotspot is based on classic-quantum mixed computing, quantum algorithm (VQE), quantum approximation optimization algorithm (QAOA), etc. Their application scenarios include quantum chemical computing, financial combination optimization, artificial intelligence, and so on. Once we realize quantum advantages in a certain application field, our confidence in quantum computing can continue, attract more funds and talents to join, and then overcome difficulties such as quantum errors.

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