We live in the age of computing
Humans’ thirst for computing power is insatiable. Improvements in computing power have been linked to the advancement of civilization since the days of the knot, and the Pythagoreans in ancient Greece even held it to be true. We are so used to the benefits of computing today that most people ignore its greatness. When we swipe on the screen, enter a keyword, the search engine pops up the results we want, these operations can be completed in a few seconds, how many people know how much “calculation” is going through behind this? How many people know that the machine is desperately calculating the next video that should be pushed to you when we are happily streaming and swiping small videos? When the epidemic situation is severe, each of us cooperates with scanning codes and nucleic acids. How many people can perceive the great achievements of “computing” in the fight against the epidemic? Today, our computing power has reached its peak, and machines have conquered the last intellectual fortress that humans are proud of – Go. Next, machines are trying to conquer autonomous driving and conquer the metaverse. It can be said that we live in an era of computing.
The knot of the Inca civilization: Chip
Today’s super computing power is due to a nonlinear element called “transistor”, which is made of silicon, the most mundane material in nature, but condensed the top wisdom of human beings. It is everywhere around us, but it was born in the cleanest dust-free factory. It has changed our lives so quickly, and now we Chinese find ourselves in control of others. This is the chip.
In top-of-the-line silicon semiconductor chips, tens of billions of transistors operate according to a form of binary logic known as “Boolean algebra.” This logic is not efficient, but it is so flexible and general that after more than fifty years of exponential growth with Moore’s Law, it has wiped out all opponents and has become almost the only computing tool.
It has been more than fifty years since Moore’s Law was proposed, and it is still valid today, and the corresponding computing power has also increased exponentially. As transistors get smaller and smaller, approaching the nanoscale, it’s a cliché that Moore’s Law will end sooner or later. What I want to say is that in today’s Internet era, even if Moore’s Law is valid for a long time, the actual development of computing power cannot keep up with the speed of data expansion on the Internet. The amount of information we can dig out of the Internet by calculation will be pitifully small compared to the amount of information the Internet actually contains. If we imagine data as a mine and computing power as a mining machine, then the mining machine will become smaller and smaller in front of the mine. In this case, the human demand for new computing power beyond the current paradigm is ready to emerge. In this context, we can also understand why a company like Google pays so much attention to quantum computing and does not hesitate to go into the water. Because it owns that mine. Imagine sitting on a gold mine with no tools but to dig with your hands!
Fifty Years of Moore’s Law
Quantum computing shines into reality
Having said so much, the topic finally leads to quantum computing. When many people hear quantum, it is easy to associate it with mysterious phenomena. What is both a wave and a particle, and what is instantaneous movement, etc., is actually unnecessary. When I talk about quantum with people, I am most afraid of getting into discussions such as nihilism and epistemology, because I am actually an experimenter, not a philosophical person. I like to look at quantum from a pragmatic point of view: it accurately describes the underlying behavior of matter; it is still very accurate. Well, let’s see what extraordinary things we can do under the rules of quantum? Using quantum to calculate is definitely one of the most daring ideas in the last century, because at that time, the ability to control the quantum world was so different from today, so that the first few important quantum algorithms, including Shor’s algorithm. , Grover’s algorithm is actually created by mathematicians-they treat this as a mathematical toy and never think about it.
In the 21st century, the situation is very different. The 2012 Nobel Prize in Physics was awarded to Serge Haroche and David J. Wineland for “groundbreaking experimental advances in the measurement and manipulation of independent quantum systems.” For the first time, they trapped atoms and used the interaction of light and atoms to manipulate and measure the quantum states of atoms—essentially the beginning of quantum computing in ion traps. This work opens the door to manipulating and reading quantum states and ignites hope for the physical realization of quantum computing. Since then, quantum bits, quantum gates, and quantum computing have not only stayed at the stage of mathematics and theory.
2012 Nobel Prize Winner in Physics
At the turn of the century, there was another very important breakthrough. For the first time, Cai Zhaoshen’s research group from the Institute of Physics and Chemistry in Japan discovered quantum oscillations on a superconducting “island”. The biggest difference from Haroche and Wineland’s work is that the quantum system at this time is a “macroscopic quantum system” – electrons on a macroscopic scale participate in the entire quantum process. This “superconducting Cooper pair box” is the predecessor of superconducting quantum computing, one of the most concerned quantum computing candidates today. The macroscopic quantum system is easy to manipulate and read, and its manufacturing process is largely compatible with semiconductor chips, which has led to the explosion of super vitality of this system in the following decade or so.
Macroscopic quantum bits: Cooper pair box丨Source: Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999).
Early superconducting qubits, including the “Cooper pair box” mentioned above, as well as magnetic flux qubits and phase qubits, solved many technical problems related to manipulation, coupling, and reading, but they have always been trapped in a Important metric – decoherence time (quantum “lifetime”). Decoherence time refers to the characteristic time when the quantum nature of a system disappears and tends to the classical system. We know that no system can be completely isolated, otherwise the system is the same as non-existence. As a qubit that can do “computation”, it is even less likely to be isolated. It must interact with the outside world, otherwise we will How to manipulate it and measure it? And if there is interaction, it will inevitably lead to the loss of quantum information. Particles in nature, such as atoms, can have very long lifespans, and they only interact very weakly with photons, which becomes a double-edged sword: because the interaction is weak, the quantum nature is strong; Because the interaction is weak, it is difficult for us to manipulate and measure it. That’s part of the reason why Haroche and Wineland’s work won a Nobel Prize—it’s really hard.
The situation for superconducting qubits is just the opposite. The hyperfine energy levels that make up qubits are caused by the collective behavior of a macroscopic number of Cooper pairs. The situation is much worse. Photons from nowhere, residual electrons, charges caused by disturbances in external electromagnetic fields, and changes in magnetic fields all affect qubits. Plus it’s a macroscopic degree of freedom, so the coupling to these external degrees of freedom is also strong, causing the qubit’s information to be lost in a very short period of time. But it is precisely because of this that we can manipulate and read them in a very short period of time by means of electromagnetic field regulation.
The problem of decoherence time ushered in a turning point in 2007. At that time, scientists in the field had noticed the effect of increasing capacitance on suppressing charge noise, while Koch et al. from Yale University and Jianqiang You from my country systematically studied increasing the side-by-side in the Cooper pair box and the magnetic flux qubit system at almost the same time. The effect of the circuit capacitance on the decoherence time improvement, the former is the currently popular transmon qubit. Since then, the decoherence time of superconducting qubits has rapidly increased to the order of 10 microseconds to hundreds of microseconds, which is a very long time compared with the manipulation time of the order of 10 nanoseconds. Immediately after that, Martinis’ group at the University of California, Santa Barbara, quickly proposed a scalable solution based on transmon qubits and a systematic electronics solution, laying the foundation for the engineering of superconducting quantum computing. The story behind is that this group joined Google and built the “Sycamore” chip for Google, creating the sensational milestone of quantum supremacy. This story can be opened in a single issue, please press it first.
Google’s Sycamore chip (source: wikipedia.org)
In short, today, quantum computing has gradually transformed from a mathematician’s toy and a theoretical physicist’s vision to a reality. There are a lot of efforts of experimental physicists and engineers, and it is difficult for outsiders to understand. In any case, with these experiments, technological progress and accumulation, we are qualified to talk about the future of quantum computing, and have the confidence to brag about how quantum computing will crush traditional computing. Next, start blowing!
The power of quantum computing
The concept of bit originates from Shannon’s information theory, and there is information that this concept was created by mathematicians earlier (in the 1940s). It is used to represent the smallest unit of information in binary algebraic logic. In traditional computers, information is encoded, processed, transmitted, and retrieved in bits. In the quantum world, the smallest unit of information becomes the qubit, which is also the unit of information encoding, processing, transmission and acquisition, but now it is carried out in the quantum field. Logically, it is a coherently superimposed two-state system; physically, it is some distinguishable (quasi) two-level system. Multiple qubits together can form a composite system. If they can be entangled, it is the moment to witness the miracle.
Claude Shannon, the founder of information theory丨Source: Internet
Entanglement is unique to the quantum world. It hides very deep physics, and it is still not fully understood, but we have confirmed its existence through a large number of experiments. Take the composite system formed by two qubits as an example: this system can be in a certain quantum state, at this time, considering them as a whole, the system is quantum, but once you look at a certain qubit alone, the system is no longer quantum. In other words, a composite system can only be viewed as a whole, and no information can be obtained from its subsystems. Mathematically speaking, entangled systems open up a larger direct product space, and the dimension of this direct product space grows exponentially with the number of bits. Here are a few terrifying numbers: when N=50, the dimension of this space is roughly equivalent to the number of calculations performed by the most advanced supercomputers in one second; when N=300, the dimension has exceeded all the known universes. (there are about 10 23 atoms in a glass of water).
The terrifying dimensional expansion brought about by entanglement provides a huge coding space for computational problems, allowing some problems to seek more efficient solutions in higher dimensions. 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 prices, cancer drugs… If these problems can be calculated accurately, then our world It’s going to be extra nice, and maybe extra boring. For example, we can accurately calculate how much the national football team will lose in the next game. Unfortunately, quantum computing cannot solve these problems either. Okay, so what are we doing so hard for? ! Don’t worry, we have discovered that certain problems can be solved with surprising efficiency in the framework of quantum computing, and these problems are also very meaningful.
One of them is the famous Shor algorithm. On today’s Internet, when we browse the web and enter user names and passwords, how can we ensure that we will not be peeked by others? How can we prevent others from stealing our bank card password? Some people say, cover up. In fact, on the Internet, this information is almost transparent without the protection of an encryption system. Another feature of the Internet is that information can reach any corner of the earth in an instant: the person peeking at your password may be drinking coconut milk with their feet clasped in Mauritius at this time. Traditional point-to-point encryption is not suitable for the Internet. As the number of nodes increases, it will be a disaster to store passwords alone. An asymmetric encryption system, the RSA cipher, effectively solves this problem. The so-called asymmetry means that the keys used for encryption and decryption are different: a private key is used for decryption; a public key is used for encryption. The public key is public and can be obtained by anyone. If Li Si wants to send unspeakable information to Zhang San, he needs to encrypt it with the public key released by Zhang San. After Zhang San receives it, he can open it with the private key and enjoy it. At this time, if there is a Wang Wu secretly coveting these materials, I’m sorry, although he can get the public key in his hand, he can’t open it without the private key anyway. Since anyone who wants to communicate with Zhang San can share a public key, this encryption system greatly saves the required key resources.
This encryption system has protected the Internet for many years, and it rarely goes wrong. And its encryption principle is derived from a mathematical discovery: the principle of indivisibility of large numbers. Two known large prime numbers, multiply them to get a larger number, a careful junior high school student can calculate the result. But in turn, I tell you the result of the multiplication, and ask which two prime numbers you multiply by? Top mathematicians are also dumbfounded.
At present, RSA-1024 and RSA-2048 are commonly used, and the following numbers are exponents. Since the difficulty of cracking this problem increases exponentially with the scale of the problem, modern computers can only stand tall and far behind.
Benefiting from the exponential acceleration of quantum Fourier transform, Shor’s algorithm can solve the above problems under quasi-polynomial difficulty, which originally required millions of years of cracking time, and is directly reduced to the order of seconds – a dimensionality reduction blow. Shor’s algorithm is terrifying, but it won’t be a problem in the 20th century: to implement Shor’s algorithm, in terms of technology at the time, it was harder than going to Mars.
The situation is different now, and it has been long-winded before. Everyone is afraid, because in the password world, one of the most troubled problems is: you are never sure if your password has been broken. In addition, passwords that cannot be broken now can be preserved, and even if they are broken twenty years later, they will still be very lethal. Therefore, the emergence of Shor’s algorithm, especially the possibility of technical realization, forced people to actively search for new forms of encryption. China is biased towards quantum communication and leads the world in this regard, while Americans are behind quantum cryptography, and Europeans do not want to let go… All in all, this is a problem that needs to be solved urgently. If any party can solve the problem first, international checks and balances will be eliminated. Broken in an instant, the consequences are unimaginable.
Another useful quantum algorithm is Grover’s algorithm: searching for a target in an unstructured array is N times faster than the classical algorithm, where N is the length of the array. Compared with the Shor algorithm, this acceleration capability is insignificant, but perhaps this algorithm is more useful, because the search problem is the basis for solving many problems, and it is also an important means of mining information. When N is very large, the gain of this algorithm is very significant. Doesn’t the massive amount of data generated on the Internet today correspond to the situation where N is very large?
long way to go
After the bullshit is over, we have to face the reality: the above two algorithms, as well as their derived algorithms, have extremely high requirements on manipulation and reading error rates, almost requiring qubits to be perfect and error-free. The problem is that any physical system can go wrong, and any actual operation is accurate. Error correction can be achieved by creating a certain amount of redundancy, which was also an important theme in the early research process of traditional computers. Interestingly, in today’s semiconductor chips, the probability of bit errors is so low that error correction becomes completely unnecessary. Just when the legacy of error correction theory was about to be lost, quantum computing came and inherited it.
Quantum error correction is a major challenge to achieve quantum computing, and it is difficult to achieve in the short term, even if we find a topological code error correction technology such as surface coding, which can reduce the error correction requirements to an acceptable level for today’s technology. This is a very complex interdisciplinary problem of science and engineering. Only when the number of bits reaches 1,000 and technologies such as manipulation, isolation, and reading progress simultaneously, perhaps we can truly face this problem.
During this period, should we wait patiently for the breakthrough of quantum error correction? Not everyone actually does that. Currently, scientists and engineers across the field are focusing more on “Noisy Intermediate Scale Quantum Computing (NISQ)”. This idea is to allow the existence of noise according to the current level of quantum hardware, and to search for quantum algorithms or quantum simulation methods with practical application value. Therefore, the current research hotspots are Variational Quantum Algorithms (VQE) and Quantum Approximate Optimization Algorithms (QAOA) based on classical-quantum hybrid computing. Their application scenarios include quantum chemical computing, financial portfolio optimization, artificial intelligence, and so on. Once quantum advantage is achieved in a certain application field, our confidence in quantum computing can continue, attracting more funds and talents to join in, and then overcome difficulties such as quantum error correction.
There is a long way to go! I will search up and down. Quantum computing is a difficult road, we are at the forefront, and we can’t see the way forward. Maybe we will break into the maze, draw our swords and look around in a daze, maybe we will cut through the fog and see the road ahead under our feet! Some people think that this is a contest between countries, but I think it is the shining of the human spirit. We may fail, but we will not bow our heads.
GIPHY App Key not set. Please check settings