• 原文 address: A Layman’s Intro to Quantum Computers
  • By David Mooter
  • Translation from: The Gold Project
  • This article is permalink: github.com/xitu/gold-m…
  • Translator: PingHGao
  • Proofreader: Samyu2000, nia3y

Quantum computers for the layman

Quantum computers have the potential to revolutionize information technology. Many analysts consider today’s quantum computers to be as rudimentary as the room-sized ones of the 1940s. Over the next few decades, they may grow at the same exponential rate as classical computers. Unfortunately, the literature on quantum computing is usually written by insiders (people with physics degrees) for insiders. Here, I’ll explain quantum computing in plain language: how it works, how it differs from classical computers, and why it could lead to technological change.

Classical bits vs qubits

The memory system of a classical computer is made up of classical bits. Each of these bits has two states, representing “0” or “1”. As you use more bits, you can store more information.

For example, two bits may have four states: 00 01 10 11. There are eight possible states for three bits: “000 001 010 011 100 101 110 111”.

Physically, these classical bits are circuit elements, where the “0” and “1” represent the amount of current flowing through them.

Quantum computers maintain a series of qubits, each of which also has two states, which can be represented by a “0” or a “1”. However, these qubits are not circuit elements. Instead, they’re subatomic particles stuck in one place — fixed. They represent “0” or “1” in various ways, depending on the type of quantum computer. However, you don’t need to know the details to understand their purpose.

Unlike classical bits, when you measure qubits, you don’t always get the same results. Instead, the state of a qubit can be thought of as being on the surface of a sphere. The North and South poles represent the final states “0” and “1”, respectively. When the qubit’s state is closer to the North Pole, it indicates a higher chance of entering the “0” state at the time of measurement, and so on. For example, a quantum ratio at the equator has about the same chance of going in either direction. When measuring the qubit in the figure below, it has a significantly higher chance of ending up as a “0” (north) than a “1” (south) due to its closer proximity to the North Pole.

The first difference: determined vs. random states

This is the first difference from classical computers. Classical bits correspond to an explicit “0” or “1”. In contrast, a qubit corresponds to the probability of becoming a “0” or “1”. For example, if a quantum ratio has a 60% chance of being “1”, you can think of it as storing the value “60%”. By repeating quantum calculations many times and observing the results, you can determine with some degree of certainty what the probability is. Thus, it can store an infinite number of values from 0 to 1, but at the cost of always having some degree of statistical uncertainty in this result. Quantum algorithms are usually probabilistic in that they provide correct results within a given probability range. By contrast, classical computers are deterministic in nature and can output an answer with complete certainty. As any computer scientist knows, getting classical computers to truly randomize is quite difficult, because they tend to give very deterministic answers.

Classical logic gates vs quantum logic gates

The computer performs operations through various logic gates. These logic gates generally take one or two input parameters and perform some operation on the input parameters to get the output. For example, for and, if two inputs are “1”, the output is also “1”; Otherwise it prints “0”. Two logic gates are shown below:

Quantum computers use quantum gates to operate on their qubits. These calculations move the qubits around the surface of the sphere, meaning that the inputs and outputs are different states of the same qubit. For example, a quantum gate might flip a qubit to the opposite part of a sphere or rotate around one of its axes. Some gates take an input. Some gates require two or more, where the state of each input affects all output states. In the figure below, we see that the quantum gate rotates the previous qubit around the vertical axis.

Second difference: very different logic gates

A logic gate in a classical computer outputs a new bit without changing its input bit. The logic gate of a quantum computer directly changes the state of its input bits without generating new output bits. Furthermore, all quantum gates are invertible, but not all classical gates are invertible (see the two gates above – it is not always possible to infer input from output). Finally, mathematicians have shown that all classical gates can be created using combinations of quantum gates, but that some quantum gates cannot be created by classical gates. In other words, quantum gates can do things that classical computers cannot. This means that new algorithms can be invented.

Quantum entanglement

Two or more qubits may become entangled. This means that measuring one qubit immediately affects other qubits, even if they are on the opposite side of the deep universe. A simple example is that if you have two qubits, observing one causes the other to always produce the opposite result when observed. Another possibility is that the outcome of observing one qubit affects the probability that the other qubit will turn out to be a “0” or a “1”. This provides algorithms based on the entire data system, rather than one bit at a time.

The third difference: dependencies between bits

One way to think about it is that the states of the two entangled qubits are no longer independent of each other.

The lower left image shows two unentangled qubits — A in blue and B in red. Both have a 50-50 chance of becoming either a 0 or a 1. The odds of each combination are the same: “00” has a 25% chance, “01” a 25% chance, and so on. Knowing the value of A or B does not lead to any information about the other bit.

In the lower right image, two entangled qubits are shown. In this case, knowing the value of one bit gives you some information about the other bit. If qubit B is known to be “0”, qubit A is twice as likely to be “1” as “0”. But if qubit B is “1”, then qubit A must be “0” — they are no longer independent.

Quantum superposition

Recall that when a qubit is observed, it produces a random result. You would intuitively expect the qubit to oscillate between these two states, like a coin flipping in the air, head and head, until it lands. In reality, however, a qubit is both a “0” and a “1” at the same time. This is because the particles that store qubit information can have different energy levels or be in different locations at the same time. When a quantum particle interacts with something else, such as a tool to measure its energy or position, it randomly “collapses” into a state.

Let go of your doubts

I need to break down the description of quantum superposition and remove the main obstacle for most people: disbelief and confusion. Now you might think, “How can the same thing be in two places at once? It can’t be!”

I posed this question to three quantum physics PHDS. One of them replied that you just need to stop being skeptical and believe that the mathematics and experiments that are out there have proved it to be true. The other two responded more convincingly. The macro world we live in is completely different from the micro world, so we can’t apply what we observe at the macro level to the smallest level of the universe.

In order to accept these theories, consider some macro questions. Einstein proved that the speed of light cannot travel. It also seems intuitively wrong from the point of view of our human mind: why can’t I keep my foot on the accelerator when I’m approaching the speed of light? However, the theory has gained general acceptance.

So when I say that a qubit can be in two different places at once or have two seemingly contradictory energy levels at the same time, accept it and don’t try to think more deeply about why.

Now back to the introduction to quantum superpositions…

The fourth difference: exponential growth

Whereas classical bits can only be in two deterministic states, “0” or “1”, qubits can be in a superposition of both states at the same time. A classic sequence of 32 bits can have about 4 billion combinations. A classic computer can only process one of them at a time. 32-bit qubit sequences can contain up to 4 billion combinations at once. So quantum computing power grows exponentially, whereas classical computers grow linearly.

For example, if I want to search for some 8-bit key-value combination, a 16-bit computer can perform two parallel searches at once, twice as fast as an 8-bit computer. 32-bit computers will allow four parallel searches at once, four times faster than 8-bit computers. This means that when the number of digits doubles, the power of a classical computer doubles.

Compare that to a quantum computer. If a quantum computer has a qubit, it stores two states simultaneously (” 0, 1 “) and can therefore search for both at the same time. If it has two qubits, it stores four states simultaneously (” 00 01 10 11 “) and can search for all four states simultaneously, making it twice as fast as a single qubit computer. If it has three qubits, then it stores eight states simultaneously (” 000 001 010 011 100 101 110 111 “) and can search for all eight states simultaneously, so it is four times faster than a single qubit computer. So for every qubit added, the quantum computer doubles in power.

However, as you may recall, there is a problem with quantum comparison: when we take measurements, we can only randomly get one of these combinations. That’s not very useful if we want to take advantage of its ability to be in multiple states at once. How to solve this problem? The answer is wave interference.

Wave interference

In case you forgot what you learned in high school science, let’s review the principles of waves. You can see in the pool that when two waves meet, they affect each other. When the crests and crests of two waves meet, they reinforce each other, with stronger crests and troughs. But when peaks and troughs meet, they cancel each other out, resulting in no waves.

Essentially, qubits get their properties from energy waves, which have the same properties as water waves in a pond. There are complex algorithms (the mathematics of which are beyond the scope of this paper) that use the interference effect of waves to suppress the wrong energy states while amplifying the right ones. By repeating the algorithm several times before measuring the qubit, the probability of the error state being measured can be reduced and the probability of the expected state being measured can be increased. Even if the qubits are in all the states at once, you can find the right answer to the question with a certain degree of confidence by amplifying the states you want while suppressing the states you don’t.

application

Quantum computers are expected to surpass classical computers in some areas. Here are some examples.

  • Ai and Data Science Much of ARTIFICIAL intelligence is based on complex statistics and searching for patterns in complex data. Quantum algorithms have the ability to search for all states at once, so they are well suited to finding patterns in complex data. This can be used not only in ARTIFICIAL intelligence but also in other areas of data science.
  • Cryptography Shor algorithm is a theoretical quantum algorithm that can break most asymmetric ciphers. Quantum entanglement, on the other hand, offers the possibility of new encryption modes. Two entangled qubits are related to each other even if they are moved separately to opposite sides of the universe. Qubit encryption using entanglement is mathematically unbreakable because there is no shared key. For example, if I have a pair of entangled qubits, their observations are always the same. I can give one qubit to my message receiver and then change the other qubit to the desired value. When my receiver reads the value of his qubit, he gets the same value as I set, and the message is received without transmission.
  • Financial and Weather Models The randomness of qubits makes them better suited to simulating complex random systems, such as financial markets and weather. Investors often want to evaluate the probabilities of various outcomes in a number of scenarios that are randomly generated. So many variables determine the weather that it takes more time for traditional computers to make predictions than it does for the weather to evolve. In addition, research from MIT has shown that the equations governing the weather have hidden wave properties that can be solved by a quantum computer.
  • Molecular modeling Molecular modeling is so complex that classical computers can model only the simplest molecules. In the chemical industry, quantum computers have great potential for modeling complex molecules to develop new compounds.

What should your IT organization do

There are two key bottlenecks in the application of quantum computing. The biggest limitation is that quantum computing is still in its infancy, with few commercially viable options available at the moment. The second is that quantum computers will never beat classical computers in every field. Instead, they have an advantage only for certain types of computing tasks. Classical computers will still outperform quantum computers for most computing tasks. That means classical computers are here to stay.

Still, there are steps your business can take now to prepare for the quantum race. At the current level of quantum computing, data scientists have been able to identify algorithms suitable for quantum computers and identify use cases that appear to be capable of quantum computers. Start building quantum algorithm skills in your data science team. Let them determine which computing tasks are better suited to quantum computing. More specifically, identify certain patterns that are more suitable for quantum computing and record them so that other data scientists can identify data sets containing these features based on these patterns. This will allow the data team to lay out what current business cases (and future business cases) are suitable for quantum computing, including what maturity quantum computers need to reach to be commercially viable. Finally, develop a strategic plan for leveraging quantum computing, based on the business problems that your data scientists have identified as suitable for quantum computing.

Here are some resources to help you develop your quantum skills:

  • Quantum Computing Playground is a Quantum simulator that runs in a web browser. It won’t be as powerful as a real quantum computer, but it will offer the opportunity to learn the concepts of a quantum computer.
  • Microsoft has released a quantum language called Q# that can also run in a quantum computer simulator.
  • Finally, the IBM Quantum Computer Experience Center has a real quantum computer connected to the Internet. Using the IBMid account, you can run your code on their quantum computer and access their quantum community forum.

Quantum computing is developing rapidly. By planting the seeds of quantum skills in your data science organization and immediately developing a strategic plan, your organization will eventually be able to take advantage of quantum computing just as competitors are starting to understand it.

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