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QUANTUM COMPUTING AND QUANTUM COMPUTERS

Abstract. Quantum computers are a new generation of computers that use the principles of quantum mechanics to process information. They use qubits that can exist in a superposition of states 0 and 1, allowing many calculations to be performed in parallel. Quantum entanglement allows qubits to be interconnected, which contributes to the high speed of information processing.

Keywords: Quantum computing, Quantum computers, Shor's algorithm, Quantum Fourier Transform, components of quantum computers, qubits, Quantum gates, Quantum registers

I. INTRODUCTİON

Quantum computing and quantum computers is a new and promising area in the field of information technology, which uses the quantum properties of matter to process and store information. Physical foundations of quantum computing and quantum computers

Traditional computers use the binary system to represent information and operate on it. The binary system is based on the use of bits, which can only be in two states - 0 or 1. Quantum computers, on the other hand, use qubits (or quantum bits) to store and process information. Qubits can be in a superposition of states, where they can be both 0 and 1 at the same time, allowing quantum computers to solve problems that would be impossible for traditional computers.

Quantum computers are used to solve problems that cannot be solved on classical computers, including factoring large numbers and solving optimization problems. In addition, quantum computers can be used to model complex physical systems, which is of great importance for scientific and engineering applications.

II. Shor algorithm

One of the most well-known quantum computing algorithms is the Shor algorithm, which can be used to factorize large prime numbers, a task that is the basis of many encryption algorithms used on the Internet. Quantum computers can also be used to solve optimization and simulation problems, which is of great importance for scientific and engineering applications.

Shor's algorithm is a quantum algorithm developed by Peter Shor in 1994 for fast factorization of large integers. This algorithm is one of the most famous and important examples of quantum computing.

Shor's algorithm consists of two main steps:

Determining the period of a function: The first step of Shor's algorithm is to apply quantum Fourier transforms to find the period of the function. If we know the period of the function, then we can calculate the factors of the number we are trying to factor.

Finding factors: The second step of Shor's algorithm is to use the found period of the function to find the factors of the number. This is done by solving the equation (x^r) - 1 = 0, where r is the found period of the function and x is some integer. If r is even and (x^(r/2)) + 1 is not a multiple of the number we are trying to factorize, then we can compute the factors of the number as gcd (x^(r/2) + 1, N) and gcd (x ^(r/2) - 1, N).

Shor's algorithm is very efficient for factoring large numbers and can be used to break cryptographic systems that are used to secure communications on the Internet. However, the implementation of the Shor algorithm on quantum computers is still a challenge, since it requires a large number of qubits and high stability of quantum elements.

Quantum computers, however, remain in development and there are many technical problems that need to be solved before they become practical. One of the main challenges is keeping the qubits in a state that requires very low temperatures and environmental control. It also requires the development of new algorithms and software that can use the potential of quantum computers.

Quantum computers have some unique properties that distinguish them from classical computers. For example, quantum computing can be performed in parallel, allowing a large amount of information to be processed simultaneously. In addition, quantum computing may be more efficient for certain tasks than classical computing.

There are currently several companies and research labs that are working on building quantum computers, including IBM, Google, Microsoft, and Rigetti Computing. Quantum computers are also available for experimentation and research through cloud services provided by some of these.

III. Quantum Fourier Transform

The Quantum Fourier Transform (QFT) is a quantum operation that is used in various quantum computing algorithms, including Shor's algorithm for factoring large numbers and Grover's algorithm for searching unordered databases.

The quantum Fourier transform is an analogue of the classical Fourier transform, which is used in signal processing and mathematical physics. Quantum Fourier transform works with qubits, which can be in superposition of states, and allows you to perform operations on multiple qubits at the same time.

The quantum Fourier transform is used to transfer information from the qubit state space to the frequency space, which allows you to work effectively with periodic functions and solve certain problems.

To apply the quantum Fourier transform to a set of qubits, a number of quantum gates are used, including the Hadamard gate, the phase shift gate, and the controlled phase shift gate. The quantum Fourier transform can be implemented using a chain of quantum gates and takes O(n^2) quantum operations for n qubits.

(Quantum gates are operations that are performed on quantum bits (qubits), similar to logic operations in classical computing. Quantum gates can be used to build algorithms and perform various operations, including quantum transformations such as the Quantum Fourier Transform (QFT).)

IV. History

The history of the development of quantum computers began in the 1980s, when Richard Feynman and David Deutsch suggested using quantum effects to create more powerful computers. At that time, quantum theory was already quite developed, but it was not yet clear how to apply it for practical purposes.

In the 1990s, quantum computers began to be seen as a real possibility, and the first experimental models emerged. In 1994, Peter Shor developed an algorithm that showed how a quantum computer could be used to solve problems that classical computers could not solve in an acceptable time. This was a real breakthrough in the development of quantum computers and drew attention to this direction.

In the 2000s, quantum computers have become more and more advanced, but until now it has not been possible to create a quantum computer that can perform a real-world task faster than a classical computer. However, in 2011, the D-Wave One quantum computer was put into operation, and it could solve certain problems faster than a classical computer.

Since then, quantum computers have continued to evolve, and their capabilities are constantly increasing. Currently, many companies, including IBM, Google, Microsoft, Intel and Alibaba, are working on the development of quantum computers and the creation of new quantum algorithms. Quantum computers can have great potential for solving complex problems that cannot be solved by classical computers.

V. Main Components

1) Qubits are quantum analogs of classical bits that can be in the state 0, 1, or a superposition of these states. Qubits can be implemented in various physical systems, such as electrons in wells, photons in optical fibers, or atoms in traps.

2) Quantum gates are analogues of classical logic gates that allow you to perform operations on qubits. Quantum gates can be implemented, for example, with controllable single qubits, quantum two-stage gates, or CNOT quantum gates.

3) Quantum registers are collections of qubits that are used to store and process data. Quantum registers can range from single qubits to more complex structures such as quantum networks.

4) Detectors are devices that measure the states of qubits. Measurements can be made in different bases, for example, in the basis of 0 and 1 or in the basis of superpositions. Measurements of qubits can lead to the collapse of the superposition of qubit states into one specific state.

Quantum computing and quantum computers have their pros and cons, which should be considered when using and developing them.

VI. Pros and cons of quantum computing.

Pros:

1) Speed: Quantum estimates can be much faster than classical estimates, especially when solving certain problems, such as factoring large numbers or solving certain problems.

2) Expandability: Quantum computers can be expanded to much more complex tasks than is possible with classical computers.

3) Problem Solving: Quantum solutions solve big problems that classical computers can't, such as quickly deciding on dimensional permissions.

Cons:

1) Error Sensitivity: Quantum frequencies are very sensitive to errors and noise, which can be caused by factors such as errors in the design and manufacture of quantum computers.

2) The complexity of programming.

3) Problem limitation: Some problems can be solved more efficiently with classical computers, so for problems using quantum computers will be inefficient.

VII. Pros and cons of quantum computers:

Pros:

1) Speed: Quantum computers have the potential to solve problems much faster than classical computers.

2) Expandability: Quantum computers can be scaled up to more qubits (analogous to bits), allowing for more complex tasks.

3) Solving problems that cannot be solved by classical computers: Quantum computers can solve problems for which classical computers are not powerful enough, such as factoring large numbers, which is essential for encrypting information.

Cons:

1) High price: Quantum computers are very expensive to manufacture and require complex infrastructure to operate.

2) Complexity of programming: Quantum computers require a new approach to programming, which can be difficult for programmers who do not have experience with quantum systems.

3) Error Sensitivity: Quantum computing is very sensitive to errors and noise caused by both external factors and errors in the design and manufacture of quantum computers.

4) Limitations of Problems: Some problems can be solved more efficiently with classical computers, so for these problems quantum computers will not be efficient.

VIII. Application area

Quantum computing is used in various fields such as science, engineering, finance and technology. Some specific examples of the use of quantum computing include:

1) Simulation of complex physical systems: Quantum computing can be used to create accurate simulations of complex physical systems such as molecular systems, which can be of significant value in scientific and engineering applications.

2) Optimization: Quantum computing can be used to solve optimization problems such as finding the best route for logistics companies or optimizing manufacturing processes in industry.

3) Cryptography: Quantum computing can be used to create more secure cryptographic systems such as quantum cryptography and distributed quantum key.

4) Machine learning: Quantum computing can be used to process a large amount of data, which is of great importance for machine learning and data analysis.

5) Artificial intelligence: Quantum computing can be used to create more powerful and intelligent artificial intelligence systems.

6) Finance: Quantum computing can be used in financial applications such as determining the optimal investment portfolio and assessing financial risks.

In addition, quantum computing can be used to create new materials, develop new drugs, and more. In general, quantum computing has great potential for solving complex problems that cannot be solved on classical computers.

Quantum computers are used to solve problems that classical computers cannot solve or solve very slowly. Here are some examples of the use of quantum computers:

1) Factorization of large numbers: Quantum computers can solve large number factorization problems much faster than classical computers. This is of great importance for cryptography and security.

2) Simulation of complex physical systems: Quantum computers can be used to create accurate simulations of complex physical systems such as molecular systems, which can be of significant value in scientific and engineering applications.

3) Optimization: Quantum computers can be used to solve optimization problems such as finding the best route for logistics companies or optimizing manufacturing processes in industry.

4) Cryptography: Quantum computers can be used to create more secure cryptographic systems such as quantum cryptography and distributed quantum key.

5) Machine learning: Quantum computers can be used to process a large amount of data, which is of great importance for machine learning and data analysis.

6) Artificial Intelligence: Quantum computers can be used to create more powerful and intelligent artificial intelligence systems.

7) Finance: Quantum computers can be used in financial applications such as determining the optimal investment portfolio and assessing financial risks.

In addition, quantum computers can be used to create new materials, develop new drugs, and more. In general, quantum computers have great potential for solving complex problems that cannot be solved on classical computers.

Quantum computing and quantum computers have potential applications in many areas, including:

1) Cryptography: Quantum computers can be used to break encryption that ordinary computers cannot break, as well as to create quantum ciphers.

2) Simulation: Quantum computers can be used to create more accurate and faster models that can help plan and optimize various processes and systems, such as climate and economic models.

3) Pharmaceuticals and medicine: Quantum computing can be used to develop new drugs and simulate biological systems.

4) Transportation: Quantum computing can help optimize scheduling and logistics management, and help develop new technologies such as quantum sensors and quantum compasses.

5) Artificial Intelligence: Quantum computing can help speed up the training of neural networks and the development of more sophisticated machine learning algorithms.

6) Energy: Quantum computing can help design more efficient solar panels, batteries and other renewable energy technologies.

7) Finance: Quantum computers can help you analyze markets and make better financial decisions.

8) Simulations: Quantum computers can be used to create more accurate simulations of various physical processes and systems, such as quantum simulators and molecular dynamics simulators.

CONCLUSION

In conclusion, quantum computers represent a promising area for the development of information technology.

Quantum computing has the potential to solve complex problems such as factoring large numbers, optimization, modeling complex systems, and more. However, at the moment, quantum computers are at an early stage of development, and many technical and algorithmic problems need to be solved before their widespread commercial use.

REFERENCE

1. "Programming Quantum Computers: Essential Algorithms and Code Samples" by Eric R. Johnston, Nic Harrigan, and Mercedes Gimeno-Segovia.

2. "Quantum Computing: An Applied Approach" by Jack D. Hidary.

3. "Quantum Computing Since Democritus" by Scott Aaronson.

4. "Quantum Computing: A Gentle Introduction" by Eleanor G. Rieffel and Wolfgang H. Polak.

5. "Quantum Computing for Computer Scientists" by Noson S. Yanofsky and Mirco A. Mannucci.

6. IBM Quantum - Official site of IBM Quantum.

7. Microsoft Quantum Computing - Official Microsoft Quantum Computing website

8. Google Quantum Computing - Official site of Google Quantum Computing.

9. arXiv - Repository of scientific articles

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