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Quantum Mechanics and its Application

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Quantum mechanics has been controversial since its birth, and its abstract, uncertain nature makes it hard for the public to understand. However, with the development of science, more and more quantum theories and interesting facts has been discovered. Some of the theories have already been applied to many fields such as the quantum computer. The purpose of this essay is to try to explain the basic theories of quantum physics as well as its history development in a simple language. Then this essay is going to introduce the realization principle of quantum computer, the quantum annealing algorithm used by quantum computer and the application of quantum computer.

History

The beginning of quantum mechanics can be followed back to the double slits experiment which scientists tried to discover whether the nature of light is in the form of wave or particle in the 18th century [2]. The double slit experiment was conducted by putting a cover with two parallel slits in front of a light source and observing the shape of light on a distant screen.

Tomas Young conducted this experiment in 1803 and the result showed that light is in the form of wave [1]. However, when scientists repeat this experiment with single particle, for example, shoot the electron one by one through the double slits, the result still shows a diffraction pattern on the screen (graph at the bottom left).

This weird result shocked the world of physics because it is impossible for electron to interfere with itself as electrons pass the slits one by one. Then, scientists put a particle detector at the slits in order to determine which slit an electron pass each time. Something inexplicable happened, the result changed from diffraction pattern to two bright lines on the screen (the graph at the top right). Till today, scientists still cannot explain why electron presents the wave-like form when there is no particle detector at the slits and how come an equipment particle detector can change the present of the form of particles and affect the results. Although this question has not been answered yet, it led a large group of scientists get interested and studying on the nature of the quantum world. The foundations of quantum mechanics were established in the early 20th century by Max Planck, Niels Bohr and other scientists [2].

Basic theory of quantum mechanics

1. Quantum state: Scientists are not able to determine the position and the momentum of a quantum particle at the same time. For example, scientists can only detect the probability of the electron appearing in an electron cloud.

2. Quantum coherence: Quantum coherence is based on the theory that all objects have wave-like properties [3]. If the wave of the particle is separated in 2, then the 2 waves might coherently interfere with each other which make it form a superposition of 2 states [3]. The Schrödinger’s cat is a famous example that explains the concept of quantum superposition state, which the cat is both alive and dead at the same time in a box if human do not observe it. The theory of quantum coherence has been applied in the quantum computing because a quantum bit is in the superposition of two states, representing 0 and 1 at the same time.

3. Quantum entanglement: It describes how two particles are entangled with each other, even at great distances, and the behavior of one particle affects the state of the other. When one of them is manipulated (such as a quantum measurement) and its state changes, the other immediately changes accordingly.

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Gordon Moore, one of the founders of Intel, a chip giant, came up with the famous Moore’s law, which states that the number of components that can be accommodated on an integrated circuit doubles every 18-24 months or so, and the performance doubles, when the manufacturing price stays the same. In other words, every dollar can buy more than twice as much computer power/ability every 18-24 months. This law reveals the rate of progress in information technology.

For decades, Moore’s law seemed to be constant and correct, but it turns out that since the end of 2013, the growth multiples of components have slowed to double in three years. For the gradual density of components, there is always a limit, and people are thinking about how to deal with this problem. In 2014, the first commercial quantum computer was produced, and its powerful information processing capability was recognized by world-class enterprises such as Google and Microsoft. Since then, quantum computer has been applied to research, development and opening.

In order to understand how quantum computers operate, it is important to understand the bits 0 and 1 in a classic computer which is the smallest unit of data storage. The storage or processing of information in a classic computer is achieved by controlling the electrical level of the transistor, where the binary ‘1’ represents the high level and ‘0’ represents the low level. Information can be saved by continuously saving a string of binary numbers. In other words, a classical bit can only hold certain ‘0’ or ‘1’ information at one time. For instance, if I wanted to save the four messages ’00’, ’01’, ’10’ and ’11’ at the same time, I would have to use eight bits to save them, i.e. ‘00011011’.

Quantum bits: A bit in a quantum bit has the same meaning as a classical bit. The most important difference is ‘quantum’. A quantum bit can be understood as a unit of information in a quantum superposition state. Although it is a bit, it is uncertain in digital ‘0’ or ‘1’ state. In fact, it is in the two states in a certain weight stack up on the status. This characteristic of a quantum bit gives it the extraordinary ability to hold information ‘0’ and ‘1’ at the same time.

For example, what happens when there are two quantum bits? If each quantum bit can store information ‘0’ and information ‘1’ at the same time, two quantum bits can store information ’00’, ’01’, ’10’ and ’11’ at the same time, while the classical bit needs eight bits to store this information at the same time. Therefore, by a simple calculation, if you have N classical bits, it can hold N units of information at the same time. However, for N quantum bits, they can hold 2N units of information at the same time! With a small increase in the number N, the number can grow rapidly, and a 250-bit quantum bits can hold more information than the number of particles in the entire universe.

Quantum annealing is a quantum computer algorithm based on quantum properties. In fact, the idea of simulated annealing algorithm is similar to that of metal annealing. In order to understand quantum annealing, the concept of quantum tunneling effect needs to be introduced. Quantum tunneling effect describes quantum particles have a certain probability of passing through an impenetrable barrier and appearing on the other side of the barrier, because a quantum doesn’t have an exact location (quantum superposition state), it’s distributed over a region as illustrated below and that’s what the electron cloud in chemistry is all about.

To compare with the quantum annealing algorithm, we need to look at a common algorithm called the mountain climbing algorithm which is widely used in the classic computers. Mountain climbing algorithm refers to calculating the adjacent solution with an arbitrary value as the starting point, and then continuously judging the difference between this solution and the real solution. Then computer chooses the more suitable direction to continue the calculation until reaching a position where any direction is a ‘fail’ which leads further away from the real solution.

As illustrated above, assume the blue line represents the real solution. Firstly, a climber starts anywhere in the FE section. For him, going down is definitely closer to the real solution. However, when he reaches the valley which is the point E, he will find that no matter which way he goes, he will be further away from the real solution. Therefore, the climber is trapped at the bottom of the valley and will never reach to the real solution.

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Quantum Mechanics and its Application. (2022, September 15). Edubirdie. Retrieved February 3, 2023, from https://edubirdie.com/examples/quantum-mechanics-and-its-application/
“Quantum Mechanics and its Application.” Edubirdie, 15 Sept. 2022, edubirdie.com/examples/quantum-mechanics-and-its-application/
Quantum Mechanics and its Application. [online]. Available at: <https://edubirdie.com/examples/quantum-mechanics-and-its-application/> [Accessed 3 Feb. 2023].
Quantum Mechanics and its Application [Internet]. Edubirdie. 2022 Sept 15 [cited 2023 Feb 3]. Available from: https://edubirdie.com/examples/quantum-mechanics-and-its-application/
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