The principles of quantum computing were laid out about 15 years ago by computer scientists applying the superposition principle of quantum mechanics to computer operation. Quantum computing has recently become a hot topic in physics, with the recognition that a two-level system can be presented as a quantum bit, or “qubit,” and that an interaction between such systems could lead to the building of quantum gates obeying nonclassical logic. (See PHYSICS TODAY, October 1995, page 24 and March 1996, page 21.)
The principles of quantum computing were laid out about 15 years ago by computer scientists applying the superposition principle of quantum mechanics to computer operation. Quantum computing has recently become a hot topic in physics, with the recognition that a two-level system can be presented as a quantum bit, or “qubit,” and that an interaction between such systems could lead to the building of quantum gates obeying nonclassical logic. (See PHYSICS TODAY, October 1995, page 24 and March 1996, page 21.)
It has recently been recognized that computers could be profoundly more powerful, if the possibilities offered by the basic principles of quantum mechanics were exploited more completely in machine design. It is physically possible for the binary state of a computer itself to obey quantum mechanics, i.e., to evolve along a superposition of different (logical) pathways that could interfere with one another. This is what is meant by a quantum computer. It has recently been shown that such a computer can perform a class of computational problems, including prime factorization, very rapidly. Quantum computers will require an art that is radically different from any that the computer industry practices today. The bits of such a computer will have to be represented by the states of individual atoms. The use of one such atomic degree of freedom, the "spin", is illustrated below.
It took only 40 years from the first ideas about using quantum physics as a basis for computing to the first working computers and the topic is gaining speed. Progress in quantum computer hardware development is accelerating significantly. When scientists started keeping a single qubit alive some 20 years ago, they struggled manipulating it in any useful manner. We now not only have quantum computers with hundreds and even over a thousand of qubits available, but they also provide a set of universal logical gates. This chapter lays the foundation to understand the mathematics behind this fascinating development by investigating the fundamental principles of quantum computing and quantum communications. We introduce the basic concepts like superposition, entanglement, and qubits.
In the twentieth century, quantum physics is one of the most successful approaches in scientific progress. To theorize the concept of quantum computing Max Planck's idea of the existence of energy in individual units like matter was used. Since then, the idea of manufacturing quantum computers for everyday use is becoming more plausible with technological advances in quantum theory. A classical computer carries out logical operations using a bit which is either 1 or 0. In contrast to a classical computer, a quantum computer works with a quantum bit or qubit, which is not limited to two states only. Qubits can exist in a superposition of the two states creating parallelism. Qubit represents the state of atoms, ions, photons or electrons. These qubits which work together with a control device act as a computer memory.Quantum computers have the potential to become million times more potent than present-day supercomputers due to the presence of these multiple states simultaneously. Concepts and ideas of quantum computing have been demonstrated by different methods like Ion Trap, Quantum Dot methods etc. However, the actual realization of such a superior system is still in the future. A strategy must be formulated to maintain decoherence and other potential sources of error at a permissible level.Astonishingly, quantum computing took a long time to take off, even though the physicists have known about the world of subatomic particles. Even so, it took computer scientists another half-century to consider harnessing quantum effects for computation. Also, it was later discovered that quantum computers could solve quantum mechanical many-body problems that are impractical to solve on a classical computer. The foundations of the subject of quantum computation may have become well-published, but the knowledge is still growing. Hence here is a research paper based on the study of quantum computation.
Quantum computing represents a transformative approach to computation by leveraging the fundamental principles of quantum mechanics. Unlike classical computing, which operates on bits, quantum computing uses quantum bits or qubits that exist in superposition, enabling parallel processing of information. This paper introduces the foundational concepts of quantum computing—such as superposition, entanglement, and quantum gates—and explores how these principles differ from classical models. Further, it highlights the implications of quantum computing in modern physics, especially in areas like quantum simulation, cryptography, and quantum field theory. By avoiding complex mathematical derivations, this paper aims to make quantum computing accessible to a broader academic audience, emphasizing both theoretical insights and practical impacts.
Today's computers work on bits that exist as either 0 or 1. Quantum computers aren't limited to two states; they encode information as quantum bits, or qubits, which can exist in superposition. Qubits represent atoms, ions, photons or electrons and their respective control devices that are working together to act as computer memory and a processor. Because a quantum computer can contain these multiple states simultaneously, it has the potential to be millions of times more powerful than today's most powerful supercomputers. A processor that can use registers of qubits will be able to perform calculations using all the possible values of the input registers simultaneously. This superposition causes a phenomenon called quantum parallelism, and is the motivating force behind the research being carried out in quantum computing. Due to technical obstacles, till date, a quantum computer has not yet been realized. But the concepts and ideas of quantum computing has been demonstrated using various methods like NMR, Ion Trap, Quantum Dot, Optical Methods, etc. A quantum computer manipulates qubits by executing a series of quantum gates, each a unitary transformation acting on a single qubit or pair of qubits. In applying these gates in succession, a quantum computer can perform a complicated unitary transformation to a set of qubits in some initial state. The qubits can then be measured, with this measurement serving as the final computational result. Research must devise a way to maintain decoherence and other potential sources of error at an acceptable level. Probably the most important idea in this field is the application of error correction in phase coherence as a means to extract information and reduce error in a quantum system without actually measuring that system. Thereby, quantum computers will emerge as the superior computational devices and perhaps one day make today's modern computer obsolete.
Quantum mechanics has proven its position as the primary theory for accurately describing microscopic domains. Numerous fields in physics utilize quantum mechanics to great effects, with one prominent application being quantum computing. Quantum computing extends the field of quantum mechanics to information theory, striving to perform computational tasks utilizing quantum phenomena with notably greater efficiency compared to classical alternatives. In this thesis, I will go through the basics required in the field of quantum computing. To understand quantum computing demands adapting a new type of matrix mechanical view. This involves considering Hilbert spaces, which are linear vector space having a well defined inner product. Hilbert spaces contain state vectors describing quantum states, as well as operators for altering and measuring these states. The dynamics of quantum systems are governed by three quantum postulates. These specify Hilbert spaces and state vectors as the fundamental components of quantum systems, Hermitian operators as providing the physical manifestation of these systems, and finally, the Schrödinger's equation to describe the time evolution of such systems. These notions are required in producing quantum computing. Quantum computing uses qubits as the computational basis, analogous to classical bits but with the added capability of quantum superposition. Qubits are represented as two-state vectors, and can be physically realized with any quantum-behaving binary-valued system, like the electron spins. Qubits can be combined into higher dimensional states with the use of tensor products, causing the system's Hilbert space to expand as 2^n with n being the number of qubits, allowing for exponential computational speedup. Computational logic can be constructed by acting on the qubits using unitary operators, known as quantum gates. The combinations of qubits and quantum gates can be visualized as quantum circuits, depicted using specialized circuit diagram notations. An essential part of quantum computing, and the phenomena enabling exponential computational speedup, is quantum entanglement. Entanglement arises in interacting qubits, intertwining them so that the individual states become correlated. Entanglement can be characterized by being unable to reduce a combined state into its pure constituents. The amount of entanglement in a system can be measured using von Neumann entropy, analogous to Shannon entropy in classical information theory. Entanglement serves various purposes in quantum computing and is a defining feature distinguishing it from the classical domain. In this thesis, the entanglement properties of a periodic four-qubit circuit with alternating quantum gates were simulated. The simulation was performed computationally, and measured entanglement entropy as a function of the amount of circuit periods. The results demonstrated different characteristics of entanglement depending on the parameters used for the quantum gates, with the entanglement either being periodic, non-occurring or chaotic in nature.