In regard to the important of qubits role and quantum gate in quantum computers, in this article we will consider to the qubit structure and quantum gate on the basis of theory and quantum principles and in various from we will show the qubit and quantum gate (quantum operator).Finally we will express cloning theorem the quantum computers by binary gate.
In regard to the important of qubits role and quantum gate in quantum computers, in this article we will consider to the qubit structure and quantum gate on the basis of theory and quantum principles and in various from we will show the qubit and quantum gate (quantum operator).Finally we will express cloning theorem the quantum computers by binary gate.
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.
The world is changing very fast, and so are the ways of communication and computation. This article is about a new communication and information technology based on the principles of the quantum physics. At first we discuss about some fundamental paradigms of Quantum Computers World, and then introducing the basis of quantum computation: "QBit". After that we explain some magic properties of this atomic QBit including quantum measurement, superposition, entanglement, etc. Then we introduce quantum gates the basic modules of the next generation computers, their relation with the ordinary logical gates and the properties of some of the most useful quantum gates. And finally, we have a brief talk on some magic algorithm and the relation between these new born creatures and other fields of computers world, based on the quantum theories and manipulated by the quantum circuits
A quantum gate is the quantum analog of the classical logic gate of digital computers. It is a basic structural unit of a quantum circuit which operates on a small number of qubits to deliver a predefined output. A quantum circuit is a graphical representation of the sequence of the quantum gates used and the measurements performed in a quantum computation. Various quantum logic gates, namely, the Hadamard, T phase, NOT, Pauli-X, controlled NOT (CNOT), controlled-Z, SWAP and controlled phase gates as well as higher-level Toffoli and Fredkin gates are described. Conventions of reading quantum circuit diagrams are explained. Operation of a quantum full adder consisting of registers and gates is discussed, elaborating the role of the NOT gate, the sum calculation with CNOTgates and the carry C-out calculation with Toffoli gates. A primary tool used for performing arithmetic operations on a quantum computer is the quantum Fourier transform (QFT). The QFT adder and multiplier circuits are presented.
This chapter briefly describes the basic concepts and principles of quantum computing. Firstly, the concepts of qubit, quantum coherence, quantum decoherence, quantum entanglement, quantum density operators, linear operators, inner products, outer products, tensor products, Hermite operators, and unitary operators are described. Then, the four basic assumptions of quantum mechanics are introduced, focusing on the measurement assumptions of quantum mechanics. Finally, the definition of commonly used quantum logic gates is given including single qubit gates, double qubit gates, and multiple qubit gates. These contents provide the necessary theoretical basis for subsequent chapters.
This chapter connects key quantum mechanics principles to quantum computing. It begins by contrasting classical computing's binary logic with quantum computing's use of superposition, entanglement, and interference. It explains how qubits differ from bits by existing in multiple states simultaneously, allowing parallel computation. The chapter introduces quantum gates (Pauli-X, CNOT) and their functions in manipulating qubit states. It describes quantum circuits, measurement, and the collapse of qubit states upon observation. Key mathematical tools, such as Dirac notation and complex vector spaces, are introduced to support quantum operations. The no-cloning theorem is noted for its role in quantum information integrity. Finally, the chapter outlines current challenges in coherence, error correction, and decoherence in quantum systems. It closes by emphasizing how these principles form the operational basis for quantum algorithms, providing the foundation for later discussions on security applications and quantum resilience.