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CRC Press eBooks

Nonlocal Quantum Computing (I)

Cheng Hsiao Wu

Published Nov 21, 2025• 0 citations
Publisher

Abstract

New four sets of 16 nonlocal operator–state relations are presented to describe the quantum computing from a chain of atoms that are in superpositions and in entanglement with each together. The derivation of those tensor relations is a presentation to prove the existence of four new nonlocal mathematics based on correct physics foundation. New concepts are presented to establish the correct quantum computing theory. Why qubit-gated approach is not adequate is explained thoroughly.

DOI
10.1201/9781003542032-5

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New four sets of 16 nonlocal operator–state relations are presented to describe the quantum computing from a chain of atoms that are in superpositions and in entanglement with each together. The derivation of those tensor relations is a presentation to prove the existence of four new nonlocal mathematics based on correct physics foundation. New concepts are presented to establish the correct quantum computing theory. Why qubit-gated approach is not adequate is explained thoroughly.
This presentation provides a comprehensive overview of the foundational principles of quantum computation. It begins by contrasting classical and quantum information, highlighting how quantum bits (qubits) leverage superposition, entanglement, and interference to process information in ways that surpass classical limits. The document explains the four postulates of quantum mechanics: state space (qubits as unit vectors in a Hilbert space), time evolution (via unitary operators), measurement (probabilistic collapse of the state), and composite systems (tensor products of subsystems). Key concepts such as the Bloch sphere representation, quantum gates (e.g., Hadamard, CNOT, Pauli gates), and quantum circuits are discussed, illustrating how quantum operations manipulate qubit states. The presentation also covers quantum evolution, the gate model for computation, and the universality of certain gate sets, emphasizing the potential for quantum parallelism and the transformative impact of quantum computing on fields like cryptography and optimization.
Nonlocal Quantum Computing Theory offers a fresh perspective on quantum computing, moving beyond the traditional qubit-based approach to a physics-driven interpretation of computation. This book highlights the limitations and logical flaws in mainstream quantum computing theories and introduces a rule-based, nonlocal quantum computing framework. Covering general-purpose quantum computing, biological applications, and atomic chains in full superposition and entanglement, this book presents a bold new theoretical foundation for the field. Key Features: Provides a comprehensive introduction to quantum computing from a nonlocal perspective. Critically examines the limitations of the standard qubit-based approach. Explores applications in biological systems and atomic chain computations. Introduces rule-based nonlocal quantum computing theory as an alternative framework. Includes a historical overview and discussion of quantum parallelism. This book is an essential resource for graduate students in physics and computer science, as well as researchers and professionals engaged in quantum information theory and quantum computing. Its innovative approach contributes to ongoing discussions in the field, making it valuable for those seeking a deeper understanding of the foundations and future 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.
Entanglement and quantum teleportation are two inter-related subjects and can be explained through four fundamental non-local quantum computing diagonal operator-state relations, which model the conservative phase-interaction between two adjacent atoms of an entangled atomic chain. Each model atom possesses four eigen-states. There exists a minimum focus distance between the two atoms for the entanglement to exist. Consequently, there exist perpetual elastic phase-changing events on the entire entangled chain at every discrete time interval that is evaluated and shown here. It is analogous to Newton’s first law of motion in discrete time. Quantum teleportation means every extra 2π2\pi2π phase between the atoms can be translated in Fourier space into an additional separation distance, a quantized value.