Quantum states and quantum computing

Abstract: In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by position vectors as functions of time, $\vec{x}(t)$, while waves are modeled by tensor fields in space-time, $\Phi(t, \vec{x})$. These functions are embedded in, and evolve within space-time. All information about the physical system are coded in these mathematical functions, upon which the classical technologies are developed. In contrast, quantum theory models the physical system using a quantum state $\vert \alpha ,t\rangle$, situated in an evolving within Hilbert space, portraying the system's reality with inherent uncertainty. Despite the probabilistic nature of reality observation, the quantum state $\vert \alpha ,t\rangle$ can be precisely determined due to the unitary principle, provided we know the initial state. Therefore, it can serve as a foundation for developing quantum technologies, which we call quantum state-tronics similar to electronics. This discussion focuses on quantum computation, given its expansive scope. One of the paramount challenges in quantum computing is the scarcity of individuals equipped with the requisite knowledge of quantum field theory and the training necessary for this field. This article aims to elucidate the fundamental concepts of quantum field theory and their interconnections with quantum computing, striving to simplify them for those engaged in quantum computing.