Preliminaries: From Quantum Mechanics to Quantum Computation

Bart D’Hooghe, Jarosław Pykacz

Dongsheng Wang

A preliminary overview of measurement-based quantum computation (QC) in the setting of symmetry and topological (TOP) phases of quantum matter is given. The underlying mechanism for universal QC by teleportation or symmetry are analyzed, with the emphasis on the relation with tensor-network states in the presence of various symmetries. Perspectives are also given for the role of symmetry and phases of quantum matter in measurement-based QC and fault tolerance.

Alain Aspect, Anthony J. Leggett, John P. Preskill +2 more

Jincheng Zhang

This paper introduces a novel geometric simulation framework based on quantum computing, designed to accelerate and enhance geometric simulation capabilities through the exploitation of quantum mechanics. The framework utilizes quantum algorithms to efficiently handle high-dimensional geometric problems, offering improved accuracy and computational speed compared to traditional methods. This work demonstrates the potential of quantum computing to revolutionize geometric modeling, particularly for complex and intricate geometries. This paper will outline the core mechanism, the rationale behind its development, and preliminary results demonstrating the framework's effectiveness.

Huimin Zheng, Haixing Hu, Wu, Nan +1 more

Inspired by the work of Feynman, Deutsch, We formally propose the theory of physical computability and accordingly, the physical complexity theory. To achieve this, a framework that can evaluate almost all forms of computation using various physical mechanisms is discussed. Here, we focus on using it to review the theory of Quantum Computation. As a preliminary study on more general problems, some examples of other physical mechanism are also given in this paper.

Craig S. Lent