Theoretical Foundations of Quantum Computing

Masahito Hayashi, Satoshi Ishizaka, Akinori Kawachi +2 more

Jincheng Zhang

Probability Information Theory (PIT) is a foundational branch of theoretical computer science concerned with the mathematical properties of probability and its relationship to computation. This paper investigates the convergence of PIT with quantum computing, specifically exploring the nature and application of probability information within quantum algorithms. We propose a novel framework where PIT's theoretical foundations are integrated with quantum algorithm design, leveraging PIT's inherent strengths to guide and optimize quantum computations. This investigation aims to uncover potential new applications of quantum algorithms based on the unique properties of probability information, pushing the boundaries of computational exploration.

Bang-Hai Wang

The emergence of quantum information and quantum computing is the inevitable choice in the development of information science. Introduces the historical development of quantum logic,research and the theoretical foundation of quantum logic related to orthomodular lattice on the basis of the closed subspace of Hilbert space and several open issues. Based on the above content,introduces the enormous computing power source of quantum computing and looks forward to the possibility of a quantum logic research.

Stephen Fenner

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

Dr Kola Srimannaryana

The transition from theoretical quantum mechanics to practical quantum computing represents one of the most significant technological developments of the 21st century. This comprehensive survey examines the evolution from foundational quantum mechanical principles to contemporary quantum computing implementations. We analyze how fundamental quantum phenomena—superposition, entanglement, and unitary evolution—are systematically harnessed to achieve computational advantages over classical systems. The paper provides detailed analysis of key quantum algorithms including Deutsch-Jozsa, Grover's search, and Shor's factorization algorithm, emphasizing their theoretical foundations and computational complexity advantages. We present a comparative evaluation of current hardware platforms including superconducting qubits, trapped ions, photonic systems, and semiconductor quantum dots, analyzing their respective merits, limitations, and scalability prospects. The challenges of quantum error correction, decoherence mitigation, and the path toward fault-tolerant quantum computation are critically examined within the context of the current Noisy Intermediate-Scale Quantum (NISQ) era. This interdisciplinary synthesis bridges theoretical quantum mechanics and practical quantum computing, highlighting the remarkable progress achieved and the substantial challenges that remain in realizing the full potential of quantum computation.