Theory and Methodology of Information Security: Quantum Parallelism

Abstract In modern computational paradigms, quantum parallelism emerges as a fundamental aspect of quantum algorithms, leveraging the principle of quantum superposition to perform multiple computations simultaneously. One notable application is the use of black-box operations, allowing the evaluation of a function f(x) for multiple inputs concurrently. Quantum verification of matrix operations, particularly matrix multiplication, constitutes a key subroutine in quantum linear algebra. This study examines the Coppersmith–Winograd algorithm as one of the most efficient methods for matrix multiplication and explores its implications for quantum computation. Additionally, we consider the group isomorphism problem, originally formulated by Max Dehn, which provides insights into algebraic structures and their relationships. By integrating these concepts, this work highlights the potential of quantum parallelism for optimizing quantum algorithms and enhancing computational efficiency, with applications in secure information processing and complex problem solving.