Twenty-First Century Quantum Mechanics: Hilbert Space to Quantum Computers

Jean-Pierre Antoine

Angelo Cei, Steven French

G. Fano, S. M. Blinder

Chris Heunen, Andre Kornell

Significance Hilbert spaces and their operators are the mathematical foundation of quantum mechanics. The problem of reconstructing this foundation from first principles has been open for nearly a century. What is mathematically special about Hilbert spaces and their operators? This paper gives a categorical axiomatization. Unlike previous partial results of this type, the axioms do not presuppose probabilities, complex amplitudes, or continuity and are not limited to finite dimension.

Eduard Prugovečki, Yuh‐Kang Pan

Dr. Ashish Mishra, Alexander Mutiso Mutua, Dr. Meena Tiwari, Ms. Roopali Kachhi

Quantum computing represents one of the most profound technological and intellectual advances of the twenty-first century. Rooted in the principles of quantum mechanics and enriched by developments in computer science, mathematics, and engineering, quantum computing offers fundamentally new ways of processing information. By exploiting phenomena such as superposition, entanglement, and quantum interference, quantum computers promise to solve certain classes of problems that remain intractable for even the most powerful classical machines.