3 papers
quant-ph2026
Vistas of Algebraic Probability: Quantum Computation and Information
Antonio Falcó, Hermann G. Matthies
Kolmogorov's foundation of probability takes measure spaces, -algebras, and probability measures as basic objects. It is, however, widely recognized that this classical framewor…
quant-ph2026
Geometric Complexity of Quantum Channels via Unitary Dilations
Alberto Acevedo, Antonio Falcó
Nielsen's geometric approach to quantum circuit complexity provides a Riemannian framework for quantifying the cost of implementing unitary (closed--system) dynamics. For open dyna…
quant-ph2025
A mathematical model for a universal digital quantum computer with an application to the Grover-Rudolph algorithm
Antonio Falcó, Daniela Falcó--Pomares, Hermann G. Matthies
In this work, we develop a novel mathematical framework for universal digital quantum computation using algebraic probability theory. We rigorously define quantum circuits as finit…