4 papers · 1 filter
Elementary Quantum Gates from Lie Group Embeddings in : Geometry, Universality, and Discretization
Antonio Falco, Daniela Falco-Pomares, Hermann G. Matthies
In the standard circuit model, elementary gates are defined relative to a chosen tensor factorization and are therefore extrinsic to the ambient group . Writing , we…
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…
A Rigorous and Self--Contained Proof of the Grover--Rudolph State Preparation Algorithm
Antonio Falco, Daniela Falco-Pomares, Hermann G. Matthies
We give a rigorous and self-contained analysis of the Grover--Rudolph quantum state-preparation algorithm, which encodes a probability distribution as an -qubit amplit…
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…