5 papers
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…
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 framewo…
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…
Reduced Order Models and Conditional Expectation -- Analysing Parametric Low-Order Approximations
Hermann G. Matthies
Systems may depend on parameters which one may control, or which serve to optimise the system, or are imposed externally, or they could be uncertain. This last case is taken as the…