Quantum Control Theory: Probabilistic and Geometric Aspects

Randa Herzallah, Abdessamad Belfakir

Nemoto, Ryusho

This paper reexamines the patent entitled “Quantum Computer Based on Probabilistic Geometry” (Publication No. 2019-220121, Japan Patent Office, 2019) in light of the Tenson Theory. By combining probabilistic number theory with geometric tensor analysis, we propose a control algorithm that represents quantum bit transitions on a probabilistic manifold. The aim is to reinterpret quantum information processing as a geometrical regulation of uncertainty, bridging mathematical physics, information science, and the philosophy of probability.

Jeffrey L. Krause

Claudio Altafini, F. Ticozzi

The scope of this work is to provide a self-contained introduction to a selection of basic theoretical aspects in the modeling and control of quantum mechanical systems, as well as a brief survey on the main approaches to control synthesis. While part of the existing theory, especially in the open-loop setting, stems directly from classical control theory (most notably geometric control and optimal control), a number of tools specifically tailored for quantum systems have been developed since the 1980s, in order to take into account their distinctive features: the probabilistic nature of atomic-scale physical systems, the effect of dissipation and the irreversible character of the measurements have all proved to be critical in feedback-design problems. The relevant dynamical models for both closed and open quantum systems are presented, along with the main results on their controllability and stability. A brief review of several currently available control design methods is meant to provide the interested reader with a roadmap for further studies.

Jun Zhang

Ryusho Nemoto

We propose a novel theoretical and experimental framework for controlling quan- tum states by geometrically manipulating the probability curvature R and infor- mational phase ϕ. By embedding quantum dynamics in a probabilistic geometric manifold, we derive a unified control equation and suggest realizable experimental protocols in optical, superconducting, and ion-trap systems. This approach aims at stabilizing quantum coherence via geometric feedback, mitigating decoherence and noise.