Systems Theory of Classical and Quantum Fields and Applications to Quantum Computing and Control

TL;DR

This paper develops a systems theoretical framework for quantum computing and control, integrating field theory, gauge theory, and S-matrix approaches to enhance understanding and design of quantum systems.

Contribution

It introduces a novel field theoretical approach to quantum computing, reinterprets gauge theories within systems theory, and applies S-matrix formalism to quantum gates and feedback mechanisms.

Findings

Reformulation of quantum gates using gauge theory

Application of S-matrices to quantum systems

Insights into gauge fields and feedback in quantum control

Abstract

We explore a field theoretical approach to quantum computing and control. This book consists of three parts. The basics of systems theory and field theory are reviewed in Part I. In Part II, a gauge theory is reinterpreted from a systems theoretical perspective and applied to the formulation of quantum gates. Then quantum systems are defined by introducing feedback to the gates. In Part III, quantum gates and systems are reformulated from a quantum field theoretical perspective using S-matrices. We also discuss how gauge fields are related to feedback.