Coherent Feedback Control in Quantum Circuits and Networks

Stefan Zeppetzauer

Hideo Mabuchi

Abstract : During the three-year performance period we have carried out a program of theoretical research on the foundations and potential applications of coherent-feedback quantum control. We have focused on potential applications in quantum-enhanced meterology and information processing, and on hardware platforms of an optical or opto-mechanical nature. The studies we have been performing begin to build a picture of how coherent feedback can provide a kind of circuit/network theory for quantum engineering, enabling rigorous analysis and numerical simulation of advanced devices and systems. We have begun to establish analytical approaches for comparing the performance of quantum-enhanced feedback control systems with classical counterparts, leveraging canonical results from classical control theory together with advanced methods for numerical simulations of proposed quantum systems. All of our results point to the interest of continued future study in this area, and of future investments in the experimental realization of the kinds of systems we propose.

Guofeng Zhang, M. R. James

Chuanxin Bian, Guofeng Zhang, Joseph H. W. Lee

The purpose of this article is to present an efficient coherent feedback control technique for squeezing enhancement of degenerate parametric amplifiers (DPAs). The feedback controllers to be designed are in the form of linear quantum stochastic systems which can be described by quantum feedback networks theory recently developed. The problem of squeezing enhancement is formulated as a non-convex constrained nonlinear programming problem, whose solution yields the coherent feedback controllers to be designed. Compared with the previous study, the proposed approach reveals clear advantage when DPAs are lossy, as is always the case in practice. Based on the recently developed quantum network synthesis theory, we show how the designed coherent feedback controllers can be implemented by means of quantum optical devices.

M. R. James

Hideo Mabuchi

The emerging discipline of coherent-feedback quantum control provides core concepts and methods for nanopho- tonic circuit theory, which can be assimilated within modern approaches to computer-aided design. Current research in this area includes the development of software tools to enable a schematic capture workflow for compilation and analysis of quantum stochastic models for nanophotonic circuits, exploration of elementary coherent-feedback circuit motifs, and laboratory demonstrations of quantum nonlinear photonic devices.