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World Congress on Intelligent Control and Automation

Quantum multi-channel decoupling

Pei-Lan Liu, Shin Li, Tzyh‐Jong Tarn

Published Jul 1, 2012• 1 citation
Publisher

Abstract

We study multiple-input multiple-output (MIMO) quantum systems and explore quantum decoupling techniques that can be used to facilitate the design of quantum networks. We provide a quantum state feedback control law to change the structure of a quantum system in order to decouple the multiple channels. We show that an MIMO quantum system can be decoupled as an aggregate of n separated single-input single-output (SISO) quantum systems from an input-output point of view. We also discuss the conditions under which quantum decoupling can be achieved. We illustrate our method with several qubit and atomic systems.

DOI
10.1109/wcica.2012.6358255

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We study multiple-input multiple-output (MIMO) quantum systems and explore quantum decoupling techniques that can be used to facilitate the design of quantum networks. We provide a quantum state feedback control law to change the structure of a quantum system in order to decouple the multiple channels. We show that an MIMO quantum system can be decoupled as an aggregate of n separated single-input single-output (SISO) quantum systems from an input-output point of view. We also discuss the conditions under which quantum decoupling can be achieved. We illustrate our method with several qubit and atomic systems.
The control of quantum multipartite mechanical systems is an emerging research topic in the quantum field due to the rapid development of technologies such as solid state physics and quantum optics. In this dissertation, we propose a quantum multi-channel decoupling methodology that facilitates the control of quantum multipartite mechanical systems and the design of complex quantum networks. Our approach uses bilinear input affine system models to express desired quantum control systems. This setting allows us to adopt various useful techniques from modern control theory, with some non-trivial modifications. In the quantum realm, we deal with the domain problem, and therefore the decoupling control of infinite-dimensional quantum systems is also included in our work. Our analysis is based on the operator algorithm, whose nature is the matrix operation. For quantum multipartite mechanical systems, the whole system's dimension is the product of all the single components' dimensions, yet in classical systems it is simply the sum of them. Thus, we use the tensor product method to analyze and design quantum multipartite mechanical systems. We give the conditions under which quantum multi-channel decoupling can be achieved and design the feedback control law.
Feedback control engineers have been interested in multiple-input--multiple-output (MIMO) extensions of single-input--single-output (SISO) results of various kinds due to its rich mathematical structure and practical applications. An outstanding problem in quantum feedback control is the extension of the SISO theory of Markovian feedback by Wiseman and Milburn [Phys. Rev. Lett. 70, 548 (1993)] to multiple inputs and multiple outputs. Here we generalize the SISO homodyne-mediated feedback theory to allow for multiple inputs, multiple outputs, and arbitrary diffusive quantum measurements. We thus obtain a MIMO framework which resembles the SISO theory and whose additional mathematical structure is highlighted by the extensive use of vector-operator algebra.
Characterization and exploitation of multiple channels between the transmitter and the receiver in multiple-input multiple-output (MIMO) communications brought a paradigm shift in classical communication systems. The techniques developed around MIMO communication systems not only brought unprecedented advancements in communication rates but also substantially improved the reliability of communication, measured by low error rates. We develop a framework for MIMO quantum communications with discrete-variable quantum systems. We propose a general model of MIMO quantum channels incorporating noise, losses, and crosstalk among multiple channels. We leverage the approximate quantum cloning to transmit imperfect clones of the input state over this channel setup. We demonstrate that transmitting multiple imperfect clones achieves better communication fidelity as compared to transmitting a single perfect copy of the state due to the diversity of the MIMO setup. We also demonstrate a practical tradeoff between fidelity and rate of communication and call it quantum diversity multiplexing tradeoff (DMT) due to its similarity with the well-known DMT in classical MIMO setups.
This study focused on a controller application of a quantum neural network, using qubit neurons as an information processing unit, and investigated its characteristics when controlling a multiple-input and multiple-output (MIMO) nonlinear system. Using a multilayer quantum neural network, a direct controller that conducts the online training of the quantum neural network was investigated. Computational experiments on the control of a MIMO non-linear discrete-time plant were conducted to evaluate the performance of the quantum neural network-based controller. The experimental results confirmed the effectiveness of the proposed quantum neural network-based controller and elucidated its characteristics.