Quantum state transfer for multi-input linear quantum systems

Effective state transfer is one of the most important problems in quantum information processing. Typically, a quantum information device is composed of many subsystems with multi-input ports. In this paper, we develop a general theory describing the condition for perfect state transfer from the multi-input ports to the internal system components, for general passive linear quantum systems. The key notion used is the zero of the transfer function matrix. Application to entanglement generation and distribution in a quantum network is also discussed.Comment: 6 pages, 3 figures. A preliminary condensed version of this work will appear in Proceedings of the 55th IEEE Conference on Decision and Contro

Analysis of Quantum Linear Systems' Response to Multi-photon States

The purpose of this paper is to present a mathematical framework for analyzing the response of quantum linear systems driven by multi-photon states. Both the factorizable (namely, no correlation among the photons in the channel) and unfactorizable multi-photon states are treated. Pulse information of multi-photon input state is encoded in terms of tensor, and response of quantum linear systems to multi-photon input states is characterized by tensor operations. Analytic forms of output correlation functions and output states are derived. The proposed framework is applicable no matter whether the underlying quantum dynamic system is passive or active. The results presented here generalize those in the single-photon setting studied in (Milburn, 2008) and (Zhang and James, 2013}). Moreover, interesting multi-photon interference phenomena studied in (Sanaka, Resch, and Zeilinger, 2006), (Ou, 2007), and (Bartley, et al., 2012) can be reproduced in the proposed frameworkComment: 26 pages, 2 figures, accepted by Automatic

Nonlinear quantum input-output analysis using Volterra series

Quantum input-output theory plays a very important role for analyzing the dynamics of quantum systems, especially large-scale quantum networks. As an extension of the input-output formalism of Gardiner and Collet, we develop a new approach based on the quantum version of the Volterra series which can be used to analyze nonlinear quantum input-output dynamics. By this approach, we can ignore the internal dynamics of the quantum input-output system and represent the system dynamics by a series of kernel functions. This approach has the great advantage of modelling weak-nonlinear quantum networks. In our approach, the number of parameters, represented by the kernel functions, used to describe the input-output response of a weak-nonlinear quantum network, increases linearly with the scale of the quantum network, not exponentially as usual. Additionally, our approach can be used to formulate the quantum network with both nonlinear and nonconservative components, e.g., quantum amplifiers, which cannot be modelled by the existing methods, such as the Hudson-Parthasarathy model and the quantum transfer function model. We apply our general method to several examples, including Kerr cavities, optomechanical transducers, and a particular coherent feedback system with a nonlinear component and a quantum amplifier in the feedback loop. This approach provides a powerful way to the modelling and control of nonlinear quantum networks.Comment: 12 pages, 7 figure

Programming multi-level quantum gates in disordered computing reservoirs via machine learning and TensorFlow

Novel machine learning computational tools open new perspectives for quantum information systems. Here we adopt the open-source programming library TensorFlow to design multi-level quantum gates including a computing reservoir represented by a random unitary matrix. In optics, the reservoir is a disordered medium or a multi-modal fiber. We show that trainable operators at the input and the readout enable one to realize multi-level gates. We study various qudit gates, including the scaling properties of the algorithms with the size of the reservoir. Despite an initial low slop learning stage, TensorFlow turns out to be an extremely versatile resource for designing gates with complex media, including different models that use spatial light modulators with quantized modulation levels.Comment: Added a new section and a new figure about implementation of the gates by a single spatial light modulator. 9 pages and 4 figure

Direct and Indirect Couplings in Coherent Feedback Control of Linear Quantum Systems

The purpose of this paper is to study and design direct and indirect couplings for use in coherent feedback control of a class of linear quantum stochastic systems. A general physical model for a nominal linear quantum system coupled directly and indirectly to external systems is presented. Fundamental properties of stability, dissipation, passivity, and gain for this class of linear quantum models are presented and characterized using complex Lyapunov equations and linear matrix inequalities (LMIs). Coherent $H^\infty$ and LQG synthesis methods are extended to accommodate direct couplings using multistep optimization. Examples are given to illustrate the results.Comment: 33 pages, 7 figures; accepted for publication in IEEE Transactions on Automatic Control, October 201