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arXiv:1611.07110

Implementation of Bilinear Hamiltonian Interactions between Linear Quantum Stochastic Systems via Feedback

Symeon Grivopoulos, Ian R. Petersen

Published Nov 22, 2016• 1 citation
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Abstract

A number of recent works employ bilinear Hamiltonian interactions between Linear Quantum Stochastic Systems (LQSSs). Contrary to naturally occurring Hamiltonian interactions between physical systems, such interactions must be engineered. In this work, we propose a simple model for the implementation of an arbitrary bilinear interaction between two given LQSSs via a feedback interconnection.

DOI
10.48550/arxiv.1611.07110

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A number of recent works employ bilinear Hamiltonian interactions between Linear Quantum Stochastic Systems (LQSSs). Contrary to naturally occurring Hamiltonian interactions between physical systems, such interactions must be engineered. In this work, we propose a simple model for the implementation of an arbitrary bilinear interaction between two given LQSSs via a feedback interconnection.
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Recently, Nurdin, James and Doherty have demonstrated that an arbitrary linear quantum stochastic system can be realized as a cascade connection of simple one degree of freedom quantum harmonic oscillators together with a direct interaction Hamiltonian which is bilinear in the canonical operators of the oscillators. However, from an experimental point of view, direct interaction Hamiltonians are challenging to implement for systems with more than just a few degrees of freedom. In order to facilitate simpler experimental realizations of these systems, this paper develops a new synthesis algorithm for linear quantum stochastic systems that relies solely on field-mediated interactions, including in implementation of the direct interaction Hamiltonian. An explicit synthesis example is provided to illustrate the realization of a two degrees of freedom linear quantum stochastic system using the new algorithm.
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Recently, the influences and applications of indirect and direct couplings in coherent feedback control of linear quantum stochastic systems have been investigated. However, bilinear quantum stochastic systems escape the realm of the current known results. Furthermore, as fast tunable coupling of a set of two level quantum systems (qubits) with high coherence plays a vital role in quantum computing operations, in this paper we study direct and indirect couplings in the interconnection of qubits. A physical model described by bilinear quantum stochastic differential equations is presented, and physical realizability conditions (necessary and sufficient algebraic constraints) are provided to guarantee these bilinear quantum stochastic differential equations to correspond to the dynamics of directly or indirectly coupled open two level systems. These results shed light on network synthesis of bilinear quantum stochastic systems and coherent control of multiple qubits.
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