Trapped charged particles have been at the forefront of quantum information processing (QIP) for a few decades now, with deterministic two-qubit logic gates reaching record fidelities of 99.9% and single qubit operations of much higher fidelity. In a hybrid system involving trapped charges, quantum degrees of freedom of macroscopic objects such as bulk acoustic resonators, superconducting circuits or nano-mechanical membranes, couple to the trapped charges and ideally inherit the coherent properties of the charges. The hybrid system therefore implements a "quantum transducer", where the quantum reality (i.e. superpositions and entanglement) of small objects is extended to include the larger object. Although a hybrid quantum system with trapped charges could be valuable both for fundamental research and for QIP application, no such system exists today. Here we study theoretically the possibilities of coupling the quantum mechanical motion of a trapped charged particle (e.g. ion or electron) to quantum degrees of freedom of superconducting devices, nano-mechanical resonators and quartz bulk acoustic wave resonators. For each case, we estimate the coupling rate between the charged particle and its macroscopic counterpart and compare it to the decoherence rate, i.e. the rate at which quantum superposition decays. A hybrid system can only be considered quantum if the coupling rate significantly exceeds all decoherence rates. Our approach is to examine specific examples, using parameters that are experimentally attainable in the foreseeable future. We conclude that those hybrid quantum system considered involving an atomic ion are unfavorable, compared to using an electron, since the coupling rates between the charged particle and its counterpart are slower than the expected decoherence rates. A system based on trapped electrons, on the other hand, might have coupling rates which significantly exceed decoherence rates. Moreover it might have appealing properties such as fast entangling gates, long coherence and flexible electron interconnectivity topology. Realizing such a system, however, is technologically challenging, since it requires accommodating both trapping technology and superconducting circuitry in a compatible manner. We review some of the challenges involved, such as the required trap parameters, electron sources, electrical circuitry and cooling schemes in order to promote further investigations towards the realization of such a hybrid system.
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