  Quantum Hall edge states have some characteristic features that can prove
useful to measure and control solid state qubits. For example, their high
voltage to current ratio and their dissipationless nature can be exploited to
manufacture low-loss microwave transmission lines and resonators with a
characteristic impedance of the order of the quantum of resistance $h/e^2\sim
25\mathrm{k\Omega}$. The high value of the impedance guarantees that the
voltage per photon is high and for this reason high impedance resonators can be
exploited to obtain larger values of coupling to systems with a small charge
dipole, e.g. spin qubits. In this paper, we provide a microscopic analysis of
the physics of quantum Hall effect devices capacitively coupled to external
electrodes. The electrical current in these devices is carried by edge
magnetoplasmonic excitations and by using a semiclassical model, valid for a
wide range of quantum Hall materials, we discuss the spatial profile of the
electromagnetic field in a variety of situations of interest. Also, we perform
a numerical analysis to estimate the lifetime of these excitations and, from
the numerics, we extrapolate a simple fitting formula which quantifies the $Q$
factor in quantum Hall resonators. We then explore the possibility of reaching
the strong photon-qubit coupling regime, where the strength of the interaction
is higher than the losses in the system. We compute the Coulomb coupling
strength between the edge magnetoplasmons and singlet-triplet qubits, and we
obtain values of the coupling parameter of the order $100\mathrm{MHz}$;
comparing these values to the estimated attenuation in the resonator, we find
that for realistic qubit designs the coupling can indeed be strong.
