  We investigate the behavior of qubits consisting of three electron spins in
double and triple quantum dots subject to external electric fields. Our model
includes two independent bias parameters, $\varepsilon$ and $\varepsilon_{M}$,
which both couple to external electromagnetic fields and can be controlled by
gate voltages applied to the quantum dot structures. By varying these
parameters one can switch the qubit type by shifting the energies in the single
quantum dots thus changing the electron occupancy in each dot. Starting from
the asymmetric resonant (ARX) exchange qubit with a (2,0,1) and (1,0,2) charge
admixture one can smoothly cross over to the resonant exchange (RX) qubit with
a detuned (1,1,1) charge configuration, and to the exchange-only (EO) qubit
with the same charge configuration but equal energy levels down to the hybrid
qubits with (1,2,0) and (0,2,1) charge configurations. Here, ($l,m,n$)
describes a configuration with $l$ electrons in the left dot, $m$ electrons in
the center dot, and $n$ electrons in the right dot. We first focus on random
electromagnetic field fluctuations, i.e., "charge noise", at each quantum dot
resulting in dephasing of the qubit and provide a complete map of the resulting
dephasing time as a function of the bias parameters. We pay special attention
to the so-called sweet spots and double sweet spots of the system which are
least susceptible to noise. In the second part we investigate the coupling of
the qubit system to the coherent quantized electromagnetic field in a
superconducting strip-line cavity and also provide a complete map of the
coupling strength as a function of the bias parameters. We analyze the
asymmetric qubit-cavity coupling via $\varepsilon$ and the symmetric coupling
via $\varepsilon_{M}$.
