Circuit quantum electrodynamics (circuit QED) provides a means of studying the fundamental interaction between light and matter (quantum optics). As in the field of cavity quantum electrodynamics, a single photon within a single mode cavity coherently couples to a quantum object (atom). In contrast to cavity QED, the photon is stored in a one-dimensional on-chip resonator and the quantum object is no natural atom but an artificial one. These artificial atoms usually are mesoscopic devices which exhibit an atom-like energy spectrum. The field of circuit QED is a prominent example for quantum information processing and a promising candidate for future quantum computation.

In the late 2010s decade, experiments involving cQED in 3 dimensions have demonstrated deterministic gate teleportation and other operations on multiple qubits.

The resonant devices in the circuit QED architecture can be implemented using a superconducting LC resonator, a high purity cavity, or a superconducting coplanar waveguide microwave resonators, which are two-dimensional microwave analogues of the Fabry–Pérot interferometer, in which the capacitance and inductances are distributed. Coplanar waveguides consist of a signal carrying centerline flanked by two grounded planes. This planar structure is put on a dielectric substrate by a photolithographic process. Superconducting materials used are mostly aluminium (Al), niobium (Nb) and lately tantalum (Ta). Dielectrics typically used as substrates are either surface oxidized silicon (Si) or sapphire (Al₂O₃). The line impedance is given by the geometric properties, which are chosen to match the 50 ${\displaystyle \Omega }$ of the peripheric microwave equipment to avoid partial reflection of the signal. The electric field is basically confined between the center conductor and the ground planes resulting in a very small mode volume ${\displaystyle V_{m}}$ which gives rise to very high electric fields per photon ${\displaystyle E_{0}}$ (compared to three-dimensional cavities). Mathematically, the field ${\displaystyle E_{0}}$ can be found as

${\displaystyle E_{0}={\sqrt {\frac {\hbar \omega _{r}}{2\varepsilon _{0}V_{m}}}}}$,

where ${\displaystyle \hbar }$ is the reduced Planck constant, ${\displaystyle \omega _{r}}$ is the angular frequency, and ${\displaystyle \varepsilon _{0}}$ is the permittivity of free space.

One can distinguish between two different types of resonators: ${\displaystyle \lambda /2}$ and ${\displaystyle \lambda /4}$ resonators. Half-wavelength resonators are made by breaking the center conductor at two spots with the distance ${\displaystyle \ell }$. The resulting piece of center conductor is in this way capacitively coupled to the input and output and represents a resonator with ${\displaystyle E}$-field antinodes at its ends. Quarter-wavelength resonators are short pieces of a coplanar line, which are shorted to ground on one end and capacitively coupled to a feed line on the other. The resonance frequencies are given by

${\displaystyle \lambda /2:\quad \nu _{n}={\frac {c}{\sqrt {\varepsilon _{\text{eff}}}}}{\frac {n}{2\ell }}\quad (n=1,2,3,\ldots )\qquad \lambda /4:\quad \nu _{n}={\frac {c}{\sqrt {\varepsilon _{\text{eff}}}}}{\frac {2n+1}{4\ell }}\quad (n=0,1,2,\ldots )}$

with ${\displaystyle \varepsilon _{\text{eff}}}$ being the effective dielectric permittivity of the device.