Transmon qubits are superconducting qubits built from a Josephson junction shunted by a large capacitor. The capacitor suppresses the circuit's sensitivity to charge noise, which was the main limitation of the earlier Cooper pair box design. Transmons are the workhorse of most large-scale superconducting quantum processors today, including those from IBM and Google.

The circuit behaves like a nonlinear LC oscillator. The Josephson junction supplies the nonlinear inductance, and the shunt capacitance sets the charging energy. The two lowest energy levels of this anharmonic oscillator are used as $\lvert 0 \rangle$ and $\lvert 1 \rangle$.

$$H = 4 E_C (n - n_g)^2 - E_J \cos\varphi$$

Here $E_C$ is the charging energy, $E_J$ is the Josephson energy, $n$ is the Cooper pair number operator, $n_g$ is an offset charge, and $\varphi$ is the superconducting phase across the junction. The transmon regime is defined by $E_J / E_C \gg 1$, which flattens the energy bands against $n_g$ and makes the qubit frequency nearly immune to charge fluctuations, at the cost of a smaller but still useful anharmonicity.

Qubit state is manipulated with microwave pulses at the qubit's transition frequency, typically in the 4-8 GHz range, delivered through a capacitively coupled drive line. Readout is done dispersively: the qubit is coupled to a microwave resonator whose frequency shifts depending on the qubit state, and that shift is measured by probing the resonator.

• Gate operations: microwave pulses shaped to minimize leakage to higher levels (e.g. DRAG pulses)
• Two-qubit gates: tunable couplers or cross-resonance drives between neighboring transmons
• Readout: dispersive shift of a coupled resonator, read out via a parametric amplifier

Coherence times for transmons are typically in the tens to hundreds of microseconds, limited mostly by dielectric loss in the materials surrounding the junction.