Dispersive Readout
Dispersive readout measures a superconducting qubit without exciting it, by sensing a qubit-state-dependent shift in the frequency of a coupled resonator.
The Dispersive Regime
A qubit is coupled to a microwave resonator. When the qubit and resonator are far detuned compared with their coupling strength, they cannot exchange energy directly, but they still influence each other's frequency. In this dispersive regime the resonator frequency shifts by an amount that depends on the qubit state: the resonator sits at one frequency if the qubit is in the ground state and at a slightly different frequency if it is excited. The size of this shift is the dispersive shift, chi.
Reading the Shift
To read the qubit, a microwave probe tone is sent through the readout resonator and the transmitted or reflected signal is measured. Because the resonator frequency depends on the qubit state, the phase and amplitude of the returned tone carry the qubit's state. The probe is chosen weak and detuned enough that it does not itself flip the qubit, making the measurement quantum-nondemolition to good approximation.
- The dispersive shift chi scales as coupling squared divided by detuning, adjusted for anharmonicity.
- Larger chi gives faster readout but stronger measurement-induced dephasing when the qubit is idle.
- The probe photon number must stay well below the critical photon number to avoid exciting the qubit.
The Signal Chain
The tiny returned signal is amplified by a chain that begins, in the best systems, with a near-quantum-limited parametric amplifier at the coldest stage, followed by high-electron-mobility transistor amplifiers at higher stages, then room-temperature electronics that demodulate the I and Q quadratures. The integrated signal is thresholded to assign the qubit state, and the assignment fidelity depends on how far apart the two states' signals are relative to the noise.
Trade-offs
Dispersive readout is fast, high-fidelity, and gentle, but the same qubit-resonator coupling that enables it also opens a decay path, the Purcell effect, discussed in the Purcell-filter page. Designers balance readout speed against protection of qubit lifetime, using filters and careful choice of chi. Dispersive readout is the standard measurement technique for transmons and is widely adapted to spin qubits as well.