Purcell filter
To find out what state a qubit is in, engineers attach a small readout resonator to it and bounce a microwave signal off it. But that readout line is also an open door: the qubit can leak its energy out through the same path and relax before you even finish the measurement. This unwanted leak is called Purcell decay, and it shortens the qubit's lifetime (T1). A Purcell filter is a tiny circuit placed between the qubit and the outside world that acts like a smart gate, letting the readout signal pass while turning the qubit away.
The trick is frequency. The readout photons and the qubit live at different microwave frequencies, usually a few hundred megahertz to a gigahertz apart. A Purcell filter is built to be transparent at the readout frequency, so measurement photons flow out fast and the result arrives quickly, but to look like a mirror at the qubit frequency, so the qubit's energy is reflected back instead of escaping. Common designs use an extra resonator, a notch, or a short transmission-line stub tuned to the band you want to block.
The payoff is that you get fast readout and a long-lived qubit at the same time, two goals that normally fight each other. The catch is that the filter only protects a narrow band, so on a chip with many qubits at crowded, slightly different frequencies, one filter cannot shield them all perfectly. Designing and tuning these filters, and fitting them into the limited space and wiring of a real chip, is ongoing engineering work, not a solved problem.
The qubit's Purcell decay rate grows with the resonator's leak rate kappa and the coupling g, and shrinks with the detuning Delta between qubit and resonator; a filter cuts kappa seen at the qubit frequency without slowing readout.
A Purcell filter does not improve the qubit itself; it just stops the readout wiring from draining it, so the benefit only holds in the frequency band the filter was tuned for.