Purcell Filters
A Purcell filter blocks the qubit-frequency decay channel opened by the readout resonator, protecting qubit lifetime without slowing readout.
The Purcell Problem
Dispersive readout couples a qubit to a resonator, and that resonator is deliberately coupled to a lossy output line so measurement signals can escape. But the same path lets the qubit lose energy: through its coupling to the resonator, the qubit can decay into the output line at the qubit frequency. This Purcell decay sets an upper bound on the qubit lifetime that gets worse as the coupling is made stronger for faster readout.
The Filter Solution
A Purcell filter is a frequency-selective element placed between the readout resonator and the output line. It is engineered to present a high impedance, effectively a block, at the qubit frequency, while presenting a low impedance, an open door, at the readout-resonator frequency. Measurement photons at the resonator frequency pass freely, but qubit-frequency energy sees a mismatch and cannot escape.
- Transparent at the readout frequency, so readout speed is preserved.
- Reflective at the qubit frequency, so Purcell decay is suppressed.
- Implemented as a bandpass or a notch, on chip or as a separate element.
Design Forms
The simplest form is a bandpass filter centered on the readout band. A notch, or band-stop, filter tuned to the qubit frequency achieves the same protection differently. On-chip transmission-line resonators, lumped-element sections, or dedicated filter cavities are all used. The filter must be broad enough to pass every multiplexed readout tone yet sharp enough to reject the nearby qubit frequencies.
Why It Matters
Purcell filtering breaks the otherwise unavoidable trade between readout speed and qubit lifetime. Without it, designers would have to weaken the readout coupling and accept slower measurement to protect coherence. With it, both fast, high-fidelity readout and long qubit lifetime are achievable at once. Purcell filters are now standard in high-performance superconducting processors and are part of the coherence budget of any well-designed device.