Quantum theory of a bandpass Purcell filter for qubit readout

TL;DR

This paper analyzes a bandpass Purcell filter that significantly reduces qubit energy relaxation in superconducting qubits, enhancing readout fidelity without sacrificing measurement speed, and demonstrates its effectiveness through semiclassical and quantum analyses.

Contribution

It provides a detailed semiclassical and quantum analysis of a bandpass Purcell filter, showing its ability to suppress qubit relaxation while maintaining measurement performance.

Findings

Suppresses qubit relaxation rate by up to two orders of magnitude

Maintains measurement rate despite filtering

Further relaxation reduction with increased microwave drive

Abstract

The readout fidelity of superconducting transmon and Xmon qubits is partially limited by the qubit energy relaxation through the resonator into the transmission line, which is also known as the Purcell effect. One way to suppress this energy relaxation is to employ a filter which impedes microwave propagation at the qubit frequency. We present semiclassical and quantum analyses for the bandpass Purcell filter realized by E.\ Jeffrey \textit{et al}.\ [Phys.\ Rev.\ Lett.\ 112, 190504 (2014)]. For typical experimental parameters, the bandpass filter suppresses the qubit relaxation rate by up to two orders of magnitude while maintaining the same measurement rate. We also show that in the presence of a microwave drive the qubit relaxation rate further decreases with increasing drive strength.