Coherence limitations of a Fourier-engineered $\cos(2\varphi)$ transmon qubit

TL;DR

This paper experimentally realizes a Fourier-engineered $ ext{cos}(2 ext{phi})$ superconducting qubit, revealing coherence limitations due to residual flux noise affecting interference-based protection mechanisms.

Contribution

It demonstrates a $ ext{cos}(2 ext{phi})$ qubit with suppressed odd harmonics and investigates its coherence limitations caused by flux noise.

Findings

Good agreement between measured spectrum and theoretical model.

Qubit lifetime at flux symmetry point is limited by $1/f$ flux noise.

Residual first harmonic fluctuations cause sensitivity to flux noise.

Abstract

Intrinsically protected superconducting qubits are a promising route toward enhancing coherence times and advancing hardware towards applications in quantum computing. The $\cos(2\varphi)$ qubit achieves protection against qubit relaxation by allowing only the coherent tunneling of pairs of Cooper pairs, resulting in Cooper-pair parity symmetry and thereby suppressing charge-induced errors. In this work, we experimentally realize a $\cos(2\varphi)$ qubit by Fourier engineering the energy-phase relation in a multi-junction superconducting circuit. Using an interference-based architecture, we are able to suppress the odd harmonics of an effective qubit potential and we observe good agreement between the measured transition spectrum and the effective theoretical model. We further investigate the energy relaxation time as a function of external flux and find that the qubit lifetime at the flux symmetry point is limited by $1/f$ flux noise. This strong sensitivity arises from residual fluctuations in the first harmonic, which possesses a large prefactor despite being nominally canceled. In contrast, a fluxonium qubit with a similar energy spectrum and noise amplitude is less affected by flux noise, highlighting a key challenge for interference-based protection schemes.