Demonstration of Protection of a Superconducting Qubit from Energy Decay

Long-lived transitions occur naturally in atomic systems due to the abundance of selection rules inhibiting spontaneous emission. By contrast, transitions of superconducting artificial atoms typically have large dipoles, and hence their lifetimes are determined by the dissipative environment of a macroscopic electrical circuit. We designed a multilevel fluxonium artificial atom such that the qubit's transition dipole can be exponentially suppressed by flux tuning, while it continues to dispersively interact with a cavity mode by virtual transitions to the noncomputational states. Remarkably, energy decay time ${T}_{1}$ grew by 2 orders of magnitude, proportionally to the inverse square of the transition dipole, and exceeded the benchmark value of ${T}_{1}>2\text{ }\text{ }\mathrm{ms}$ (quality factor ${Q}_{1}>4\ifmmode\times\else\texttimes\fi{}{10}^{7}$) without showing signs of saturation. The dephasing time was limited by the first-order coupling to flux noise to about $4\text{ }\text{ }\ensuremath{\mu}\mathrm{s}$. Our circuit validated the general principle of hardware-level protection against bit-flip errors and can be upgraded to the $0\ensuremath{-}\ensuremath{\pi}$ circuit [P. Brooks, A. Kitaev, and J. Preskill, Phys. Rev. A 87, 052306 (2013)], adding protection against dephasing and certain gate errors.