Passive two-photon dissipation for bit-flip error correction of a cat code

Bosonic codes offer a resource-efficient method to quantum error correction. Of particular

interest, autonomous correction was successfully demonstrated for cat codes, where the logical

|0〉 and |1〉 states are coherent states of opposite amplitudes |α〉 and | − α〉 in a superconducting

resonator with single-photon loss rates κ1 as low as possible. They correct bit-flip errors by either

using the non-linearity of the oscillator or parametrically pumping couplers to produce two-photon

dissipation at a rate κ2. The bit-flip time increases exponentially with |α|2 while the phase-flip rate

only increases linearly with |α|2.

In this work, we introduce and experimentally demonstrate a new superconducting circuit designed

to correct for bit-flip errors of cat codes. Crucially, the two-photon dissipation does not require any

pump, so that a single drive is required to stabilize the qubit manifold. This is obtained by non-

linearly coupling the cat qubit to a buffer mode that resonates at twice the frequency of the cat qubit.

We experimentally demonstrate unprecedented ratios κ2/κ1, so that bit flip times well over a ms can

be reached with a few photons only. We also demonstrate quantum gates on this corrected cat qubit.

This work was partly supported by the grant ANR-19-QUAN-0006.