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A quantum system interacts with its environment, if ever so slightly, nomatter how much care is put into isolating it. As a consequence, quantum bits(qubits) undergo errors, putting dauntingly difficult constraints on thehardware suitable for quantum computation. New strategies are emerging tocircumvent this problem by encoding a qubit non-locally across the phase spaceof a physical system. Since most sources of decoherence are due to localfluctuations, the foundational promise is to exponentially suppress errors byincreasing a measure of this non-locality. Prominent examples are topologicalqubits which delocalize quantum information over real space and where spatialextent measures non-locality. In this work, we encode a qubit in the fieldquadrature space of a superconducting resonator endowed with a specialmechanism that dissipates photons in pairs. This process pins down twocomputational states to separate locations in phase space. As we increase thisseparation, we measure an exponential decrease of the bit-flip rate while onlylinearly increasing the phase-flip rate. Since bit-flips are continuously andautonomously corrected at the single qubit level, only phase-flips are left tobe corrected via a one-dimensional quantum error correction code. Thisexponential scaling demonstrates that resonators with non-linear dissipationare promising building blocks for universal fault-tolerant quantum computationwith drastically reduced hardware overhead.

Exponential suppression of bit-flips in a qubit encoded in an oscillator