  A quantum system interacts with its environment, if ever so slightly, no
matter how much care is put into isolating it. As a consequence, quantum bits
(qubits) undergo errors, putting dauntingly difficult constraints on the
hardware suitable for quantum computation. New strategies are emerging to
circumvent this problem by encoding a qubit non-locally across the phase space
of a physical system. Since most sources of decoherence are due to local
fluctuations, the foundational promise is to exponentially suppress errors by
increasing a measure of this non-locality. Prominent examples are topological
qubits which delocalize quantum information over real space and where spatial
extent measures non-locality. In this work, we encode a qubit in the field
quadrature space of a superconducting resonator endowed with a special
mechanism that dissipates photons in pairs. This process pins down two
computational states to separate locations in phase space. As we increase this
separation, we measure an exponential decrease of the bit-flip rate while only
linearly increasing the phase-flip rate. Since bit-flips are continuously and
autonomously corrected at the single qubit level, only phase-flips are left to
be corrected via a one-dimensional quantum error correction code. This
exponential scaling demonstrates that resonators with non-linear dissipation
are promising building blocks for universal fault-tolerant quantum computation
with drastically reduced hardware overhead.
