  Autonomous quantum error correction has gained considerable attention to
avoid complicated measurements and feedback. Despite its simplicity compared
with the conventional measurement-based quantum error correction, it is still a
far from practical technique because of significant hardware overhead. We
propose an autonomous quantum error correction scheme for a rotational
symmetric bosonic code in a four-photon Kerr parametric oscillator. Our scheme
is the simplest possible error correction scheme that can surpass the
break-even point -- it requires only a single continuous microwave tone. We
also introduce an unconditional reset scheme that requires one more continuous
microwave tone in addition to that for the error correction. The key properties
underlying this simplicity are protected quasienergy states of a four-photon
Kerr parametric oscillator and the degeneracy in its quasienergy level
structure. These properties eliminate the need for state-by-state correction in
the Fock basis. Our schemes greatly reduce the complexity of autonomous quantum
error correction and thus may accelerate the use of the bosonic code for
practical quantum computation.
