  Bosonic codes offer the possibility of storing quantum information in a
single infinite-dimensional physical system endowed with the capability to
correct errors, thereby reducing the number of physical components needed to
protect against noise. Much of the current efforts in bosonic codes are on
correcting only loss errors, while deferring the correction of phase errors --
perhaps actively suppressed -- to subsequent layers of encoding with standard
qubit codes. Rotationally symmetric bosonic codes, which include the well-known
cat and binomial codes, are capable of simultaneous correction of both loss and
phase errors, offer an alternate route that deals with arbitrary errors already
at the base layer. Grimsmo et al. [PRX 10, 011058 (2020)] analyzed the family
of such codes and proposed general error-correction circuits to correct both
loss and phase errors, reporting high noise thresholds in the presence of loss
and phase errors on the input, while the error-correction circuits remain
noiseless. A proper assessment, however, requires consideration of
circuit-level noise, where the individual circuit components can themselves be
faulty and introduce errors on the encoded information. Here, we carry out such
a circuit-level analysis, and assess the performance of the error-correction
circuits for the storage of information encoded with cat codes. While the
circuits of Grimsmo et al.~are formally fault tolerant even under circuit-level
noise, the thresholds are significantly worse. We show how, through
waiting-time optimization and the use of squeezing, we can restore the noise
requirements to ones plausibly achievable with near-term quantum hardware. Our
circuit-level analysis also reveals important features of the error-correction
circuits not visible in the earlier ideal-circuit perspective.
