  The remarkable discovery of Quantum Error Correction (QEC), which can
overcome the errors experienced by a bit of quantum information (qubit), was a
critical advance that gives hope for eventually realizing practical quantum
computers. In principle, a system that implements QEC can actually pass a
"break-even" point and preserve quantum information for longer than the
lifetime of its constituent parts. Reaching the break-even point, however, has
thus far remained an outstanding and challenging goal. Several previous works
have demonstrated elements of QEC in NMR, ions, nitrogen vacancy (NV) centers,
photons, and superconducting transmons. However, these works primarily
illustrate the signatures or scaling properties of QEC codes rather than test
the capacity of the system to extend the lifetime of quantum information over
time. Here we demonstrate a QEC system that reaches the break-even point by
suppressing the natural errors due to energy loss for a qubit logically encoded
in superpositions of coherent states, or cat states of a superconducting
resonator. Moreover, the experiment implements a full QEC protocol by using
real-time feedback to encode, monitor naturally occurring errors, decode, and
correct. As measured by full process tomography, the enhanced lifetime of the
encoded information is 320 microseconds without any post-selection. This is 20
times greater than that of the system's transmon, over twice as long as an
uncorrected logical encoding, and 10% longer than the highest quality element
of the system (the resonator's 0, 1 Fock states). Our results illustrate the
power of novel, hardware efficient qubit encodings over traditional QEC
schemes. Furthermore, they advance the field of experimental error correction
from confirming the basic concepts to exploring the metrics that drive system
performance and the challenges in implementing a fault-tolerant system.
