  Noise and errors are inevitable parts of any practical implementation of a
quantum computer. As a result, large-scale quantum computation will require
ways to detect and correct errors on quantum information. Here, we present such
a quantum error correcting scheme for correcting the dominant error sources,
phase decoherence and energy relaxation, in qubit architectures, using a hybrid
approach combining autonomous correction based on engineered dissipation with
traditional measurement-based quantum error correction. Using numerical
simulations with realistic device parameters for superconducting circuits, we
show that this scheme can achieve a 5- to 10-fold increase in storage-time
while using only six qubits for the encoding and two ancillary qubits for the
operation of the autonomous part of the scheme, providing a potentially large
reduction of qubit overhead compared to typical measurement-based error
correction schemes. Furthermore, the scheme relies on standard interactions and
qubit driving available in most major quantum computing platforms, making it
implementable in a wide range of architectures.
