I stumbled upon a pretty old paper from 2003 by C. Ahn, H.M. Wiseman and G.J. Milburn. They use quantum control with feedback Hamiltonian to perform error correction. The paper proposes to encode $n-1$ logical qubits into $n$ physical qubits. The core assumptions are as stated in the paper:
This simplification is possible because, in this paper we assume that the errors are detected. That is, the experimenter knows precisely what sort of error has occurred because the environment that caused the errors is being continuously measured. Since the environment is thus acting as part of the measurement apparatus, the errors it produces could be considered measurement-induced errors.
I would like to know:
How practical are these assumptions? Specifically, they state that the errors are detected because the environment is continuously measured. Is this something that can always be done?
Encoding $n-1$ logical qubits into $n$ physical qubits is pretty good; why these kinds of quantum control techniques are not as dominant as quantum error correction with codes?
