Decoherence Correction by the Zeno Effect and Non-Holonomic Control

We show that multidimensional Zeno effect combined with non-holonomic control allows to efficiently protect quantum systems from decoherence by a method similar to classical coding. Contrary to the conventional approach, our method is applicable to arbitrary error-inducing Hamiltonians and general quantum systems. We also propose algorithms of finding encoding that approaches the Hamming upper bound along with methods of practical realizations of the encodings. Two new codes protecting 2 information qubits out of 7 and 4 information qubits out of 9 against a single error with arbitrarily small probability of failure are constructed as an example.