Dissipative encoding of quantum information
(pp737-770)
Giacomo
Baggio, Francesco Ticozzi, Peter D. Johnson, and Lorenza Viola
doi:
https://doi.org/10.26421/QIC21.9-10-2
Abstracts:
We formalize the problem of
dissipative
quantum encoding, and explore the advantages of using
Markovian
evolution to prepare a quantum code in the desired logical space, with
emphasis on discrete-time dynamics and the possibility of exact
finite-time convergence. In particular, we investigate robustness of the
encoding dynamics and their ability to tolerate initialization errors,
thanks to the existence of non-trivial basins of attraction. As a
key application, we show that for stabilizer quantum codes on
qubits,
a finite-time dissipative
encoder may always be constructed, by using at most a number of quantum
maps determined by the number of stabilizer generators. We find that
even in situations where the target code lacks gauge degrees of freedom
in its subsystem form, dissipative
encoders afford nontrivial robustness against initialization errors,
thus overcoming a limitation of purely unitary encoding procedures. Our
general results are illustrated in a number of relevant examples,
including
Kitaev's
toric
code.
Key words:
Quantum encoding,
engineered dissipation, stabilizer codes |