t b a b a

CHAPTER 5
QUANTUM ERROR CORRECTION CODES
5.1 Quantum Errors
All physical systems, quantum or classical, are subject to errors. The main problems include
environmental noise, which is due to incomplete isolation of the system from the outside, and
control errors, which are caused by calibration errors and random fluctuations in operations.
However, a classical system may be stabilized to a very high degree, either by making the
ratio of system size to perturbation size very large (passive stabilization), or by continuously
monitoring the system and providing greatly enhanced ‘inertia’ against random fluctuation
be means of feedback control (active stabilization). When applied in the quantum regime,
the passive stabilization needs to build the system beyond a certain degree which is not
easy by any currently attemptable method. The active stabilization seems also impossible
from a quantum mechanics point of view since the feedback control involves dissipation, and
therefore is non-unitary.
Is active stabilization of a quantum bit possible? The answer is YES. The stabilization,
the quantum error correction, is based on the classical theory of error correction, which
provides a very powerful technique by which classical information can be transmitted without
errors through the medium of a noisy channel.
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