36,504 research outputs found
Algebraic and information-theoretic conditions for operator quantum error-correction
Operator quantum error-correction is a technique for robustly storing quantum
information in the presence of noise. It generalizes the standard theory of
quantum error-correction, and provides a unified framework for topics such as
quantum error-correction, decoherence-free subspaces, and noiseless subsystems.
This paper develops (a) easily applied algebraic and information-theoretic
conditions which characterize when operator quantum error-correction is
feasible; (b) a representation theorem for a class of noise processes which can
be corrected using operator quantum error-correction; and (c) generalizations
of the coherent information and quantum data processing inequality to the
setting of operator quantum error-correction.Comment: 4 page
Recovery in quantum error correction for general noise without measurement
It is known that one can do quantum error correction without syndrome
measurement, which is often done in operator quantum error correction (OQEC).
However, the physical realization could be challenging, especially when the
recovery process involves high-rank projection operators and a superoperator.
We use operator theory to improve OQEC so that the implementation can always be
done by unitary gates followed by a partial trace operation. Examples are given
to show that our error correction scheme outperforms the existing ones in
various scenarios.Comment: 10 page
Stabilizer Formalism for Operator Quantum Error Correction
Operator quantum error correction is a recently developed theory that
provides a generalized framework for active error correction and passive error
avoiding schemes. In this paper, we describe these codes in the stabilizer
formalism of standard quantum error correction theory. This is achieved by
adding a "gauge" group to the standard stabilizer definition of a code that
defines an equivalence class between encoded states. Gauge transformations
leave the encoded information unchanged; their effect is absorbed by virtual
gauge qubits that do not carry useful information. We illustrate the
construction by identifying a gauge symmetry in Shor's 9-qubit code that allows
us to remove 4 of its 8 stabilizer generators, leading to a simpler decoding
procedure and a wider class of logical operations without affecting its
essential properties. This opens the path to possible improvements of the error
threshold of fault-tolerant quantum computing.Comment: Corrected claim based on exhaustive searc
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