Session S16 - Quantum symmetries

No date set.

Real quantum error correction

Diego Arturo Romero Fonseca

Universidad de los Andes, Colombia   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The poster aims to show part of the theory developed for the correction of errors in quantum codes, showing first the necessary and sufficient conditions that make a code error-correcting. Later we move to some of the construction of subspaces of n-cubit that can be protected against certain sets of errors; to arrive at these results we will provide the set of error operators with a symplectic space structure. We will describe its isotropic subspaces, group of symplectic transformations, among other characteristics.

Finally, since errors on a quantum codes are the action of complex unitary matrices, we will show how the results change when we consider only real errors. In this case, the symplectic structure will be replaced by a quadratic space and Its orthogonal group will take the role of the symplectic group. These changes result in a theory of great harmony where the real errors do not need to pass into the complex world to be corrected.

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