The Stabilizer Formalism and Quantum Error Correction Through the Lens of Tensors Part 2

David Gross
Universität zu Köln

Many-body systems of interest in quantum information are described by tensor products of hundreds or thousands of Hilbert spaces. The exponentially large dimension of such spaces makes some constructions extremely challenging. For example, in quantum error correction, one needs to find a large subspace of tensors such that no two elements of the space can be mapped onto each other by a "local error". The latter is described by a linear map that acts non-trivially only on a small number of tensor factors. (Didn't get this? No worries, I'll explain in detail). To address such challenges, quantum information has developed the stabilizer formalism. It allows one to describe a certain class of tensors using group-theoretical data. It turns out that this class strikes an attractive balance between (a) being small enough to allow for a concise description, while (b) being large enough to contain solutions to many challenges in quantum fault tolerance. The lectures will touch on the theory of error correction, connections to finite symplectic geometries, and the toric code (undoubtedly the coolest of all stabilizer codes).

Following advice attributed to Fulton by Joseph Landsberg, I won't use coordinates unless the problem holds a pickle to my head. No physics knowledge needed.

I'll give the tutorial on an electronic whiteboard which can be accessed

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