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Seminars»04.02.2019 - Burak Şahinoğlu : Error Detection at Low Energies

04.02.2019 - Burak Şahinoğlu : Error Detection at Low Energies

Error Detection at Low Energies

Burak Şahinoğlu
Institute for Quantum Information and Matter, Caltech, USA
04 February 2019, Monday, 14:40
Cavid Erginsoy Seminar Room, Physics Department, 3rd floor

Abstract: Motivated by the close relationship between error-correcting codes, topological order, holographic AdS/CFT duality and tensor networks, we initiate the study of approximate quantum error correcting codes in matrix product states (MPS). We first see that using open-boundary MPS to define boundary to bulk encoding maps only yields constant distance codes. These are degenerate ground spaces of gapped local Hamiltonians. Later, to get around this no-go result, we consider excited states of local gapped Hamiltonians, and low energy states of gapless Heisenberg-XXX model obtained by algebraic Bethe ansatz. All these codes protect against arbitrary alamos linear distance (not necessarily geometrically local) errors even though they are not permutation-invariant. This suggests that a wide range of naturally occurring many-body systems possess intrinsic error-correcting features. This is a joint work with Martina Geschwedtner, Robert König and Eugene Tang.