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IQI Weekly Seminar

Tuesday, May 1, 2018
3:00pm to 4:00pm
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Annenberg 107
Undecidability of the Spectral Gap in 1D
Johannes Bausch, University of Cambridge,

Abstract: In this work, we show that for local Hamiltonians in 1D with translationally invariant nearest neighbour interactions, deciding whether or not the system is gapped or gapless, is undecidable. In order to prove this, we need to go beyond the already-known 2D case, and replace a fractal Robinson tiling---only possible in more than one dimension---with a specific Hamiltonian that has a type of attractive force in its ground state. We further need to augment the quantum phase estimation algorithm to self-detect whether it succeded in its expansion.
Joint work with Toby Cubitt, Angelo Lucia and David Perez-Garcia.


















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