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arXiv · 2206.13228

NLTS Hamiltonians from good quantum codes

Anurag Anshu·Nikolas P. Breuckmann·Chinmay Nirkhe
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Abstract

The NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings [2014] posits that there exist families of Hamiltonians with all low energy states of non-trivial complexity (with complexity measured by the quantum circuit depth preparing the state). We prove this conjecture by showing that the recently discovered families of constant-rate and linear-distance QLDPC codes correspond to NLTS local Hamiltonians.

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Anurag Anshu, Nikolas P. Breuckmann, Chinmay Nirkhe. 2022-06-27. NLTS Hamiltonians from good quantum codes. https://doi.org/10.1145/3564246.3585114

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