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.
Original language | Undefined/Unknown |
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DOIs | |
Publication status | Published - 27 Jun 2022 |
Bibliographical note
12 pages, 1 figure, added funding information and discussionsKeywords
- quant-ph
- cond-mat.stat-mech
- cs.CC