NLTS Hamiltonians from good quantum codes

Anurag Anshu, Nikolas P. Breuckmann, Chinmay Nirkhe

Research output: Working paperPreprint

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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 languageUndefined/Unknown
Publication statusPublished - 27 Jun 2022

Bibliographical note

12 pages, 1 figure, added funding information and discussions


  • quant-ph
  • cond-mat.stat-mech
  • cs.CC

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