NLTS Hamiltonians from Good Quantum Codes
Abstract. The no low-energy trivial state (NLTS) conjecture of Freedman and Hastings [ Quantum Inf. Comput., 14 (2014), pp. 144–180] posits that there exist families of Hamiltonians with all low energy states of nontrivial complexity (with complexity measured by the quantum circuit depth preparing the state). We prove this conjecture by showing that families of constant-rate and linear-distance qLDPC codes correspond to NLTS local Hamiltonians.
Authors
- Nikolas P. Breuckmann (ORCID: https://orcid.org/0000-0002-7211-5515)
- Chinmay Nirkhe (ORCID: https://orcid.org/0000-0002-5808-4994)
Institutions
- Harvard University (US)
- University of Washington (US)
- University of Bristol (GB)
Publication Details
- Journal
- SIAM Journal on Computing
- Published
- 2026-09-04
- DOI
- https://doi.org/10.1137/23m1608045
- Citations
- 2
- Primary Topic
- Quantum Computing Algorithms and Architecture
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Harvard University
- University College London
- Simons Institute for the Theory of Computing, University of California Berkeley
- Engineering and Physical Sciences Research Council