SIAM Journal on Computing· 2026Q1
NLTS Hamiltonians from Good Quantum Codes
- 2citations
- Q1SCImago
- 2026year
Short summary
Researchers prove the no low-energy trivial state (NLTS) conjecture by constructing NLTS local Hamiltonians from constant-rate and linear-distance qLDPC quantum error-correcting codes.
AI-generated from the title and abstract; the full text is not read.
Key points
- The no low-energy trivial state (NLTS) conjecture is proven.
- NLTS local Hamiltonians are constructed from quantum error-correcting codes.
- Specifically, constant-rate and linear-distance qLDPC codes yield NLTS Hamiltonians.
- This provides a constructive proof for the existence of such Hamiltonians.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. SIAM Journal on Computing, 2026 · DOI ↗
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Field: Artificial Intelligence
Artificial IntelligenceComputer Science