NLTS Hamiltonians from Good Quantum Codes
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.
Fields of Study & Subjects
Quantum Computing Algorithms and Architecture
Quantum and electron transport phenomena
Low-power high-performance VLSI design
Publication details
- Journal / source
- SIAM Journal on Computing
- Publisher
- Society for Industrial & Applied Mathematics (SIAM)
- Pages
- STOC23–397
- Publication date
- 4 September 2026
- Language
- EN