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Paper 1
NLTS Hamiltonians from classical LTCs
Zhiyang He, Chinmay Nirkhe
- Year
- 2022
- Journal
- arXiv preprint
- DOI
- arXiv:2210.02999
- arXiv
- 2210.02999
We provide a completely self-contained construction of a family of NLTS Hamiltonians [Freedman and Hastings, 2014] based on ideas from [Anshu, Breuckmann, and Nirkhe, 2022], [Cross, He, Natarajan, Szegedy, and Zhu, 2022] and [Eldar and Harrow, 2017]. Crucially, it does not require optimal-parameter quantum LDPC codes and can be built from simple classical LTCs such as the repetition code on an expander graph. Furthermore, it removes the constant-rate requirement from the construction of Anshu, Breuckmann, and Nirkhe.
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Topological Charge of Causality at a PT-Symmetric Exceptional Point
Kejun Liu
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2605.00117
- arXiv
- 2605.00117
Causality in linear response is conventionally treated as a binary property: a response function is either analytic in the upper half-plane or it is not. We show that in a PT-symmetric open dimer it instead carries a topological charge. As the gain-loss parameter crosses the exceptional point, a single pole of the reflection coefficient migrates into the upper half-plane, the Blaschke winding number jumps from 0 to 1, and standard Kramers-Kronig (KK) reconstruction acquires a Lorentzian residual fixed by the pole residue. The transition is sharp, protected by the codimension-one structure of the exceptional point, and directly measurable in a one-port reflection experiment. Most strikingly, the violation magnitude scales as Delta_KK ~ |gamma - gamma_c|^nu with nu ~ -1.08 in the single-port geometry: the breakdown of standard KK is strongest at threshold and weakens deeper in the broken phase. We derive the exact reflection coefficient, verify the residue-corrected dispersion relation, and propose a THz time-domain spectroscopy protocol that detects the topological charge through the residual itself.
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