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Preprint Sep 2026

Good Quantum Locally Testable Codes from Product Expansion

We construct quantum locally testable codes (LTCs) with constant rate, distance, soundness and locality under a variant of a product expansion conjecture of Bafna and Vyas about Reed-Solomon codes. In particular, we use the high-dimensional expansion framework of Dinur, Lin and Vidick for constructing quantum LTCs, ins...

Mitali Bafna, An-Qi Li, Q. T. Nguyen · 4 citations · ⚡2
Preprint Sep 2026

Rank-1-perturbed trickledown theorems: Mixing time of Glauber dynamics for the Sherrington-Kirkpatrick model up to $\beta\leq \frac{1}{2}+\varepsilon$

We introduce a new family of trickledown theorems, a.k.a., local to global technique to bound the spectral gap of the Glauber dynamics for multi-state spin systems. In this technique instead of upper-bounding the influence matrix of a link of co-dimension 2 by $\lambda I$ (where $\lambda$ is the second eigenvalue of th...

Mathews Boban, An-Qi Li, Shayan Oveis Gharan · 0 citations

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