We construct a new explicit family of good quantum low-density parity-check codes which
additionally have linear time decoders. Our codes are based on a three-term chain (2 m× m) …

Two recent and seemingly-unrelated techniques for proving mixing bounds for Markov
chains are:(i) the framework of Spectral Independence, introduced by Anari, Liu and Oveis …

We prove an optimal mixing time bound for the single-site update Markov chain known as
the Glauber dynamics or Gibbs sampling in a variety of settings. Our work presents an …

We say a probability distribution μ is spectrally independent if an associated pairwise
influence matrix has a bounded largest eigenvalue for the distribution and all of its …

For general antiferromagnetic 2-spin systems, including the hardcore model on weighted
independent sets and the antiferromagnetic Ising model, there is an for the partition function …

We introduce a notion called entropic independence that is an entropic analog of spectral
notions of high-dimensional expansion. Informally, entropic independence of a background …

We extend the notion of spectral independence (introduced by Anari, Liu, and Oveis
Gharan) from the Boolean domain to general discrete domains. This property characterises …

The spectral independence approach of Anari et al.(2020) utilized recent results on high-
dimensional expanders of Alev and Lau (2020) and established rapid mixing of the Glauber …

We show fully polynomial time randomized approximation schemes (FPRAS) for counting
matchings of a given size, or more generally sampling/counting monomer-dimer systems in …

A d-dimensional simplicial complex X is said to support a direct product tester if any locally
consistent function defined on its k-faces (where k≪ d) necessarily come from a function …