4 papers
Short proof of a spectral Chernoff bound for local Hamiltonians
Nilin Abrahamsen
We give a simple proof of a Chernoff bound for the spectrum of a -local Hamiltonian based on Weyl's inequalities. The complexity of estimating the spectrum's -th quantile…
Sharp implications of AGSPs for degenerate ground spaces
Nilin Abrahamsen
We generalize the `off-the-rack' AGSPentanglement bound implication of [Arad, Landau, and Vazirani '12] from unique ground states to degenerate ground spaces. Our cond…
A polynomial-time algorithm for ground states of spin trees
Nilin Abrahamsen
We prove that the ground states of a local Hamiltonian satisfy an area law and can be computed in polynomial time when the interaction graph is a tree with discrete fractal dimensi…
Sparse Gaussian ICA
Nilin Abrahamsen, Philippe Rigollet
Independent component analysis (ICA) is a cornerstone of modern data analysis. Its goal is to recover a latent random vector S with independent components from samples of X=AS wher…