6 papers · 1 filter
Optimal Sparsifiers for Minkowski Sums and Sums of Seminorms
Arpon Basu, Joshua Brakensiek, Yeyuan Chen +3
We extend the recent work of Reis and Rothvoss on sparsifying sums of norms to the more general task of sparsifying (Minkowski) sums of centrally symmetric, convex sets. A…
Sharp Bounds on Ground State Energy of the SYK Model
Arpon Basu, Pravesh K. Kothari, Siddhant Midha
We study the Sachdev-Ye-Kitaev (SYK) Hamiltonian on Majorana modes with -body interactions, and prove that $\mathbb{E}\|H_{\operatorname{SYK}}\|_{\o…
Optimal Sparsifiers for Abelian Cayley Graphs
Arpon Basu, Pravesh K. Kothari, Raghu Meka +1
We prove that for every Cayley graph over any finite abelian group , there is a weighted Cayley graph with generators that is a spectral sparsifier f…
Quantum Cut Sparsifiers
Arpon Basu, Joshua Brakensiek, Pravesh K. Kothari +1
In this paper, we continue a line of research initiated by Basu, Brakensiek, and Putterman [2026] studying the sparsifiability of Hamiltonians. We focus particularly on the sparsif…
Sharp Bounds on the Eigenvalues of Kikuchi Graphs and Applications to Quantum Max Cut
Ainesh Bakshi, Arpon Basu, Pravesh Kothari +1
We prove that the maximum eigenvalue of the (both signed and unsigned) Laplacian of level Kikuchi graph of any graph with edges is at most . This confirms four rec…
Many Hamiltonians Are Sparsifiable
Arpon Basu, Joshua Brakensiek, Aaron Putterman
We study the problem of Hamiltonian sparsification: given a parameter and an -qubit Hamiltonian which is the sum of -local positive semi-definite…