608 citations · 2k across the 55 of their papers we have counts for
55 papers
Spectral geometry of Khovanov Laplacians
Jernej Grlj, Aaron D. Lauda
For an oriented link diagram , the Khovanov cochain complex carries a canonical Hermitian inner product that defines a combinatorial Hodge Laplacian. Its kernel is naturally iso…
Analytic Torsion and Spectral Gap Capture Persistent-Laplacian Performance
Jernej Grlj, Aaron D. Lauda
While persistent Laplacians (PL) offer a richer geometric representation of data than persistent homology, utilizing their full eigenspectrum for learning tasks is often hampered b…
Robust Universal Braiding with Non-semisimple Ising Anyons
Filippo Iulianelli, Sung Kim, Joshua Sussan +1
Non-semisimple extensions of the Ising anyon model developed in our previous work enable universal topological quantum computation via braiding alone, overcoming the Clifford-only…
Action of the Witt algebra on categorified quantum groups
Jernej Grlj, Aaron D. Lauda
We construct an action of the positive Witt algebra on the categorified quantum group associated to a simply-laced Lie algebra. In the type A case, we show that this action induces…
A quantum algorithm for Khovanov homology
Alexander Schmidhuber, Michele Reilly, Paolo Zanardi +2
Khovanov homology is a topological knot invariant that categorifies the Jones polynomial, recognizes the unknot, and is conjectured to appear as an observable in supersymmetri…
Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory
Filippo Iulianelli, Sung Kim, Joshua Sussan +1
We propose a framework for topological quantum computation using newly discovered non-semisimple analogs of topological quantum field theories in 2+1 dimensions. These enhanced the…