20 citations · 43 across the 10 of their papers we have counts for
11 papers
A very brief introduction to quantum computing and quantum information theory for mathematicians
J. M. Landsberg
This is a very brief introduction to quantum computing and quantum information theory, primarily aimed at geometers. Beyond basic definitions and examples, I emphasize aspects of i…
Polynomials and the exponent of matrix multiplication
Luca Chiantini, Jonathan D. Hauenstein, Christian Ikenmeyer +2
We define tensors, corresponding to cubic polynomials, which have the same exponent as the matrix multiplication tensor. In particular, we study the symmetrized matrix multipli…
On the complexity of the permanent in various computational models
Christian Ikenmeyer, J. M. Landsberg
We answer a question in [Landsberg, Ressayre, 2015], showing the regular determinantal complexity of the determinant det_m is O(m^3). We answer questions in, and generalize results…
On the geometry of border rank algorithms for n x 2 by 2 x 2 matrix multiplication
J. M. Landsberg, Nicholas Ryder
We make an in-depth study of the known border rank (i.e. approximate) algorithms for the matrix multiplication tensor encoding the multiplication of an n x 2 matrix by a 2 x 2 matr…
Permanent v. determinant: an exponential lower bound assumingsymmetry and a potential path towards Valiant's conjecture
Joseph M. Landsberg, Nicolas Ressayre
We initiate a study of determinantal representations with symmetry. We show that Grenet's determinantal representation for the permanent is optimal among determinantal representati…
Connections between conjectures of Alon-Tarsi, Hadamard-Howe, and integrals over the special unitary group
Shrawan Kumar, J. M. Landsberg
We show the Alon-Tarsi conjecture on Latin squares is equivalent to a very special case of a conjecture made independently by Hadamard and Howe, and to the non-vanishing of some in…