21 citations · 210 across the 36 of their papers we have counts for
3 papers · 1 filter
Dimension of Tensor Network varieties
Alessandra Bernardi, Claudia De Lazzari, Fulvio Gesmundo
The tensor network variety is a variety of tensors associated to a graph and a set of positive integer weights on its edges, called bond dimensions. We determine an upper bound on…
Optimization at the boundary of the tensor network variety
Matthias Christandl, Fulvio Gesmundo, Daniel Stilck Franca +1
Tensor network states form a variational ansatz class widely used, both analytically and numerically, in the study of quantum many-body systems. It is known that if the underlying…
Matrix product states and the quantum max-flow/min-cut conjectures
Fulvio Gesmundo, J. M. Landsberg, Michael Walter
In this note we discuss the geometry of matrix product states with periodic boundary conditions and provide three infinite sequences of examples where the quantum max-flow is stric…