1.1k citations · 1.4k across the 8 of their papers we have counts for
4 papers · 1 filter
Random tensor theory: extending random matrix theory to random product states
Andris Ambainis, Aram W. Harrow, Matthew B. Hastings
We consider a problem in random matrix theory that is inspired by quantum information theory: determining the largest eigenvalue of a sum of p random product states in (C^d)^{otime…
Quantum Adiabatic Computation With a Constant Gap is Not Useful in One Dimension
M. B. Hastings
We show that it is possible to use a classical computer to efficiently simulate the adiabatic evolution of a quantum system in one dimension with a constant spectral gap, starting…
Entanglement vs. gap for one-dimensional spin systems
Daniel Gottesman, M. B. Hastings
We study the relationship between entanglement and spectral gap for local Hamiltonians in one dimension. The area law for a one-dimensional system states that for the ground state,…
An Area Law for One Dimensional Quantum Systems
M. B. Hastings
We prove an area law for the entanglement entropy in gapped one dimensional quantum systems. The bound on the entropy grows surprisingly rapidly with the correlation length; we dis…