1.1k citations · 1.4k across the 8 of their papers we have counts for
8 papers
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,…
Inference from Matrix Products: A Heuristic Spin Glass Algorithm
M. B. Hastings
We present an algorithm for finding ground states of two dimensional spin glass systems based on ideas from matrix product states in quantum information theory. The algorithm works…
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…
Locality in Quantum and Markov Dynamics on Lattices and Networks
M. B. Hastings
We consider gapped systems governed by either quantum or Markov dynamics, with the low-lying states below the gap being approximately degenerate. For a broad class of dynamics, we…