48 citations · 107 across the 7 of their papers we have counts for
7 papers
Improving Perturbation Theory with the Sum-of-squares II: Large Density-Density Terms
Matthew B. Hastings
In Ref. 1, a method was given for self-consistently generating sum-of-squares decompositions of quartic fermionic Hamiltonians. Perturbation theory was used to generate a useful ch…
Limitations and Separations in the Quantum Sum-of-squares, and the Quantum Knapsack Problem
M. B. Hastings
We answer two questions regarding the sum-of-squares for the SYK model left open in Ref. 1, both of which are related to graphs. First (a "limitation"), we show that a fragment of…
Field Theory and The Sum-of-Squares for Quantum Systems
M. B. Hastings
This is a collection of various result and notes, addressing the sum-of-squares hierarchy for spin and fermion systems using some ideas from quantum field theory, including higher…
Classical and Quantum Bounded Depth Approximation Algorithms
M. B. Hastings
We consider some classical and quantum approximate optimization algorithms with bounded depth. First, we define a class of "local" classical optimization algorithms and show that a…
Duality in Quantum Quenches and Classical Approximation Algorithms: Pretty Good or Very Bad
M. B. Hastings
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solut…
The Short Path Algorithm Applied to a Toy Model
M. B. Hastings
We numerically investigate the performance of the short path optimization algorithm on a toy problem, with the potential chosen to depend only on the total Hamming weight to allow…
Light Cone Matrix Product
M. B. Hastings
We show how to combine the light-cone and matrix product algorithms to simulate quantum systems far from equilibrium for long times. For the case of the XXZ spin chain at ,…