74 citations · 668 across the 48 of their papers we have counts for
54 papers
Relaxations and Exact Solutions to Quantum Max Cut via the Algebraic Structure of Swap Operators
Adam Bene Watts, Anirban Chowdhury, Aidan Epperly +2
The Quantum Max Cut (QMC) problem has emerged as a test-problem for designing approximation algorithms for local Hamiltonian problems. In this paper we attack this problem using th…
Matrix Extreme Points and Free extreme points of Free spectrahedra
Aidan Epperly, Eric Evert, J. William Helton +1
A spectrahedron is a convex set defined by a linear matrix inequality, i.e., the set of all such that \[ L_A(x) = I + A_1 x_1 + A_2 x_2 + \dots + A_g x_g \succ…
Satisfiability Phase Transtion for Random Quantum 3XOR Games
Adam Bene Watts, J. William Helton, Zehong Zhao
Recent results showed it was possible to determine if a modest size 3XOR game has a perfect quantum strategy. We build on these and give an explicit polynomial time algorithm which…
Noncommutative Nullstellensätze and Perfect Games
Adam Bene Watts, John William Helton, Igor Klep
The foundations of classical Algebraic Geometry and Real Algebraic Geometry are the Nullstellensatz and Positivstellensatz. Over the last two decades the basic analogous theorems f…
Synchronous Values of Games
J. William Helton, Hamoon Mousavi, Seyed Sajjad Nezhadi +2
We study synchronous values of games, especially synchronous games. It is known that a synchronous game has a perfect strategy if and only if it has a perfect synchronous strategy.…
3XOR Games with Perfect Commuting Operator Strategies Have Perfect Tensor Product Strategies and are Decidable in Polynomial Time
Adam Bene Watts, J. William Helton
We consider 3XOR games with perfect commuting operator strategies. Given any 3XOR game, we show existence of a perfect commuting operator strategy for the game can be decided in po…