Conjectured Bounds for 2-Local Hamiltonians via Token Graphs
The authors connect spectral properties of 'token graphs' derived from a graph G to the maximum energy of Quantum MaxCut, XY, and EPR Hamiltonians. They propose conjectures about these spectral radii based on graph properties, which lead to new combinatorial bounds. These bounds allow for tighter analysis and improved approximation ratios for algorithms solving these quantum problems.