Simultaneous stoquasticity

Stoquastic Hamiltonians play a role in the computational complexity of local Hamiltonian problem as well study classical simulability. In particular, stoquastic can be straightforwardly simulated using Monte Carlo techniques. We address question whether two or more may made simultaneously via unitary transformation. This has important implications for simulating quantum annealing where advantage is related to stoquasticity involved anneal. find that almost all problems no such exists and show determining existence equivalent identifying if there solution system polynomial (in)equalities matrix elements initial transformed Hamiltonians. Solving equations NP-hard. highlight geometric understanding this terms collection generalized Bloch vectors.