Why is stoquastic hamiltonian sometimes mentioned together with quantum annealing?

Definition

"Stoquastic" Hamiltonians are sign-problem free Hamiltonians.

Background:

On attending a meeting last year, I heard the term stoquastic hamiltonian in a talk and noticed the term stoquastic hamiltonian was mentioned in a poster of quantum annealing. I myself work on a different area so I did not pay enough attention to the name of the talk and poster. So on two occasions I noticed the two terms stoquastic hamiltonian and quantum annealing were mentioned together. I also search the two terms together in google search engine and they do indeed appear together. This seems interesting to me at least.

Research effort:

1. 
   

   My initial guess is that by the use of stoquastic hamiltonian, the first order quantum phase transition during the minimum gap is eliminated (since the first order phase quantum transition is a difficulty in quantum annealing). However I cannot find evidence supporting this.

   
   


2. 
   

   The ability to perform quantum monte carlo with it. Reference of this reason: Monte Carlo simulation of stoquastic hamiltonians.

   
   
   


3. 
   

   On The Complexity of Stoquastic Local Hamiltonian Problems, Stoquastic Hamiltonian is common. Spin-1/2 models, the well-studied ferromagnetic Heisenberg models and the quantum transverse Ising model have it. So I think since they are sometimes used in quantum annealing, Stoquastic Hamiltonian is mentioned. Stoquastic Hamiltonian is common, while non-stoquastic Hamiltonian is uncommon. Therefore actually doing quantum annealing on non-stoquastic Hamiltonian would be interesting, like Non-Stoquastic Hamiltonians and Quantum Annealing of Ising Spin Glass. This is my another hypothesis why "Stoquastic" is stressed.