How to design reliable embeddings and/or annealing schedule?
Some of my larger embeddings (~200 qubits) do not anneal down to the ground state while some of my embeddings of comparable size wind up at the ground state configuration quite easily.
I've gathered from reading other forums that this discrepancy is due to properties of the gap between the ground state and the first excited state of the eigenspectrum of the embedding hamiltonian. Is this correct?
If so, how does one ensure that they are designing an embedding with the desired spectral properties?
Or, alternatively, I've also gathered that one can use the eigenspectrum of the embedding hamiltonian to determine an annealing schedule that will work for the embedding. Is this true?
If so, what methods can be used to determine the spectrum of an embedding hamiltonian and how is this information used to determine an annealer schedule?
Are there any other considerations for designing reliable annealer emebeddings that I'm unaware of?
P.S. Sorry if this question is all over the place, this seems like a deep topic and I'm still just trying to sort out the fundamentals.