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Some of my larger annealer embeddings (~200 qubits) don't anneal down to the ground state while some of them do very easily.

Are there established guidelines for designing annealer embeddings to ensure that ground state configurations can be easily found? If so, where can this information be found?

If not, is addressing this issue more a matter of properly setting annealer parameters/annealing schedule. What are some good papers with information on this?

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  • $\begingroup$ Do you have estimates of the gap of $H_t$ as you adiabat from $H_0$ to $H_1$ $\endgroup$ – AHusain Jan 11 at 3:31
  • $\begingroup$ I don't know what this is. What is 'the gap'? Or, Where do I find out about it? $\endgroup$ – Malcolm Regan Jan 11 at 3:33
  • $\begingroup$ Is this in reference to the 'band structure' of the embedding? If i did have an estimate of the gap, how would i use it? $\endgroup$ – Malcolm Regan Jan 11 at 3:40
  • $\begingroup$ Meaning the energy of the next lowest eigenstate relative to the ground state as H_t varies. Tells you if adiabicity still holds. $\endgroup$ – AHusain Jan 11 at 3:43
  • $\begingroup$ Ah i see so it may be a question of whether the embedding is even valid per the adiabatic theorem? I will read more about this thank you. $\endgroup$ – Malcolm Regan Jan 11 at 4:08
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On parameter setting, check our work: https://journals.aps.org/prx/abstract/10.1103/PhysRevX.5.031040 (Basically you want to make sure that the chains representing the logical qubit have a phase transition synchronized with the minimum gap). But in general this is a hard problem, and precision issues connected to the embedding characteristics are probably the dominant effect that influences performance.

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