A gap between the ground state and the first excited
As I understand it, a gap between the ground state and the first excited during quantum annealing affects the final results. So, how does the gap changes with a number of qubits? Are there estimations for it(exponentially, polynomially, etc)? For example, consider factoring from the demo. Doesn't gap change exponentially with increasing the size of the register?
Comments
It is not necessarily proportionate to the number of qubits, but rather depends on a number of factors.
At present there is no library to show this information, but this is of interest for future development.
It is also possible to calculate the gap size by solving the Schrodinger equation for the Hamiltonian:
https://docs.dwavesys.com/docs/latest/c_qpu_annealing.html#qa-implementation
This is only really feasible for system sizes up to about 30 qubits in general.
Good question. You might be interested to read this paper reporting results for a problem with a gap that has been engineered to be very small (much smaller than temperature T)
https://www.nature.com/articles/ncomms2920
A small gap is considered to be a fatal flaw in Adiabatic QC (AQC) theory where it is implicitly assumed that T=0 and you are completely uncoupled from an environment. In this case occupying any excited state is thought of as an "error". However in quantum annealing (QA) occupation of a set of states at low temperature is the principle of operation. If your goal is to find the global optimum and no other state then QA is not an oracle in and of itself. There is still work to be done in pre- and post-processing.
Thank everyone for answering
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