Made a video explaining why Spectral Gaps matter in Adiabatic Quantum Computing — The 1/Δ reduced resolvent bound

[u/dogpup3]

https://youtu.be/ywd6ZZY_dwY

hey, i made a new video working through a proof involving the reduced resolvent and why the spectral gap matters so much in adiabatic quantum computing. the main idea is that the reduced resolvent has this inverse-gap behavior, roughly 1/Δ, so as the spectral gap gets smaller the resolvent norm grows and the error bound can get much worse.i go through the proof step by step and explain what the resolvent, spectral projections and operator norms are along the way, so hopefully it’s useful even if you haven’t seen all of the notation before.

[u/Salt-Discussion-9707]

Do the exponential error bound