



01752nas a2200133   4500008004100000245009000041210007000131260001400201520130500215100002201520700002001542700001901562856003701581       2023                        eng d00aOn the stability of solutions to Schrödinger's equation short of the adiabatic limit0 astability of solutions to Schrödingers equation short of the adi  c3/23/20233 a<p>We prove an adiabatic theorem that applies at timescales short of the adiabatic limit. Our proof analyzes the stability of solutions to Schrodinger&#39;s equation under perturbation. We directly characterize cross-subspace effects of perturbation, which are typically significantly less than suggested by the perturbation&#39;s operator norm. This stability has numerous consequences: we can (1) find timescales where the solution of Schrodinger&#39;s equation converges to the ground state of a block, (2) lower bound the convergence to the global ground state by demonstrating convergence to some other known quantum state, (3) guarantee faster convergence than the standard adiabatic theorem when the ground state of the perturbed Hamiltonian (H) is close to that of the unperturbed H, and (4) bound tunneling effects in terms of the global spectral gap when H is ``stoquastic&#39;&#39; (a Z-matrix). Our results apply to quantum annealing protocols with faster convergence than usually guaranteed by a standard adiabatic theorem. Our upper and lower bounds demonstrate that at timescales short of the adiabatic limit, subspace dynamics can dominate over global dynamics. Thus, we see that convergence to particular target states can be understood as the result of otherwise local dynamics.</p>1 aBringewatt, Jacob1 aJarret, Michael1 aMooney, T., C.  uhttps://arxiv.org/abs/2303.13478