[PAST EVENT] Mathematics Colloquium - Michael Jarret (George Mason University)
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- Free food
- Open to the public
Title: On the Stability of Schrödinger's Equation Short of the Adiabatic Limit
Abstract: Quantum adiabatic theorems govern the large timescale behavior of Schrödinger's equation and form the basis for variational quantum algorithms. In particular, when a quantum system is initially prepared into one of its eigenstates, then, for sufficiently large time, the solution to Schrödinger's equation always remains close to an eigenstate. Despite this, theorems that analyze the stability of these solutions under perturbation are rare. In this talk, I will review some basic adiabatic theory and use connections to graph theory to derive appropriate stability bounds. These bounds illuminate the role of the spectral gap in adiabatic quantum computing, as well as provide conditions for "computationally local" convergence and global divergence.