Classical Algorithms for Quantum Dynamics: Progress and Prospects
Standard Monte Carlo techniques are unable to access real-time quantum dynamics due to a sign problem. A wide variety of methods have arisen for overcoming this obstacle, many inspired by analogous methods for the fermion sign problem. I will discuss machine-learning-inspired approaches for the real-time sign problem. One such approach, based on the complexification of "normalizing flows", connects naturally to the Lefschetz thimble program for the fermionic case. Considering the behavior of these complexified normalizing flows as a function of coupling suggests that manifolds exactly solving bosonic, real-time sign problems exist in all cases. Although efficient algorithms for finding these manifolds are not known, various approximations are available.
In some cases, overcoming the sign problem is probably hard in the following sense: in some field theories, arbitrary correlation functions can be shown to be BQP-hard to compute. I will describe the extension of this result to the computation of S-matrix elements (albeit for a smaller class of field theories). I will conclude by outlining the landscape of computational tasks in field theories: what is provably intractable, what is doable today, and what we might hope for in the future.
Zoom link will be available via announcement email, or by contacting: ikolbe[at]uw.edu