Quantum Matter Seminar

Simulating dynamics of strongly interacting systems is a core challenge of quantum many-body physics. At high temperature, generic strongly interacting spin systems are expected to display hydrodynamics: local transport of conserved quantities, governed by classical partial differential equations like the diffusion equation. I argue that the emergence of hydrodynamics is explained certain properties of the system's Heisenberg dynamics, and that these properties lead to an effective model that is tractable in 1+1d and potentially 2+1d, but not in 3 dimensions or for gauge theories. I then turn to the prospects for simulation on error-corrected quantum computers, where resource costs will likely be dominated by non-Clifford gate counts. I present suggestive evidence that simulating hydrodynamics requires relatively small non-Clifford resources, or "magic". I then discuss a phase transition in magic induced by measurements, which may be useful as a first stage of magic-state distillation.