YQI Talk - Ben McDonough - UC Boulder

 

Quantum information in a locally interacting system is constrained to propagate at a finite velocity. The key technical tool underlying this principle is Lieb-Robinson bounds, an important and well-known set of mathematical techniques in many-body physics which constrain the difficulty of common quantum information processing tasks, including preparing entangled states and simulating local quantum dynamics with a classical or quantum computer.

 

This talk will explore two recent extensions of Lieb-Robinson bounds to control the simulability of quantum dynamics. In truth, the Lieb-Robinson lightcone is not strict; there is a small leakage of operator growth outside of the lightcone. The traditional understanding is that these “operator tails” decay exponentially in the linear distance outside the lightcone. In the first part of the talk (based on [1]), we will develop a dramatic qualitative improvement to operator decay outside the lightcone, and then use these stronger bounds to close a large complexity gap in the difficulty of classical simulation of local quantum systems.

 

The second part of the talk (based on [2]) will address a different question, which is important to the search for problems with near-term quantum advantage; are disordered quantum systems actually harder to simulate? Non-interacting particles in a disordered system are known to Anderson-localize. So-called many-body localization is expected to similarly constrain the dynamics of interacting particles at finite energy density, but this has never been proven rigorously and is strongly believed on theoretical grounds to exist only in one-dimensional spin chains. We rigorously demonstrate for the first time that many-body localization is a prethermal effect in local spin-networks in any dimension, and even beyond the prethermal timescale, correlations must spread with a Lieb-Robinson velocity that is incredibly small. As a consequence, these systems are remarkably easy to simulate up to incredibly long times, and are poor test-beds for quantum advantage.