Tuesday, February 18, 2020
Emergence and entanglement are two central concepts in the field of modern quantum condensed matter physics. Emergence was popularized nearly a half-century ago by P.W. Anderson: the collective low-energy behavior of an interacting many-body system can exhibit features strikingly different from the individual constituent degrees of freedom. Entanglement, while a more recent notion in the context of the many-body problem, is equally important: it quantifies the "quantumness" of the system of interest. Profoundly, for physicists trying to unravel the low-energy emergent behavior of quantum matter through classical simulations, entanglement is at once our worst enemy and best friend. On the one hand, entanglement is that very feature of quantum many-body systems which makes their general classical simulation exponentially difficult. However, it is indeed the structure of the system's entanglement which arguably gives the clearest window into the universal properties of the quantum phase in question, and it is an understanding of this structure which permits the design and usage of efficient classical simulation techniques in certain situations. In this talk, I will present a survey of recent results in the areas of frustrated quantum magnetism and the fractional quantum Hall effect which dramatically illustrate these points. I will conclude by discussing the prospects of performing related simulations on near-term (NISQ) and long-term (fault-tolerant) *quantum* hardware---wherein we are no longer bound by entanglement-based constraints. Intriguingly, classical simulation techniques of the type discussed earlier will play a crucial role in the path towards the latter---in particular in the design and simulation of both topological quantum hardware and topological quantum error correcting codes, both of which exhibit their own remarkable emergent behavior.