AbstractIn this talk, we will present how a Heisenberg spin chain emerges from the two-dimensional N=(2,2) gauge theory at an intermediate scale, which relies on the renormalization group flow guided by the global symmetries and the dynamics of domain walls. Two examples will be discussed: XX-model and its K-theoretic version. Finally, we will briefly comment on the unification of gauge theorie...
AbstractSampling from a given distribution is a fundamental computational problem and has broad applications in statistics, machine learning, physics, etc. We systematically investigate the quantum speedup of Monte Carlo methods, quantum mean estimation, and fast-forwarding of reversible Markov chains. We develop quantum algorithms for sampling log-concave distributions (with density e^{-f(x)} ...