CM Seminar: "Quantum Functions and Applications to Continuous Classical Systems" (Miles Stoudenmire, Flatiron Institute)

Tensor networks have a long history by now of capturing functions of many discrete variables, notably quantum wavefunctions. A simple reinterpretation of tensor indices as "bits", as in decimal representations of numbers, allows continuous variables as input to tensor networks. In this representation, wide classes of functions have low "entanglement" and operations can be performed classically with quantum algorithms (the Fourier transform becomes the quantum Fourier transform). A natural application of this technology is representing partition functions of continuous-variable classical systems. We explore this idea for the one- and two-dimensional XY model, finding decisive advantages over previous discretization schemes and the emergence of an extra "scale" dimension.