Theory Seminar: Digitization of field theories for quantum simulation

Prof. Torsten Zache
Universität Innsbruck
Quantum Info & Computing Seminar at the Lecture Hall
Tuesday January 13th, 11:30 CET

The simulation of quantum field theories is a prime target for future quantum computers. In addition to the conventional lattice regularisation of continuum field theories, this typically requires a digitization in field space, often realised as a truncation of an infinite-dimensional local Hilbert space.

In this talk, I will discuss the concept of "field digitisation scaling” (FDS), generalizing a finite-size scaling approach, to tackle this problem. For the example of classical-statistical ZN clock models in two spatial dimensions, I will demonstrate how FDS can relate these models across different N. In this example, FDS can be understood via the emergence of a U(1) symmetry, giving rise to a well-known Sine-Gordon model with an explicitly N-dependent perturbation. Our predictions are tested with numerical tensor network simulations of the partition function where we find that the environment bond dimension of the employed CTMRG algorithm can also be taken into account in the FDS analysis. To conclude, I will draw connections to ZN lattice gauge theories and speculate about possible extensions of FDS to non-abelian lattice gauge theories.