Quantum Simulation of Hyperbolic Space with Circuit Quantum Electrodynamics: From Graphs to Geometry
Abstract
We show how quantum manybody systems on hyperbolic lattices with nearestneighbor hopping and local interactions can be mapped onto quantum field theories in continuous negatively curved space. The underlying lattices have recently been realized experimentally with superconducting resonators and therefore allow for a tabletop quantum simulation of quantum physics in curved background. Our mapping provides a computational tool to determine observables of the discrete system even for large lattices, where exact diagonalization fails. As an application and proof of principle we quantitatively reproduce the ground state energy, spectral gap, and correlation functions of the noninteracting lattice system by means of analytic formulas on the Poincaré disk, and show how conformal symmetry emerges for large lattices. This sets the stage for studying interactions and disorder on hyperbolic graphs in the future. Our analysis also reveals in which sense discrete hyperbolic lattices emulate the continuous geometry of negatively curved space and thus can be used to resolve fundamental open problems at the interface of interacting manybody systems, quantum field theory in curved space, and quantum gravity.
 Publication:

arXiv eprints
 Pub Date:
 October 2019
 arXiv:
 arXiv:1910.12318
 Bibcode:
 2019arXiv191012318B
 Keywords:

 Quantum Physics;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 4+ pages and supplemental material