Quantum Simulation of Hyperbolic Space with Circuit Quantum Electrodynamics: From Graphs to Geometry
ORAL
Abstract
We show how quantum many-body systems on hyperbolic lattices with nearest-neighbor 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 table-top 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 Poincare disk, and show how conformal symmetry emerges for large lattices.
*This work was supported by DOE BES award DE-SC0019449 (hyperbolic lattice generation and analytical results), by the United States Army Research Labs Center for Distributed Quantum Information (CDQI) at the University of Maryland (numerical implementation), and by the National Science Foundation Physics Frontier Center at the Joint Quantum Institute award PHYS-1430094 (applications and asymptotic limits), and NSERC and FRQNT.
–
Presenters
-
Igor Boettcher
- Univ of Alberta
- University of Maryland, College Park