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Quantum simulation of hyperbolic space with circuit quantum electrodynamics: From graphs to geometry
Igor Boettcher1, Przemyslaw Bienias1,2, Ron Belyansky1
1Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA.
Physical Review. A
|June 17, 2021
Summary
We demonstrate mapping quantum many-body systems on hyperbolic lattices to quantum field theories in curved space. This enables table-top quantum simulations of complex physics, offering insights into quantum gravity and many-body systems.
Area of Science:
- Quantum physics
- Condensed matter physics
- Quantum field theory
Background:
- Quantum many-body systems on hyperbolic lattices are challenging to study.
- Experimental realization with superconducting resonators allows for quantum simulations.
- Curved space physics is fundamental to quantum gravity.
Purpose of the Study:
- To map quantum many-body systems on hyperbolic lattices to quantum field theories in curved space.
- To provide a computational tool for analyzing large discrete systems.
- To enable table-top quantum simulations of physics in curved backgrounds.
Main Methods:
- Mapping discrete hyperbolic lattices to continuous curved space quantum field theories.
- Utilizing analytic formulas on the Poincaré disk for calculations.
- Comparing simulation results with theoretical predictions.
Main Results:
- Quantitative reproduction of ground state energy, spectral gap, and correlation functions for noninteracting systems.
- Emergence of conformal symmetry in large hyperbolic lattices.
- Demonstration that small discrete lattices emulate continuous curved geometry.
Conclusions:
- Discrete hyperbolic lattices serve as a powerful platform for quantum simulation.
- This approach facilitates the study of interacting many-body systems in curved space.
- The research opens avenues for exploring quantum gravity and field theory in curved space.
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