We demonstrate that a recent proposal for simulating planar hyperbolic lattices using circuit quantum electrodynamics can be extended to include higher-dimensional lattices in both Euclidean and non-Euclidean spaces by allowing circuits that involve more than three polygons at each vertex. The quantum dynamics of these circuits, which we are developing with current technology, are governed by effective tight-binding Hamiltonians that correspond to higher-dimensional Kagomé-like structures (such as $n$-dimensional zeolites). These structures are known for exhibiting strong frustration and flat bands. We analyze the spectra of both hyperbolic and positive-curvature lattices and derive exact expressions for the fraction of flat-band states. Our findings significantly broaden the possibilities for realizing non-Euclidean geometries using circuit quantum electrodynamics, a research direction we are actively pursuing in microwave-guide circuits constructed with sputtered niobium films on silicon substrates.

Close

PrevNext

View figure in article

• Photonic crystals
• Quantum electrodynamics
• Quantum fields in curved spacetime
• Quantum simulation
• Quantum state engineering
• Superconducting quantum optics