Circuit quantum electrodynamics is one of the most promising platforms for efficient quantum simulation and computation. In recent groundbreaking experiments, the immense flexibility of superconducting microwave resonators was utilized to realize hyperbolic lattices that emulate quantum physics in negatively curved space. Here we investigate experimentally feasible settings in which a few superconducting qubits are coupled to a bath of photons evolving on the hyperbolic lattice. We compare our numerical results for finite lattices with analytical results for continuous hyperbolic space on the Poincaré disk. We find good agreement between the two descriptions in the long-wavelength regime. We show that photon-qubit bound states have a curvature-limited size. We propose to use a qubit as a local probe of the hyperbolic bath, for example by measuring the relaxation dynamics of the qubit. We find that, although the boundary effects strongly impact the photonic density of states, the spectral density is well described by the continuum theory. We show that interactions between qubits are mediated by photons propagating along geodesics. We demonstrate that the photonic bath can give rise to geometrically-frustrated hyperbolic quantum spin models with finite-range or exponentially-decaying interaction.

%8 5/13/2021 %G eng %U https://arxiv.org/abs/2105.06490 %0 Journal Article %D 2021 %T Crystallography of Hyperbolic Lattices %A Igor Boettcher %A Alexey V. Gorshkov %A Alicia J. Kollár %A Joseph Maciejko %A Steven Rayan %A Ronny Thomale %XHyperbolic lattices are a revolutionary platform for tabletop simulations of holography and quantum physics in curved space and facilitate efficient quantum error correcting codes. Their underlying geometry is non-Euclidean, and the absence of Bloch's theorem precludes a simple understanding of their band structure. Motivated by recent insights into hyperbolic band theory, we initiate a crystallography of hyperbolic lattices. We show that many hyperbolic lattices feature a hidden crystal structure characterized by unit cells, hyperbolic Bravais lattices, and associated symmetry groups. Using the mathematical framework of higher-genus Riemann surfaces and Fuchsian groups, we derive, for the first time, a list of example hyperbolic {p,q} lattices and their hyperbolic Bravais lattices, including five infinite families and several graphs relevant for experiments in circuit quantum electrodynamics and topolectrical circuits. Our results find application for both finite and infinite hyperbolic lattices. We describe a method to efficiently generate finite hyperbolic lattices of arbitrary size and explain why the present crystallography is the first step towards a complete band theory of hyperbolic lattices and apply it to construct Bloch wave Hamiltonians. This work lays the foundation for generalizing some of the most powerful concepts of solid state physics, such as crystal momentum and Brillouin zone, to the emerging field of hyperbolic lattices and tabletop simulations of gravitational theories, and reveals the connections to concepts from topology and algebraic geometry.

%8 5/3/2021 %G eng %U https://arxiv.org/abs/2105.01087 %0 Journal Article %J Phys. Rev. A %D 2020 %T Quantum Simulation of Hyperbolic Space with Circuit Quantum Electrodynamics: From Graphs to Geometry %A Igor Boettcher %A Przemyslaw Bienias %A Ron Belyansky %A Alicia J. Kollár %A Alexey V. Gorshkov %XWe 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 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 many-body systems, quantum field theory in curved space, and quantum gravity.

%B Phys. Rev. A %V 102 %8 9/11/2020 %G eng %U https://arxiv.org/abs/1910.12318 %N 032208 %R https://doi.org/10.1103/PhysRevA.102.032208 %0 Journal Article %D 2019 %T Quantum Simulators: Architectures and Opportunities %A Ehud Altman %A Kenneth R. Brown %A Giuseppe Carleo %A Lincoln D. Carr %A Eugene Demler %A Cheng Chin %A Brian DeMarco %A Sophia E. Economou %A Mark A. Eriksson %A Kai-Mei C. Fu %A Markus Greiner %A Kaden R. A. Hazzard %A Randall G. Hulet %A Alicia J. Kollár %A Benjamin L. Lev %A Mikhail D. Lukin %A Ruichao Ma %A Xiao Mi %A Shashank Misra %A Christopher Monroe %A Kater Murch %A Zaira Nazario %A Kang-Kuen Ni %A Andrew C. Potter %A Pedram Roushan %XQuantum simulators are a promising technology on the spectrum of quantum devices from specialized quantum experiments to universal quantum computers. These quantum devices utilize entanglement and many-particle behaviors to explore and solve hard scientific, engineering, and computational problems. Rapid development over the last two decades has produced more than 300 quantum simulators in operation worldwide using a wide variety of experimental platforms. Recent advances in several physical architectures promise a golden age of quantum simulators ranging from highly optimized special purpose simulators to flexible programmable devices. These developments have enabled a convergence of ideas drawn from fundamental physics, computer science, and device engineering. They have strong potential to address problems of societal importance, ranging from understanding vital chemical processes, to enabling the design of new materials with enhanced performance, to solving complex computational problems. It is the position of the community, as represented by participants of the NSF workshop on "Programmable Quantum Simulators," that investment in a national quantum simulator program is a high priority in order to accelerate the progress in this field and to result in the first practical applications of quantum machines. Such a program should address two areas of emphasis: (1) support for creating quantum simulator prototypes usable by the broader scientific community, complementary to the present universal quantum computer effort in industry; and (2) support for fundamental research carried out by a blend of multi-investigator, multi-disciplinary collaborations with resources for quantum simulator software, hardware, and education.

%8 12/14/2019 %G eng %U https://arxiv.org/abs/1912.06938