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 Poincar{\'e} 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.

}, doi = {10.1103/PhysRevLett.128.013601}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.128.013601}, author = {Bienias, Przemyslaw and Boettcher, Igor and Belyansky, Ron and Kollar, Alicia J. and Gorshkov, Alexey V.} } @article { ISI:000571399800001, title = {Minimal Model for Fast Scrambling}, journal = {Phys. Rev. Lett.}, volume = {125}, number = {13}, year = {2020}, month = {SEP 21}, pages = {130601}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {We study quantum information scrambling in spin models with both long-range all-to-all and shortrange interactions. WC argue that a simple global, spatially homogeneous interaction together with local chaotic dynamics is sufficient to give rise to fast scrambling, which describes the spread of quantum information over the entire system in a time that is logarithmic in the system size. This is illustrated in two tractable models: (1) a random circuit with Haar random local unitaties and a global interaction and (2) a classical model of globally coupled nonlinear oscillators. We use exact numerics to provide further evidence by studying the time evolution of an out-of-time-order correlator and entanglement entropy in spin chains of intermediate sizes. Our results pave the way towards experimental investigations of fast scrambling and aspects of quantum gravity with quantum simulators.}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.125.130601}, author = {Belyansky, Ron and Bienias, Przemyslaw and Kharkov, Yaroslav A. and Gorshkov, V, Alexey and Swingle, Brian} } @article {17096, title = {Quantum simulation of hyperbolic space with circuit quantum electrodynamics: From graphs to geometry}, journal = {Phys. Rev. A}, volume = {102}, year = {2020}, month = {Sep}, pages = {032208}, 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 Poincar{\'e} 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. Importantly, our analysis reveals that even relatively small discrete hyperbolic lattices emulate the continuous geometry of negatively curved space, and thus can be used to experimentally resolve fundamental open problems at the interface of interacting many-body systems, quantum field theory in curved space, and quantum gravity.

}, keywords = {hyperbolic geometry, quantum simulation}, doi = {10.1103/PhysRevA.102.032208}, url = {https://link.aps.org/doi/10.1103/PhysRevA.102.032208}, author = {Boettcher, Igor and Bienias, Przemyslaw and Belyansky, Ron and Kollar, Alicia J. and Gorshkov, Alexey V.} } @article {19026, title = {Symmetry Breaking and Error Correction in Open Quantum Systems}, journal = {Phys. Rev. Lett.}, volume = {125}, year = {2020}, month = {Dec}, pages = {240405}, abstract = {Symmetry-breaking transitions are a well-understood phenomenon of closed quantum systems in quantum optics, condensed matter, and high energy physics. However, symmetry breaking in open systems is less thoroughly understood, in part due to the richer steady-state and symmetry structure that such systems possess. For the prototypical open system{\textemdash}a Lindbladian{\textemdash}a unitary symmetry can be imposed in a {\textquotedblleft}weak{\textquotedblright} or a {\textquotedblleft}strong{\textquotedblright} way. We characterize the possible\ Zn\ symmetry-breaking transitions for both cases. In the case of\ Z2, a weak-symmetry-broken phase guarantees at most a classical bit steady-state structure, while a strong-symmetry-broken phase admits a partially protected steady-state qubit. Viewing photonic cat qubits through the lens of strong-symmetry breaking, we show how to dynamically recover the logical information after any gap-preserving strong-symmetric error; such recovery becomes perfect exponentially quickly in the number of photons. Our study forges a connection between driven-dissipative phase transitions and error correction.

}, doi = {10.1103/PhysRevLett.125.240405}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.125.240405}, author = {Lieu, Simon and Belyansky, Ron and Young, Jeremy T. and Lundgren, Rex and Albert, Victor V. and Gorshkov, Alexey V.} } @article { ISI:000498063400002, title = {Nondestructive Cooling of an Atomic Quantum Register via State-Insensitive Rydberg Interactions}, journal = {Phys. Rev. Lett.}, volume = {123}, number = {21}, year = {2019}, month = {NOV 20}, pages = {213603}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {We propose a protocol for sympathetically cooling neutral atoms without destroying the quantum information stored in their internal states. This is achieved by designing state-insensitive Rydberg interactions between the data-carrying atoms and cold auxiliary atoms. The resulting interactions give rise to an effective phonon coupling, which leads to the transfer of heat from the data atoms to the auxiliary atoms, where the latter can be cooled by conventional methods. This can be used to extend the lifetime of quantum storage based on neutral atoms and can have applications for long quantum computations. The protocol can also be modified to realize state-insensitive interactions between the data and the auxiliary atoms but tunable and nontrivial interactions among the data atoms, allowing one to simultaneously cool and simulate a quantum spin model.}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.123.213603}, author = {Belyansky, Ron and Young, Jeremy T. and Bienias, Przemyslaw and Eldredge, Zachary and Kaufman, Adam M. and Zoller, Peter and Gorshkov, V, Alexey} }