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We consider the quantum simulation of relativistic quantum mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. Firstly, we study the bidimensional relativistic scattering of single Dirac particles by a linear potential. Secondly, we explore the case of a Dirac particle in a magnetic field and its topological properties. Finally, we analyze the problem of two Dirac particles that are coupled by a controllable and confining potential. The latter interaction may be useful to study important phenomena such as the confinement and asymptotic freedom of quarks. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. ; LL thanks the European Commission for funding through a Marie Curie IEF grant. JC acknowledges support from the Basque Government grant number BFI08.211. JJG-R acknowledges funding from the Spanish MICINN project number FIS2009-10061 and the CAM research consortium QUITEMAD S2009-ESP-1594. ES is grateful to the Spanish MICINN project number FIS2009-12773-C02-01, the Basque Government grant number IT472-10 and the European projects SOLID and CCQED. ; Peer Reviewed

6 pags., 2 figs. ; Matrix product states and projected entangled pair states (PEPS) are powerful analytical and numerical tools to assess quantum many-body systems in one and higher dimensions, respectively. While matrix product states are comprehensively understood, in PEPS fundamental questions, relevant analytically as well as numerically, remain open, such as how to encode symmetries in full generality, or how to stabilize numerical methods using canonical forms. Here, we show that these key problems, as well as a number of related questions, are algorithmically undecidable, that is, they cannot be fully resolved in a systematic way. Our work thereby exposes fundamental limitations to a full and unbiased understanding of quantum many-body systems using PEPS. ; This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grants No. 648913 and No. 636201). S. I., D. P. G., and G. S. acknowledge financial support from MINECO (Grants No. MTM2014-54240-P and No. MTM2017- 88385-P), CAM research consortium QUITEMAD-CM (Grant No. P2018/TCS-4342), and Severo Ochoa Project No. SEV-2015-556. S. I. also acknowledges funding by the Ministerio de Ciencias, Innovacion y Universidades, PGC2018-095862-B-C22 (Spain) and by Quantum CAT (001-P-001644), Generalitat de Catalunya, and María de Maeztu Project No. CEX2019-000918-M (Spain). J. J. G. R. acknowledges financial support from MINECO Project No. FIS2015-70856-P, CAM research consortion QUITEMAD-CM Grant No. P2018/TCS-4342, MINECO research network FIS2016-81891-REDT. A. M., Y. G., and N. S. acknowledge support from the DFG (German Research Foundation) under Germany's Excellence Strategy (EXC2111-390814868).

We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes. © 2011 American Physical Society. ; J. C. acknowledges support from Basque Government Grant No. BFI08.211. L. L. thanks the European Commission for a Marie Curie IEF grant. I. L. E. is grateful to Basque Government Grant No. IT559-10. J. J. G.-R. acknowledges funding from Spanish MICINN Projects No. FIS2009-10061 and CAM Project No. QUITEMAD S2009-ESP-1594. E. S. is grateful to Basque Government Grant No. IT472-10, Spanish MICINN FIS2009-12773- C02-01, SOLID and CCQED European projects. ; Peer Reviewed

arXiv:1305.4844v1 ; The scattering through a Josephson junction (JJ) interrupting a superconducting line is revisited including power leakage. We also discuss how to make tunable and broadband resonant mirrors by concatenating junctions. As an application, we show how to construct cavities using these mirrors, thus connecting two research fields: JJ quantum metamaterials and coupled-cavity arrays. We finish by discussing the first nonlinear corrections to the scattering and their measurable effects. © 2013 IOP Publishing Ltd. ; This work was supported by Spanish government projects FIS2009-10061, and FIS2011-25167 conanced by FEDER funds. We thanks Aragon government support to group FENOL, CAM research consortium QUITEMAD and PROMISCE European project. ; Peer Reviewed

We design a quantum simulator for the Majorana equation, a non-Hamiltonian relativistic wave equation that might describe neutrinos and other exotic particles beyond the standard model. Driven by the need of the simulation, we devise a general method for implementing a number of mathematical operations that are unphysical, including charge conjugation, complex conjugation, and time reversal. Furthermore, we describe how to realize the general method in a system of trapped ions. The work opens a new front in quantum simulations. ; The authors acknowledge funding from Basque Government Grants No. BFI08.211, IT559-10, and No. IT472-10; Spanish MICINN FIS2008-05705, FIS2009- 10061, and FIS2009-12773-C02-01; QUITEMAD; the EC Marie-Curie program; and the CCQED and SOLID European projects. ; Peer Reviewed

We report on quantum simulations of relativistic scattering dynamics using trapped ions. The simulated state of a scattering particle is encoded in both the electronic and vibrational state of an ion, representing the discrete and continuous components of relativistic wave functions. Multiple laser fields and an auxiliary ion simulate the dynamics generated by the Dirac equation in the presence of a scattering potential. Measurement and reconstruction of the particle wave packet enables a frame-by-frame visualization of the scattering processes. By precisely engineering a range of external potentials we are able to simulate text book relativistic scattering experiments and study Klein tunneling in an analogue quantum simulator. We describe extensions to solve problems that are beyond current classical computing capabilities.© 2011 American Physical Society. ; We gratefully acknowledge support by the Austrian Science Fund (FWF), by the European Commission (Marie-Curie program), by the Institut fu¨r Quanteninformation GmbH and IARPA. E. S. thanks for support from the Spanish MICINN project FIS2009- 12773-C02-01, Basque Government Grant IT472-10, ITN CCQED and SOLID European projects. J. C. acknowledges the Basque Government BFI08.211.J. J. G.-R. acknowledges the Spanish projects MICINN FIS2009-10061 and QUITEMAD. ; Peer Reviewed

We study the quantum spin dynamics of nearly isotropic Gd3+ ions entrapped in polyoxometalate molecules and diluted in crystals of a diamagnetic Y3+ derivative. The full energy-level spectrum and the orientations of the magnetic anisotropy axes have been determined by means of continuous-wave electron paramagnetic resonance experiments, using X-band (9-10 GHz) cavities and on-chip superconducting waveguides and 1.5-GHz resonators. The results show that seven allowed transitions between the 2S+1 spin states can be separately addressed. Spin coherence T2 and spin-lattice relaxation T1 rates have been measured for each of these transitions in properly oriented single crystals. The results suggest that quantum spin coherence is limited by residual dipolar interactions with neighbor electronic spins. Coherent Rabi oscillations have been observed for all transitions. The Rabi frequencies increase with microwave power and agree quantitatively with predictions based on the spin Hamiltonian of the molecular spin. We argue that the spin states of each Gd3+ ion can be mapped onto the states of three addressable qubits (or, alternatively, of a d=8-level >qudit>), for which the seven allowed transitions form a universal set of operations. Within this scheme, one of the coherent oscillations observed experimentally provides an implementation of a controlled-controlled-NOT (or Toffoli) three-qubit gate. ; Funds were provided by the Spanish MINECO (Grants No. MAT2015-68204-R, No. CTQ2015-64486-R, No. MAT- 2014-56143-R, No. CTQ2014-52758-P, and No. FIS2015-70856-P and Excellence Unit María de Maeztu MDM-2015-0538), the European Union (ERC Grants No. SPINMOL and DECRESIM and COST 15128 Molecular Spintronics project), the Gobierno de Aragón (Grants No. E98-MOLCHIP and No. E33), Comunidad de Madrid (Research Network QUITEMAD+), and the Generalidad Valenciana (Prometeo and ISIC-Nano Programs of Excellence). A.G.-A. thanks MINECO for a Ramón y Cajal Fellowship. ; Peer Reviewed

APS March Meeting, Boston, MA, March 4-8, 2019. -- https://www.aps.org/meetings/meeting.cfm?name=MAR19 ; Funds were provided by the Spanish MINECO (grants MAT2015-68204-R and Excellence Unit Maria de Maeztu MDM-2015- 0538) and the European Union (COST 15128 Molecular Spintronics and QUANTERA SUMO projects) ; Peer reviewed

Under the terms of the Creative Commons Attribution license.-- et al. ; We report on ultrastrong coupling between a superconducting flux qubit and a resonant mode of a system comprised of two superconducting coplanar stripline resonators coupled galvanically to the qubit. With a coupling strength as high as 17.5% of the mode frequency, exceeding that of previous circuit quantum electrodynamics experiments, we observe a pronounced Bloch-Siegert shift. The spectroscopic response of our multimode system reveals a clear breakdown of the Jaynes-Cummings approximation. In contrast to earlier experiments, the high coupling strength is achieved without making use of an additional inductance provided by a Josephson junction. ©2016 American Physical Society ; Thiswork is supported by the German Research Foundation through SFB 631 and FE 1564/1-1; Spanish MINECO FIS2012-36673-03-02, MAT2014-53432-C5-1-R, FIS2014- 55867-P and FIS2012-33022; CAM Research Network QUITEMAD+; UPV/EHU UFI 11/55, UPV/EHU PhD Grant, and Basque Government IT472-10; the Fondo Nacional de Desarrollo Cientifico y Tecnológico (FONDECYT, Chile) under Grant 1150653; the EU projects CCQED, PROMISCE, and SCALEQIT. We further acknowledge GEFENOL. ; Peer Reviewed

Under the terms of the Creative Commons Attribution License 3.0 (CC-BY).-- et al. ; We realize a device allowing for tunable and switchable coupling between two frequency-degenerate superconducting resonators mediated by an artificial atom. For the latter, we utilize a persistent current flux qubit. We characterize the tunable and switchable coupling in the frequency and time domains and find that the coupling between the relevant modes can be varied in a controlled way. Specifically, the coupling can be tuned by adjusting the flux through the qubit loop or by controlling the qubit population via a microwave drive. Our measurements allow us to find parameter regimes for optimal coupler performance and quantify the tunability range. ; This work is supported by the German Research Foundation through SFB 631, Spanish MINECO FIS2012-36673-C03-02; UPV/EHU UFI 11/55; Basque Government IT472-10; CCQED, PROMISCE, and SCALEQIT EU projects. B.P. acknowledges support from the STC Center for Integrated Quantum Materials, NSF Grant No. DMR-1231319. ; Peer reviewed

17 pags., 9 figs., 3 tabs., 5 apps. ; Qubit readout is an indispensable element of any quantum information processor. In this work, we experimentally demonstrate a nonperturbative cross-Kerr couplingbetween a transmon and polariton mode which enables an improved quantum nondemolition (QND) readout for superconducting qubits. The new mechanism uses the same experimental techniques as the standard QND qubit readout in the dispersive approximation, but due to its nonperturbative nature, it maximizes the speed, the single-shot fidelity, and the QND properties of the readout. In addition, it minimizes the effect of unwanted decay channels such as the Purcell effect. We observe a single-shot readout fidelity of 97.4% for short 50-ns pulses and we quantify a QND-ness of 99% for long measurement pulses with repeated single-shot readouts. ; R. D. and S. L. acknowledge support from Fondation CFM pour la recherche. R. D., V. M., and O. B. acknowledge support from ANR REQUIEM (ANR-17-CE24-0012-01). J. J. G.-R. and T. R. acknowledge support from Project No. PGC2018-094792-B-I00 (MCIU/ AEI/FEDER, UE) and CAM/FEDER Project No. S2018/ TCS-4342 (QUITEMAD-CM). T. R. further acknowledges funding from the EU Horizon 2020 program under the Marie Skłodowska-Curie Grant Agreement No. 798397. S. L. acknowledges the Agence Nationale de la Recherche under the program Investissements d'avenir (ANR-15-IDEX02). K. B. and J. D. acknowledge the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 754303. J. P. acknowledges grant from the Laboratoire d'excellence LANEF in Grenoble (ANR-10-LABX-51-01).

10 pags., 5 figs. ; We realize tunable coupling between two superconducting transmission line resonators. The coupling is mediated by a non-hysteretic rf SQUID acting as a flux-tunable mutual inductance between the resonators. We present a spectroscopic characterization of the device. In particular, we observe couplings g/2π ranging between –320 MHz and 37 MHz. In the case of g 0, the microwave power cross transmission between the two resonators is reduced by almost four orders of magnitude as compared to the case where the coupling is switched on. ; The authors acknowledge support from the German Research Foundation through SFB 631 and FE 1564/1-1; the EU projects CCQED, PROMISCE and SCALEQIT; the doctorate program ExQM of the Elite Network of Bavaria; the Spanish MINECO projects FIS2012-33022, FIS2012-36673-C03-02, and FIS2015-69983-P; the CAM Research Network QUITEMAD+; the Basque Government IT472-10 and UPV/EHU UFI 11/55.