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7 pags., 5 figs. ; We propose a quantum simulation of the quantum Rabi model in an atomic quantum dot, which is a single atom in a tight optical trap coupled to the quasiparticle modes of a superfluid Bose-Einstein condensate. This widely tunable setup allows us to simulate the ultrastrong coupling regime of light-matter interaction in a system which enjoys an amenable characteristic time scale, paving the way for an experimental analysis of the transition between the Jaynes-Cummings and the quantum Rabi dynamics using cold-atom systems. Our scheme can be naturally extended to simulate multiqubit quantum Rabi models. In particular, we discuss the appearance of effective two-qubit interactions due to phononic exchange, among other features. ; under the Marie Curie Actions-COFUND of the FP7. G.R. acknowledges the support from the Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT, Chile) under Grant No. 1150653. E.S. acknowledges financial support from the Spanish MINECO/FEDER under Grant No. FIS2015-69983-P and the Basque Government under Grant No. IT986-16. Financial support by the Fundación General CSIC (Programa ComFuturo) is acknowledged by C.S as well as additional support from the Spanish MINECO/FEDER under Grant No. FIS2015-70856-P and the CAM PRICYT Project QUITEMAD+S2013/ICE-2801. ; Peer Reviewed

6 pags., 2 figs. -- ERRATUM: Publisher's Note: Simulating superluminal physics with superconducting circuit technology [Phys. Rev. A 96, 032121 (2017)] Carlos Sabín, Borja Peropadre, Lucas Lamata, and Enrique Solano Phys. Rev. A 96, 049904 (2017) ; We provide tools for the quantum simulation of superluminal motion with superconducting circuits. We show that it is possible to simulate the motion of a superconducting qubit at constant velocities that exceed the speed of light in the electromagnetic medium and the subsequent emission of Ginzburg radiation. We also consider possible setups for simulating the superluminal motion of a mirror, finding a link with the super-radiant phase transition of the Dicke model. ; Financial support from the Fundación General CSIC is acknowledged by C.S. We also acknowledge support from Spanish MINECO/FEDER FIS2015-69983-P and FIS2015- 70856-P, Ramón y Cajal Grant No. RYC-2012-11391, CAM PRICYT Project QUITEMAD+ S2013/ICE-2801, Basque Government IT986-16, and UPV/EHU UFI 11/55. ; Peer Reviewed

El pdf del artículo es la versión pre-print: arxiv:1003.2376.-- et al. ; In circuit quantum electrodynamics (QED), where superconducting artificial atoms are coupled to on-chip cavities, the exploration of fundamental quantum physics in the strong-coupling regime has greatly evolved. In this regime, an atom and a cavity can exchange a photon frequently before coherence is lost. Nevertheless, all experiments so far are well described by the renowned Jaynes-Cummings model. Here, we report on the first experimental realization of a circuit QED system operating in the ultrastrong-coupling limit, where the atom-cavity coupling rate g reaches a considerable fraction of the cavity transition frequency ‰r. Furthermore, we present direct evidence for the breakdown of the Jaynes-Cummings model. We reach remarkable normalized coupling rates g/ ‰r of up to 12% by enhancing the inductive coupling of a flux qubit to a transmission line resonator. Our circuit extends the toolbox of quantum optics on a chip towards exciting explorations of ultrastrong light-matter interaction. © 2010 Macmillan Publishers Limited. All rights reserved. ; We acknowledge financial support by the Deutsche Forschungsgemeinschaft through SFB 631 and the German Excellence Initiative through NIM. E.S. acknowledges financial support from UPV/EHU Grant GIU07/40, Ministerio de Ciencia e Innovación FIS2009-12773-C02-01, Basque Government Grant IT472-10, European Projects EuroSQIP and SOLID. D.Z. acknowledges financial support from FIS2008-01240 and FIS2009-13364-C02-0 (MICINN). ; Peer Reviewed

The logistic network design is an abstract optimization problem that, under the assumption of minimal cost, seeks the optimal configuration of the supply chain's infrastructures and facilities based on customer demand. Key economic decisions are taken about the location, number, and size of manufacturing facilities and warehouses based on the optimal solution. Therefore, improvements in the methods to address this question, which is known to be in the NP-hard complexity class, would have relevant financial consequences. Here, we implement in the D-Wave quantum annealer a hybrid classical-quantum annealing algorithm. The cost function with constraints is translated to a spin Hamiltonian, whose ground state encodes the searched result. As a benchmark, we measure the accuracy of results for a set of paradigmatic problems against the optimal published solutions (the error is on average below 1%), and the performance is compared against the classical algorithm, showing a remarkable reduction in the number of iterations. This work shows that state-of-the-art quantum annealers may codify and solve relevant supply-chain problems even still far from useful quantum supremacy. ; EU Flagship on Quantum Technologies QMiCS 820505 and OpenSuperQ 820363 ; Spanish Government PGC2018-095113-B-I00 (MCIU/ AEI/FEDER, UE), PID2019-104002GB-C21, PID2019-104002GBC22 (MCIU/AEI/FEDER, UE) ; Basque Government IT986-16 ; Shanghai Municipal Science and Technology Commission (Grant No. 2019SHZDZX01-ZX04, 18010500400, and 18ZR1415500)

The quantum perceptron is a fundamental building block for quantum machine learning. This is a multidisciplinary field that incorporates abilities of quantum computing, such as state superposition and entanglement, to classical machine learning schemes. Motivated by the techniques of shortcuts to adiabaticity, we propose a speed-up quantum perceptron where a control field on the perceptron is inversely engineered leading to a rapid nonlinear response with a sigmoid activation function. This results in faster overall perceptron performance compared to quasi-adiabatic protocols, as well as in enhanced robustness against imperfections in the controls. ; We acknowledge financial support from Spanish Government via PGC2018-095113-B-I00 (MCIU/AEI/FEDER, UE), Basque Government via IT986-16, as well as from QMiCS (820505) and OpenSuperQ (820363) of the EU Flagship on Quantum Technologies, and the EU FET Open Grant Quromorphic. J. C. acknowledges support from the UPV/EHU grant EHUrOPE. X. C. acknowledges NSFC (11474193), SMSTC (18010500400 and 18ZR1415500), the Program for Eastern Scholar and the Ramón y Cajal program of the Spanish MINECO (RYC-2017-22482). E.T. acknowledges support from Project PGC2018-094792-B-I00 (MCIU/AEI/FEDER,UE), CSIC Research Platform PTI-001, and CAM/FEDER Project No. S2018/TCS-4342 (QUITEMAD-CM).

7 pags., 5 figs. -- Open Access funded by Creative Commons Atribution Licence 4.0 ; We show that simulated relativistic motion can generate entanglement between artificial atoms and protect them from spontaneous emission. We consider a pair of superconducting qubits coupled to a resonator mode, where the modulation of the coupling strength can mimic the harmonic motion of the qubits at relativistic speeds, generating acceleration radiation. We find the optimal feasible conditions for generating a stationary entangled state between the qubits when they are initially prepared in their ground state. Furthermore, we analyse the effects of motion on the probability of spontaneous emission in the standard scenarios of single-atom and two-atom superradiance, where one or two excitations are initially present. Finally, we show that relativistic motion induces sub-radiance and can generate a Zeno-like effect, preserving the excitations from radiative decay. ; MINECO/FEDER FIS2015-69983-P and FIS2015-70856-P, Basque Government grant IT986-16, CAM PRICYT Project QUITEMAD + S2013/ICE-2801, University Sorbonne Paris Cité EQDOL contract, and Fundación General CSIC (Programa ComFuturo). ; Peer Reviewed

We study different architectures for a photonic crystal in the microwave regime based on superconducting transmission lines interrupted by Josephson junctions, both in one and two dimensions. A study of the scattering properties of a single junction in the line shows that the junction behaves as a perfect mirror when the photon frequency matches the Josephson plasma frequency. We generalize our calculations to periodic arrangements of junctions, demonstrating that they can be used for tunable band engineering, forming what we call a quantum circuit crystal. Two applications are discussed in detail. In a two-dimensional structure we demonstrate the phenomenon of negative refraction. We finish by studying the creation of stationary entanglement between two superconducting qubits interacting through a disordered media. © 2012 American Physical Society. ; This work was supported by Spanish Governement projects FIS2008-01240, FIS2009-10061, FIS2009-12773-C02-01, and FIS2011-25167 cofinanced by FEDER funds; CAM research consortium QUITEMAD; Basque Government Grants No. IT472-10, and No. UPV/EHU UFI 11/55; and PROMISCE, SOLID, and CCQED European projects. ; Peer Reviewed

We develop energy efficient, continuous microwave schemes to couple electron and nuclear spins, using phase or amplitude modulation to bridge their frequency difference. These controls have promising applications in biological systems, where microwave power should be limited, as well as in situations with high Larmor frequencies due to large magnetic fields and nuclear magnetic moments. These include nanoscale NMR where high magnetic fields achieves enhanced thermal nuclear polarization and larger chemical shifts. Our controls are also suitable for quantum information processors and nuclear polarization schemes. ; E. S. and J. C. acknowledge financial support from Spanish MINECO/FEDER FIS2015-69983-P, Basque Government IT986-16, as well as from QMiCS (820505) and OpenSuperQ (820363) of the EU Flagship on Quantum Technologies. J. C. acknowledges support by the Juan de la Cierva Grant No. IJCI-2016-29681. E. T. and J. J. G. R. acknowledge support from Spanish MINECO/FEDER Project No. FIS2015-70856-P, No. FIS2016-81891-REDT and CAM PRICYT Project QUITEMAD þ CM No. S2013-ICE2801. M. B. P. acknowledges support by the ERC Synergy grant BioQ (Grant No. 319130), the EU project HYPERDIAMOND, the QuantERA project NanoSpin, the BMBF project DiaPol, the state of Baden-Württemberg through bwHPC, and the German Research Foundation (DFG) through Grant No. INST 40/467-1 FUGG. This material is also based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advance Scientific Computing Research (ASCR), Quantum Algorithms Teams project under field work proposal ERKJ335.

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

We propose Quantum Brain Networks (QBraiNs) as a new interdisciplinary field integratingknowledge and methods from neurotechnology, artificial intelligence, and quantum computing. Theobjective is to develop an enhanced connectivity between the human brain and quantum computersfor a variety of disruptive applications. We foresee the emergence of hybrid classical-quantumnetworks of wetware and hardware nodes, mediated by machine learning techniques and brain–machine interfaces. QBraiNs will harness and transform in unprecedented ways arts, science,technologies, and entrepreneurship, in particular activities related to medicine, Internet of Humans,intelligent devices, sensorial experience, gaming, Internet of Things, crypto trading, and business. ; European Union (EU) QMiCS (820505) and OpenSuperQ (820363) projects ; Spanish GovernmentPGC2018-095113-B-I00, PID2019-104002GB-C21, PID2019-104002GB-C22 (MCIU/AEI/FEDER, UE) ; Basque Government IT986-16 ; Junta de Andalucía (P20-00617 andUS-1380840) ; National Natural Science Foundation of China (NSFC)(12075145), STCSM (2019SHZDZX01-ZX04, 18010500400 and 18ZR1415500)

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

7 pags., 4 figs. ; The quantum Rabi model describes the interaction between a two-level quantum system and a single bosonic mode. We propose a method to perform a quantum simulation of the quantum Rabi model, introducing an implementation of the two-level system provided by the occupation of Bloch bands in the first Brillouin zone by ultracold atoms in tailored optical lattices. The effective qubit interacts with a quantum harmonic oscillator implemented in an optical dipole trap. Our realistic proposal allows one to experimentally investigate the quantum Rabi model for extreme parameter regimes, which are not achievable with natural light-matter interactions.When the simulated wave function exceeds the validity region of the simulation, we identify a generalized version of the quantum Rabi model in a periodic phase space. ; This work was supported in part by the DFG (Grant No. We 5 1748-20). S.F. acknowledges funding from the PRESTIGE program, under the Marie Curie Actions-COFUND of the FP7 and from University Sorbonne Paris Cite EQDOL contract. E.R. and E.S. acknowledge funding from UPV/EHU Grant No. UFI 11/55, MINECO/FEDER Grant No. FIS2015- 69983- P, and UPV/EHU Grant No. EHUA15/17. C.S. acknowledges funding from Fundación General CSIC (Programa ComFuturo), MINECO Project No. FIS2015-70856-P (cofinanced by FEDER funds), andCAMPRICYT Project No. QUITEMAD+ S2013/ICE-2801. Basque Government Grant No. IT986-16 Spanish MINECO/FEDER FIS2015-69983-P and FIS2015-70856-P. ; 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

Pricing interest-rate financial derivatives is a major problem in finance, in which it is crucial to accurately reproduce the time evolution of interest rates. Several stochastic dynamics have been proposed in the literature to model either the instantaneous interest rate or the instantaneous forward rate. A successful approach to model the latter is the celebrated Heath-Jarrow-Morton framework, in which its dynamics is entirely specified by volatility factors. In its multifactor version, this model considers several noisy components to capture at best the dynamics of several time-maturing forward rates. However, as no general analytical solution is available, there is a trade-off between the number of noisy factors considered and the computational time to perform a numerical simulation. Here, we employ the quantum principal component analysis to reduce the number of noisy factors required to accurately simulate the time evolution of several time-maturing forward rates. The principal components are experimentally estimated with the five-qubit IBMQX2 quantum computer for 2×2 and 3×3 cross-correlation matrices, which are based on historical data for two and three time-maturing forward rates. This paper is a step towards the design of a general quantum algorithm to fully simulate on quantum computers the Heath-Jarrow-Morton model for pricing interest-rate financial derivatives. It shows indeed that practical applications of quantum computers in finance will be achievable in the near future. ; Ministerio de Ciencia, Innovación y Universidades PID2019-104002GB-C21, PID2019-104002GBC22 (MCIU/AEI/FEDER, UE) ; Ministerio de Ciencia, Innovación y Universidades PGC2018-095113-B-I00 (MCIU/AEI/FEDER, UE) ; Basque Government, Grant No. IT986-16