Dr. Lucas Lamata-Research Highlights - L. Lamata, J. León, T. Schätz, and E. Solano.
We present a method of simulating the Dirac equation in 3+1 dimensions for a free spin-1/2 particle in a single trapped ion. The Dirac bispinor is represented by four ionic internal states, and position and momentum of the Dirac particle are associated with the respective ionic variables. We show also how to simulate the simplified 1+1 case, requiring the manipulation of only two internal levels and one motional degree of freedom. Moreover, we study relevant quantum-relativistic effects, like the Zitterbewegung and Klein’s paradox, the transition from massless to massive fermions, and the relativistic and nonrelativistic limits, via the tuning of controllable experimental parameters. Phys. Rev. Lett. 98, 253005 (2007). Selected as Suggestion by the PRL Editors. Highlighted in Pro-Physik.de
About 250 citations in Google Scholar Experimental realization of this proposal: R. Gerritsma, R. Blatt, C. F. Roos, ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - L. Lamata, J. J. García-Ripoll, and J. I. Cirac.
It is possible to achieve an arbitrary amount of entanglement between two atoms using only spontaneously emitted photons, linear optics, single-photon sources, and projective measurements. This is in contrast to all current experimental proposals for entangling two atoms, which are fundamentally restricted to one entanglement bit or “ebit.” Phys. Rev. Lett. Selected as Suggestion by the PRL Editors (1st Suggestion in PRL history, in appearance order). Highlighted in Nature Photonics (Research Highlights) and in PhysOrg.com ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - L. Lamata, J. León, D. Salgado, and E. Solano.
Inductive entanglement classification of four qubits under stochastic local operations and classical communication. Using an inductive approach to classify multipartite entangled states under stochastic local operations and classical communication introduced recently by the authors [ Phys. Rev. A 74 052336 (2006)], we give the complete classification of four-qubit entangled pure states. Apart from the expected degenerate classes, we show that there exist eight inequivalent ways to entangle four qubits. In this respect, permutation symmetry is taken into account and states with a structure differing only by parameters inside a continuous set are considered to belong to the same class.Phys. Rev. A. 75, 022318 (2007).More than 145 citations in Google Scholar ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - L. Lamata, D. Porras, J. I. Cirac, J. Goldman, and G. Gabrielse.
Entanglement of isolated elementary particles other than photons has not yet been achieved. We show how building blocks demonstrated with one trapped electron might be used to make a model system and method for entangling two electrons. Applications are then considered, including two-qubit gates and more precise quantum metrology protocols. Phys. Rev. A International collaboration between the Max-Planck Institute for Quantum Optics and Harvard University. Highlighted in Science News ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - L. Lamata, D. R. Leibrandt, I. L. Chuang, J. I. Cirac, M. D. Lukin, V. Vuletic, and S. F. Yelin.
A new approach for the realization of a quantum interface between single photons and single ions in an ion crystal is proposed and analyzed. In our approach the coupling between a single photon and a single ion is enhanced via the collective degrees of freedom of the ion crystal. Applications including single-photon generation, a memory for a quantum repeater, and a deterministic photon-photon, photon-phonon, or photon-ion entangler are discussed. Phys. Rev. Lett. International collaboration among the Max-Planck Institute for Quantum Optics, Harvard University, and the Massachusetts Institute of Technology. Related experiments to this proposal: i) Experiment performed at the Massachusetts Institute of Technology: M. Cetina, I. Chuang, V. Vuletic, New J. Phys. ii) Two experiments performed at the Innsbruck trapped ion group: B. Casabone, R. Blatt, T. E. Northup, Phys. Rev. Lett. B. Casabone, R. Blatt, T. E. Northup, Phys. Rev. Lett. 114, 023602 (2015). This experiment, which is the partial realization of my proposal (the step coupling a photon to a collective ionic excitation) has reached an Altmetrics of 73. See also the PhD Thesis of Bernardo Casabone, Universität Innsbruck, including a complete analysis of the experimental realization of the proposal. - J. Casanova, L. Lamata, I. L. Egusquiza, R. Gerritsma, C. F. Roos, J. J. Garcia-Ripoll, and E. Solano.
Quantum Simulation of Quantum Field Theories in Trapped Ions. 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. International collaboration among the University of the Basque Country, the Innsbruck Trapped Ion Group, and CSIC. Experimental realization of this proposal: Xiang Zhang, Kihwan Kim, et al.,
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - J. Casanova, A. Mezzacapo, L. Lamata, and E. Solano.
Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions. We propose a method of simulating efficiently many-body interacting fermion lattice models in trapped ions, including highly nonlinear interactions in arbitrary spatial dimensions and for arbitrarily distant couplings. We map products of fermionic operators onto nonlocal spin operators and decompose the resulting dynamics in efficient steps with Trotter methods, yielding an overall protocol that employs only polynomial resources. The proposed scheme can be relevant in a variety of fields such as condensed-matter or high-energy physics, where quantum simulations may solve problems intractable for classical computers. ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - A. Mezzacapo, J. Casanova, L. Lamata, and E. Solano.
Digital Quantum Simulation of the Holstein Model in Trapped IonsWe propose the implementation of the Holstein model by means of digital methods in a linear chain of trapped ions. We show how the simulation fidelity scales with the generation of phononic excitations. We propose a decomposition and a stepwise trapped-ion implementation of the Holstein Hamiltonian. Via numerical simulations, we study how the protocol is affected by realistic gates. Finally, we show how measurements of the size of the simulated polaron can be performed. Phys. Rev. Lett. - U. Alvarez-Rodriguez, J. Casanova, L. Lamata, and E. Solano.
Quantum Simulation of Noncausal Kinematic Transformations We propose the implementation of Galileo group symmetry operations or, in general, linear coordinate transformations in a quantum simulator. With an appropriate encoding, unitary gates applied to our quantum system give rise to Galilean boosts or spatial and time parity operations in the simulated dynamics. This framework provides us with a flexible toolbox that enhances the versatility of quantum simulation theory, allowing the direct access to dynamical quantities that would otherwise require full tomography. Furthermore, this method enables the study of noncausal kinematics and phenomena beyond special relativity in a quantum controllable system. Phys. Rev. Lett. Highlighted in Materia, the Bulletin of the Spanish Royal Physical Society, La Razón, and RTVE.es. --------------------------------------------------------------------------------------------------------------------------------------------------------------- - M.-H. Yung, J. Casanova, A. Mezzacapo, J. McClean, L. Lamata, A. Aspuru-Guzik, and E. Solano.
Over the last few decades, quantum chemistry has progressed through the development of computational methods based on modern digital computers. However, these methods can hardly fulfill the exponentially-growing resource requirements when applied to large quantum systems. As pointed out by Feynman, this restriction is intrinsic to all computational models based on classical physics. Recently, the rapid advancement of trapped-ion technologies has opened new possibilities for quantum control and quantum simulations. Here, we present an efficient toolkit that exploits both the internal and motional degrees of freedom of trapped ions for solving problems in quantum chemistry, including molecular electronic structure, molecular dynamics, and vibronic coupling. We focus on applications that go beyond the capacity of classical computers, but may be realizable on state-of-the-art trapped-ion systems. These results allow us to envision a new paradigm of quantum chemistry that shifts from the current transistor to a near-future trapped-ion-based technology. International collaboration between the University of the Basque Country and Harvard University. Highlighted in MIT Technology Review, PhysOrg, Nanowerk, ScienceDaily, and Naukas. Experimental realization of this proposal: Yangchao Shen, Man Hong Yung, Kihwan Kim, et al., Quantum implementation of the unitary coupled cluster for simulating molecular electronic structure, Phys. Rev. A 95, 020501(R) (2017).--------------------------------------------------------------------------------------------------------------------------------------------------------------- - U. Las Heras, A. Mezzacapo, L. Lamata, S. Filipp, A. Wallraff, and E. Solano.
We propose the implementation of a digital quantum simulator for prototypical spin models in a circuit quantum electrodynamics architecture. We consider the feasibility of the quantum simulation of Heisenberg and frustrated Ising models in transmon qubits coupled to coplanar waveguide microwave resonators. Furthermore, we analyze the time evolution of these models and compare the ideal spin dynamics with a realistic version of the proposed quantum simulator. Finally, we discuss the key steps for developing the toolbox of digital quantum simulators in superconducting circuits. 112, 200501 (2014).International collaboration between the University of the Basque Country and ETH Zurich. Experimental realization of this proposal performed at ETH Zurich in collaboration with UPV/EHU Bilbao and published in Y. Salathé et al., Digital Quantum Simulation of Spin Models with Circuit Quantum Electrodynamics, (see below) --------------------------------------------------------------------------------------------------------------------------------------------------------------- - A. Mezzacapo, L. Lamata, S. Filipp, and E. Solano.
The efficient implementation of many-body interactions in superconducting circuits allows for the realization of multipartite entanglement and topological codes, as well as the efficient simulation of highly correlated fermionic systems. We propose the engineering of fast multiqubit interactions with tunable transmon-resonator couplings. This dynamics is obtained by the modulation of magnetic fluxes threading superconducting quantum interference device loops embedded in the transmon devices. We consider the feasibility of the proposed implementation in a realistic scenario and discuss potential applications. 113, 050501 (2014).International collaboration between the University of the Basque Country and ETH Zurich. - S. Felicetti, M. Sanz, L. Lamata, G. Romero, G. Johansson, P. Delsing, and E. Solano
The phenomenon of quantum fluctuations, consisting in virtual particles emerging from vacuum, is central to understanding important effects in nature - for instance, the Lamb shift of atomic spectra and the anomalous magnetic moment of the electron. It was also suggested that a mirror undergoing relativistic motion could convert virtual into real photons. This phenomenon, denominated dynamical Casimir effect (DCE), has been observed in recent experiments with superconducting circuits. Here, we show that the physics underlying the DCE may generate multipartite quantum correlations. To achieve it, we propose a circuit quantum electrodynamics (cQED) scenario involving superconducting quantum interference devices (SQUIDs), cavities, and superconducting qubits, also called artificial atoms. Our results predict the generation of highly entangled states for two and three superconducting qubits in different geometric configurations with realistic parameters. This proposal paves the way for a scalable method of multipartite entanglement generation in cavity networks through dynamical Casimir physics. Phys. Rev. Lett. International collaboration between the University of the Basque Country and Chalmers University of Technology. Highlighted in the Image Gallery of American Physical Society March Meeting 2014, in Naukas, and in Taringa. - A. Mezzacapo, U. Las Heras, J. S. Pedernales, L. DiCarlo, E. Solano, and L. Lamata.
Digital Quantum Rabi and Dicke Models in Superconducting Circuits.We propose the analog-digital quantum simulation of the quantum Rabi and Dicke models using circuit quantum electrodynamics (QED). We find that all physical regimes, in particular those which are impossible to realize in typical cavity QED setups, can be simulated via unitary decomposition into digital steps. Furthermore, we show the emergence of the Dirac equation dynamics from the quantum Rabi model when the mode frequency vanishes. Finally, we analyze the feasibility of this proposal under realistic superconducting circuit scenarios. International collaboration between the University of the Basque Country and Delft University of Technology. Experimental realization of this proposal: N. K. Langford, L. DiCarlo, et al., Xiang Zhang, Yangchao Shen, Junhua Zhang, Jorge Casanova, Lucas Lamata, Enrique Solano, Man- Hong Yung, Jing-Ning Zhang, and Kihwan Kim.
The understanding of symmetry operations has brought enormous advancements in physics, ranging from elementary particle to condensed matter systems. In quantum mechanics, symmetry operations are described by either unitary or antiunitary operators, where the latter are unphysical transformations that cannot be realized in physical systems. So far, quantum simulators of unitary and dissipative processes, the only allowed physical dynamics, have been realized in key experiments. Here, we present an embedding quantum simulator able to encode unphysical operations in a multilevel single trapped ion. In this sense, we experimentally observe phenomena associated with the nonunitary Majorana dynamics and implement antiunitary symmetry operations, i.e., time reversal and charge conjugation, at arbitrary evolution times. These experiments enhance the toolbox of quantum simulations towards applications involving unphysical operations. Nature Commun. International collaboration among the University of the Basque Country, Universität Ulm, and Tsinghua University. Highlighted in the Dean's Vision of Tsinghua University, Beijing, China, the Press Office from UPV/EHU, Catalunya Vanguardista, 100TEK, Tendencias21, La Razón, Cultura Científica, Science Daily, Phys Org, Demanjo, Eurekalert, Tech Times, Space Daily, Sabías.es, R&D, Brightsurf, Nanotechnology Now, Engineering Evil, Science Codex, AzoQuantum, ChemEurope, AlphaGalileo, Nanotechnology World Association, Health Medicine Network, and Europa Press. - U. Alvarez-Rodriguez, M. Sanz, L. Lamata, and E. Solano.
Quantum information provides fundamentally different computational resources than classical information. We prove that there is no unitary protocol able to add unknown quantum states belonging to different Hilbert spaces. This is an inherent restriction of quantum physics that is related to the impossibility of copying an arbitrary quantum state, i.e., the no-cloning theorem. Moreover, we demonstrate that a quantum adder, in absence of an ancillary system, is also forbidden for a known orthonormal basis. This allows us to propose an approximate quantum adder that could be implemented in the lab. Finally, we discuss the distinct character of the forbidden quantum adder for quantum states and the allowed quantum adder for density matrices. Highlighted in MIT Technology Review. Experimental realization of a probabilistic quantum adder based on these concepts performed at University of Science and Technology of China, Hefei: Xiao-Min Hu, Guang-Can Guo, Yong-Sheng Zhang, et al., as well as an experiment at the Institute for Quantum Computing in Canada, Keren Li, Raymond Laflamme, et al., Phys. Rev. A and an experiment at Technische Universität Dortmund, in collaboration with Chennai, Shruti Dogra, George Thomas, Sibasish Ghosh, and Dieter Suter, arXiv:1702.02418 See also the proposal by Oszmaniec et al., PRL'16. - L. García-Álvarez, J. Casanova, A. Mezzacapo, I. L. Egusquiza, L. Lamata, G. Romero, and E. Solano
We propose a digital-analog quantum simulation of fermion-fermion scattering mediated by a continuum of bosonic modes within a circuit quantum electrodynamics scenario. This quantum technology naturally provides strong coupling of superconducting qubits with a continuum of electromagnetic modes in an open transmission line. In this way, we propose qubits to efficiently simulate fermionic modes via digital techniques, while we consider the continuum complexity of an open transmission line to simulate the continuum complexity of bosonic modes in quantum field theories. Therefore, we believe that the complexity-simulating-complexity concept should become a leading paradigm in any effort towards scalable quantum simulations. - R. Barends, L. Lamata, J. Kelly, L. García-Álvarez, A. G. Fowler, A. Megrant, E. Jeffrey, T. C. White, D. Sank, J. Y. Mutus, B. Campbell, Yu Chen, Z. Chen, B. Chiaro, A. Dunsworth, I.-C. Hoi, C. Neill, P. J. J. O'Malley, C. Quintana, P. Roushan, A. Vainsencher, J. Wenner, E. Solano, and John M. Martinis
One of the key applications of quantum information is simulating nature. Fermions are ubiquitous in nature, appearing in condensed matter systems, chemistry and high energy physics. However, universally simulating their interactions is arguably one of the largest challenges, because of the difficulties arising from anticommutativity. Here we use digital methods to construct the required arbitrary interactions, and perform quantum simulation of up to four fermionic modes with a superconducting quantum circuit. We employ in excess of 300 quantum logic gates, and reach fidelities that are consistent with a simple model of uncorrelated errors. The presented approach is in principle scalable to a larger number of modes, and arbitrary spatial dimensions. Nature Commun. 6, 7654 (2015). International collaboration among the University of the Basque Country, Google, and the University of California Santa Barbara. About 80 citations in Google Scholar. Highlighted in Google Research Blog, La Oficina de Comunicación de la UPV/EHU, Noticias de la Ciencia y la Tecnología, El Mundo, ABC, El Correo, EFE Futuro, Catalunya Vanguardista, Universia, Ikerbasque News, El Diario Vasco, CICNetwork, AlphaGalileo, PhysOrg, AzoQuantum, Science Daily, and Deia. Experimental realization of: U. Las Heras, L. García-Álvarez, A. Mezzacapo, E. Solano, and L. Lamata,
- Y. Salathé, M. Mondal, M. Oppliger, J. Heinsoo, P. Kurpiers, A. Potocnik, A. Mezzacapo, U. Las Heras, L. Lamata, E. Solano, S. Filipp, and A. Wallraff.
Systems of interacting quantum spins show a rich spectrum of quantum phases and display interesting many-body dynamics. Computing characteristics of even small systems on conventional computers poses significant challenges. A quantum simulator has the potential to outperform standard computers in calculating the evolution of complex quantum systems. Here, we perform a digital quantum simulation of the paradigmatic Heisenberg and Ising interacting spin models using a two transmon-qubit circuit quantum electrodynamics setup. We make use of the exchange interaction naturally present in the simulator to construct a digital decomposition of the model-specific evolution and extract its full dynamics. This approach is universal and efficient, employing only resources which are polynomial in the number of spins and indicates a path towards the controlled simulation of general spin dynamics in superconducting qubit platforms. Phys. Rev. X International collaboration between the University of the Basque Country and ETH Zurich. Experimental realization of: U. Las Heras, A. Mezzacapo, L. Lamata, S. Filipp, A. Wallraff, and E. Solano. Phys. Rev. Lett.
- M. Sanz, I. L. Egusquiza, R. Di Candia, H. Saberi, L. Lamata, and E. Solano
Entanglement classification with matrix product statesWe propose an entanglement classification for symmetric quantum states based on their diagonal matrix-product-state (MPS) representation. The proposed classification, which preserves the stochastic local operation assisted with classical communication (SLOCC) criterion, relates entanglement families to the interaction length of Hamiltonians. In this manner, we establish a connection between entanglement classification and condensed matter models from a quantum information perspective. Moreover, we introduce a scalable nesting property for the proposed entanglement classification, in which the families for - U. Alvarez-Rodriguez, M. Sanz, L. Lamata, and E. Solano
Artificial Life in Quantum TechnologiesWe develop a quantum information protocol that models the biological behaviors of individuals living in a natural selection scenario. The artificially engineered evolution of the quantum living units shows the fundamental features of life in a common environment, such as self-replication, mutation, interaction of individuals, and death. We propose how to mimic these bio-inspired features in a quantum-mechanical formalism, which allows for an experimental implementation achievable with current quantum platforms. This result paves the way for the realization of artificial life and embodied evolution with quantum technologies. Highlighted in MIT Technology Review, the Press Office from UPV/EHU, Catalunya Vanguardista, La Tribuna del País Vasco, Notinet, Salud en tu vida, Physics4TheCool, Ikerbasque News, Scientific American, Cultura Científica, El Correo, and El Mundo. More than 1000 downloads in the first 2 days after publication. - A. Mezzacapo, E. Rico, C. Sabín, I. L. Egusquiza, L. Lamata, and E. Solano
Non-Abelian SU(2) Lattice Gauge Theories in Superconducting CircuitsWe propose a digital quantum simulator of non-Abelian pure-gauge models with a superconducting circuit setup. Within the framework of quantum link models, we build a minimal instance of a pure International collaboration among the University of the Basque Country, IBM, and the University of Nottingham.
- Tao Xin, Julen S. Pedernales, Lucas Lamata, Enrique Solano, and Gui-Lu Long.
Measurement of Linear Response Functions in NMR.We measure multi-time correlation functions of a set of Pauli operators on a two-level system, which can be used to retrieve its associated linear response functions. The two-level system is an effective spin constructed from the nuclear spins of International collaboration between the University of the Basque Country and Tsinghua University, Beijing.
- L. García-Álvarez, U. Las Heras, A. Mezzacapo, M. Sanz, E. Solano, and L. Lamata.
Quantum chemistry and charge transport in biomolecules with superconducting circuits.We propose an efficient protocol for digital quantum simulation of quantum chemistry problems and enhanced digital-analog quantum simulation of transport phenomena in biomolecules with superconducting circuits. Along these lines, we optimally digitize fermionic models of molecular structure with single-qubit and two-qubit gates, by means of Trotter-Suzuki decomposition and Jordan-Wigner transformation. Furthermore, we address the modelling of system-environment interactions of biomolecules involving bosonic degrees of freedom with a digital-analog approach. Finally, we consider gate-truncated quantum algorithms to allow the study of environmental effects.
- I. Arrazola, J. S. Pedernales, L. Lamata, and E. Solano.
We propose a method to simulate spin models in trapped ions using a digital-analog approach, consisting in a suitable gate decomposition in terms of analog blocks and digital steps. In this way, we show that the quantum dynamics of an enhanced variety of spin models could be implemented with substantially less number of gates than a fully digital approach. Typically, analog blocks are built of multipartite dynamics providing the complexity of the simulated model, while the digital steps are local operations bringing versatility to it. Finally, we describe a possible experimental implementation in trapped-ion technologies.
- L. Lamata
We propose a digital-analog quantum simulation of generalized Dicke models with superconducting circuits, including Fermi-Bose condensates, biased and pulsed Dicke models, for all regimes of light-matter coupling. We encode these classes of problems in a set of superconducting qubits coupled with a bosonic mode implemented by a transmission line resonator. Via digital-analog techniques, an efficient quantum simulation can be performed in state-of-the-art circuit quantum electrodynamics platforms, by suitable decomposition into analog qubit-bosonic blocks and collective single-qubit pulses through digital steps. Moreover, just a single global analog block would be needed during the whole protocol in most of the cases, superimposed with fast periodic pulses to rotate and detune the qubits. Therefore, a large number of digital steps may be attained with this approach, providing a reduced digital error. Additionally, the number of gates per digital step does not grow with the number of qubits, rendering the simulation efficient. This strategy paves the way for the scalable digital-analog quantum simulation of many-body dynamics involving bosonic modes and spin degrees of freedom with superconducting circuits.
- L. Lamata
Superconducting circuit technologies have recently achieved quantum protocols involving closed feedback loops. Quantum artificial intelligence and quantum machine learning are emerging fields inside quantum technologies which may enable quantum devices to acquire information from the outer world and improve themselves via a learning process. Here we propose the implementation of basic protocols in quantum reinforcement learning, with superconducting circuits employing feedback-loop control. We introduce diverse scenarios for proof-of-principle experiments with state-of-the-art superconducting circuit technologies and analyze their feasibility in presence of imperfections. The field of quantum artificial intelligence implemented with superconducting circuits paves the way for enhanced quantum control and quantum computation protocols.
- R. Barends, A. Shabani, L. Lamata, J. Kelly, A. Mezzacapo, U. Las Heras, R. Babbush, A. G. Fowler, B. Campbell, Yu Chen, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, E. Lucero, A. Megrant, J. Y. Mutus, M. Nee- ley, C. Neill, P. J. J. O’Malley, C. Quintana, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, E. Solano, H. Neven, and John M. Martinis.
Digitized adiabatic quantum computing with a superconducting circuit.Quantum mechanics can help to solve complex problems in physics and chemistry, provided they can be programmed in a physical device. In adiabatic quantum computing, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing, which enables the construction of arbitrary interactions and is compatible with error correction, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable. International collaboration among the University of the Basque Country, Google, and the University of California Santa Barbara. More than 70 citations in Google Scholar. Highlighted in Google Research Blog, Nature News, MIT Technology Review, Scientific American, Physics World, the Press Office from the University of the Basque Country, ComputerWorld, PC World, ABC, Inside Science, Catalunya Vanguardista, ACM, AlphaGalileo, EFE Futuro, Noticias de la Ciencia, Datacentre Management, Europa Press, TechWorld, RealClearScience, PhysOrg, ZDNet, FossBytes, NHVoice, I4U News, Eurekalert, Futurism, Bioportfolio, CIO, 20minutos, Noodls, NextBigFuture, El Diario, La Información, Gente, ScienceCodex, Zedie, Electronic Specifier, El Tuxtepecano, DifusionLibre, ScienMag, MyInforms, ScienceNewsLine, LifeBoat, HealthMedicinet, Ecodiario, Alante, El Correo, and El Pais. Altmetrics: 315 According to Nature Index, this article was one of the 5 papers with largest Altmetrics from the University of the Basque Country in the period August 1st 2015-31st July 2016. More than 10,000 downloads in 9 months Image credit: Julian Kelly, Google Inc. Last Modified 9.5.2017 © 2007-2017 Lucas Lamata |