#### The sixth biennial John Stewart Bell Prize for Research on Fundamental Issues in Quantum Mechanics and Their Applications is awarded to Ignacio Cirac (Max Planck Institute for Quantum Optics) and Peter Zoller (University of Innsbruck) for their recent groundbreaking proposals in quantum optics and atomic physics on how to engineer quantum systems to carry out novel information processing tasks, in particular for extending the applications of quantum simulators to lattice gauge theories, showing how long range entanglement can be estimated via statistical measurements, and using Projected Entangled Pair States for the theoretical study of quantum many body systems.

The second quantum revolution, in which we aim to engineer quantum systems to do novel information processing tasks, is fully under way. The rate of progress, both theoretical and experimental, is breathtaking. Novel proposals of how to engineer quantum systems are put forward and then demonstrated experimentally. Our theoretical understanding of complex quantum systems improves continuously. This continuous progress may soon give rise to the emergence of a whole new industry.

Ignacio Cirac and Peter Zoller are the driving force behind this tremendous progress. Their current work sets the agenda for the development of the whole field for years to come. Their elegant and original ideas open up whole new areas which will be investigated experimentally for many years, even decades.

The limited space we have here does not allow us to do justice to all their recent contributions. We highlight a selected few covering the areas of quantum simulators, novel methods to manipulate systems at the quantum level, as well as more abstract contributions to many body quantum systems.

Quantum simulators allow one to study in the laboratory many body quantum systems which are impossible to study numerically. A key recent advance was to show that quantum simulators could be adapted to lattice gauge theories. Theoretical proposals were put forward, see (1-5) plus several follow up papers, and a first experimental demonstration subsequently reported (6), see also the review (A). A related approach is to engineer synthetic gauge fields, as in the experimental demonstration of chiral edge states (7). The importance of these works is that they considerably expand the area of applicability of quantum simulators, and their potential impact. Indeed, they can now be applied to the whole area of elementary particle physics (described by lattice gauge theories), thereby establishing a bridge between these two areas of science, and presenting a potential new route to resolve longstanding open questions in particle physics.

Quantum simulators can also be used to investigate many questions in many body quantum physics and solid state physics. Proposals for detecting and engineering topological states using quantum simulators were put forward in (8,9), see the review (B). Topological order is a new form of matter in which long range topological order emerges from purely local interactions. The generation and propagation of quasiparticles was demonstrated in (10) which allows the investigation of entanglement propagation, transport phenomena, thermalisation. Methods for simulating exotic magnetic systems were proposed in (11). An experimental demonstration of exotic many-body quantum phases was reported in (12).

A key difficulty in quantum simulators is to efficiently characterize the underlying quantum state, for instance by measuring global observables such as its entanglement. Major progress on this question was made in (13) and using another approach based on Rényi entropies in (14) and several follow up papers. These works show that long range entanglement can be estimated via statistical measurements, and are of huge impact for experimental groups working on large qubit registers, such as optical lattices and trapped ions.

Novel proposals on how to manipulate systems at the quantum level lead to the emergence of whole new areas of experimental investigation. Ignacio Cirac and Peter Zoller have made many highly influential such proposals. Recent contributions include the self-organization of atoms along a nanophotonic waveguide (20) which provides a novel route to probe many body quantum systems; methods to decrease the separation of atoms in quantum simulators which would make them more efficient and allow new systems to be simulated, either by coupling superconducting lattices and atomic arrays (21) or using photonic crystal structures (22); novel methods to exploit spin-spin interactions in diamond nanostructures thereby creating large spin squeezing with potential applications in magnetometry and quantum information processing with spin qubits (23); interaction of single photons via optomechanical systems (25); applications of chiral quantum optics (24) (see the review C) which opens fundamentally new functionalities in quantum optics, in particular for constructing complex quantum circuits and networks. The strong coupling between freely propagating photons and quantum emitters is a new regime of quantum optics which is being explored experimentaly andfor which a theoretical framework was developed in (26,27,28).

Tensor networks, and in particular Projected Entangled Pair States (PEPS), are a powerful tool for the study of quantum many body physics, thanks to both their built-in ability of classifying and studying symmetries, and the efficient numerical calculations they allow. It is now possible to extend this method to include local gauge symmetries (30,31), including in the presence of fermionic matter (32). These methods allow one to probe the phase diagrams and dynamical phenomena of gauge invariant systems.

For the past 2 decades Ignacio Cirac and Peter Zoller, through their elegant proposals, have set the worldwide agenda for the development of quantum science and technologies. In 1995 they proposed the first realistic model of a quantum computer based on trapped ions. In 1998 they proposed a realistic approach for simulation of many body quantum systems in atomic lattices. They subsequently proposed the idea of quantum repeaters which are essential for the development of long distance quantum communication, contributed key ideas to understanding of many body entanglement, pioneered the use of quantum information tools to study many body quantum systems, as well as countless additional contributions to quantum optics and atomic physics. Their current work continues to set the worldwide agenda for the future development of quantum science and technologies. The ongoing second quantum revolution would be unfolding much slower, both now and in the forseable future, without their contributions.

**References to the work for which the prize is being awarded:**

(1) Quantum simulations of gauge theories with ultracold atoms: Local gauge invariance from angular-momentum conservation E Zohar, JI Cirac, B Reznik, Physical Review A 88, 023617 (2013).

(2) Cold-atom quantum simulator for su (2) yang-mills lattice gauge theory E Zohar, JI Cirac, B Reznik, Physical review letters 110, 125304 (2013).

(3) Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories D Banerjee, M Bögli, M Dalmonte, E Rico, P Stebler, UJ Wiese, P Zoller, Physical review letters 110 (12), 125303 (2013).

(4) Constrained dynamics via the Zeno effect in quantum simulation: Implementing non-Abelian lattice gauge theories with cold atoms K Stannigel, P Hauke, D Marcos, M Hafezi, S Diehl, M Dalmonte, P Zoller, Physical review letters 112 (12), 120406 (2014).

(5) Superconducting circuits for quantum simulation of dynamical gauge fields D Marcos, P Rabl, E Rico, P Zoller, Physical review letters 111 (11), 110504 (2013).

(6) Real-time dynamics of lattice gauge theories with a few-qubit quantum computer EA Martinez, CA Muschik, P Schindler, D Nigg, A Erhard, M Heyl, Philipp Hauke, Marcello Dalmonte, Thomas Monz, Peter Zoller, Rainer Blatt, Nature 534 (7608), 516 (2016).

(7) Observation of chiral edge states with neutral fermions in synthetic Hall ribbons M Mancini, G Pagano, G Cappellini, L Livi, M Rider, J Catani, C Sias, Science 349 (6255), 1510-1513.

(8) Topology by dissipation CE Bardyn, MA Baranov, CV Kraus, E Rico, A İmamoğlu, P Zoller, S Diehl, New Journal of Physics 15 (8), 085001.

(9) Direct imaging of topological edge states in cold-atom systems N Goldman, J Dalibard, A Dauphin, F Gerbier, M Lewenstein, P Zoller, Proceedings of the National Academy of Sciences 110 (17), 6736-6741 (2013).

(9B) Topological quantum optics in two-dimensional atomic arrays J Perczel, J Borregaard, DE Chang, H Pichler, SF Yelin, P Zoller, Physical review letters 119 (2), 023603 (2017).

(10) Quasiparticle engineering and entanglement propagation in a quantum many-body system P Jurcevic, BP Lanyon, P Hauke, C Hempel, P Zoller, R Blatt, CF Roos, Nature 511 (7508), 202 (2014).

(11) Designing frustrated quantum magnets with laser-dressed Rydberg atoms AW Glaetzle, M Dalmonte, R Nath, C Gross, I Bloch, P Zoller, Physical review letters 114 (17), 173002 (2015).

(12) Extended Bose-Hubbard models with ultracold magnetic atoms S Baier, MJ Mark, D Petter, K Aikawa, L Chomaz, Z Cai, M Baranov, Science 352 (6282), 201-205.

(13) Measuring multipartite entanglement through dynamic susceptibilities P Hauke, M Heyl, L Tagliacozzo, P Zoller, Nature Physics 12 (8), 778 (2016).

(14) Rényi entropies from random quenches in atomic hubbard and spin models A Elben, B Vermersch, M Dalmonte, JI Cirac, P Zoller, Physical review letters 120 (5), 050406 (2018).

(20) Self-organization of atoms along a nanophotonic waveguide DE Chang, JI Cirac, HJ Kimble, Physical review letters 110 (11), 113606 (2013).

(21) Superconducting vortex lattices for ultracold atoms O Romero-Isart, C Navau, A Sanchez, P Zoller, JI Cirac, Physical review letters 111 (14), 145304 (2013).

(22) Subwavelength vacuum lattices and atom–atom interactions in two-dimensional photonic crystals A González-Tudela, CL Hung, DE Chang, JI Cirac, HJ Kimble Nature Photonics 9 (5), 320 (2015).

(23) Phonon-induced spin-spin interactions in diamond nanostructures: application to spin squeezing SD Bennett, NY Yao, J Otterbach, P Zoller, P Rabl, MD Lukin, Physical review letters 110 (15), 156402 (2013).

(24) Quantum optics of chiral spin networks H Pichler, T Ramos, AJ Daley, P Zoller, Physical Review A 91, 042116 (2015).

(25) Single-photon nonlinearities in two-mode optomechanics P Komar, SD Bennett, K Stannigel, SJM Habraken, P Rabl, P Zoller, M D Lukin, Physical Review A 87 (1), 013839 (2013).

(26) Quantum dynamics of propagating photons with strong interactions: a generalized input–output formalism T Caneva, MT Manzoni, T Shi, JS Douglas, JI Cirac, DE Chang, New Journal of Physics 17 (11), 113001 (2015).

(27) Multiphoton-scattering theory and generalized master equations T Shi, DE Chang, JI Cirac Physical Review A 92 (5), 053834 (2015).

(28) Quantum emitters in two-dimensional structured reservoirs in the nonperturbative regime A González-Tudela, JI Cirac, Physical review letters 119 (14), 143602 (2017).

(30) Real-time dynamics in u (1) lattice gauge theories with tensor networks T Pichler, M Dalmonte, E Rico, P Zoller, S Montangero, Physical Review X 6 (1), 011023 (2016).

(31) Gauging quantum states: from global to local symmetries in many-body systems J Haegeman, K Van Acoleyen, N Schuch, JI Cirac, F Verstraete, Physical Review X 5 (1), 011024 (2015).

(32) Fermionic projected entangled pair states and local u (1) gauge theories E Zohar, M Burrello, TB Wahl, JI Cirac, Annals of Physics 363, 385-439 (2015).

**Further Reading**

(A) Zohar, Erez, J. Ignacio Cirac, and Benni Reznik. "Quantum simulations of lattice gauge theories using ultracold atoms in optical lattices." Reports on Progress in Physics 79.1 (2015): 014401.

(B) Topological quantum matter with ultracold gases in optical lattices N Goldman, JC Budich, P Zoller Nature Physics 12 (7), 639 (2016).

(C) Chiral quantum optics P Lodahl, S Mahmoodian, S Stobbe, A Rauschenbeutel, P Schneeweiss, ... Nature 541 (7638), 473.

(D) Schollwöck, U. (2011). The density-matrix renormalization group in the age of matrix product states. Annals of Physics, 326(1), 96-192.

(E) Bloch, I., Dalibard, J., & Nascimbene, S. (2012). Quantum simulations with ultracold quantum gases. Nature Physics, 8(4), 267.