PRX QUANTUM 2, 017003 (2021) Roadmap

Quantum Simulators: Architectures and Opportunities

Ehud Altman,1 Kenneth R. Brown,2 Giuseppe Carleo,3,† Lincoln D. Carr ,4,* Eugene Demler,5 Cheng Chin,6 Brian DeMarco,7 Sophia E. Economou,8 Mark A. Eriksson,9 Kai-Mei C. Fu,10 Markus Greiner,5 Kaden R.A. Hazzard,11 Randall G. Hulet,11 Alicia J. Kollár,12 Benjamin L. Lev,13 Mikhail D. Lukin,5 Ruichao Ma,14 Xiao Mi,15 Shashank Misra,16 Christopher Monroe,12 Kater Murch,17 Zaira Nazario,18 Kang-Kuen Ni,19 Andrew C. Potter,20 Pedram Roushan,15 Mark Saffman,9 Monika Schleier-Smith,13 Irfan Siddiqi,1 Raymond Simmonds,21 Meenakshi Singh,4 I.B. Spielman,12 Kristan Temme,18 David S. Weiss,22 Jelena Vuckoviˇ c,´ 23 Vladan Vuletic,´ 24 Jun Ye,25 and Martin Zwierlein24 1 Department of Physics, University of California, Berkeley, Carolina 94720, USA 2 Department of Electrical and Computer Engineering, Department of Physics, and Department of Chemistry, Duke University, Durham, North Carolina 27708, USA 3 Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA 4 Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA 5 Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA 6 Department of Physics, Chicago University, Chicago, Illinois 60637, USA 7 Department of Physics and IQUIST, University of Illinois, Urbana-Champaign, Illinois 61801, USA 8 Department of Physics, Virgina Tech, Blacksburg, Virginia 24061, USA 9 Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA 10 Department of Electrical and Computer Engineering and Department of Physics, University of Washington, Seattle, Washington 98195, USA 11 Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA 12 Joint Quantum Institute and Department of Physics, University of Maryland, College Park, Maryland 20742, USA and IonQ, Inc., College Park, Maryland 20740, USA 13 Department of Physics and Department of Applied Physics, Stanford University, Stanford, California 94305, USA 14 Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA 15 Google, Inc., Santa Barbara, California 93101, USA 16 Sandia National Laboratory, Albuquerque, New Mexico 87123, USA 17 Department of Physics, Washington University, St. Louis, Missouri 63130, USA 18 IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA 19 Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA 20 Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA 21 National Institute of Standards and Technology, Boulder, Colorado 80305, USA 22 Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA 23 Department of Electrical Engineering and Ginzton Laboratory, Stanford University, Stanford, California 94305, USA 24 Center for Ultracold Atoms, Research Laboratory of Electronics, and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 25 JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309, USA

(Received 20 December 2019; accepted 21 October 2020; published 24 February 2021)

*[email protected] †Present address: Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

2691-3399/21/2(1)/017003(19) 017003-1 Published by the American Physical Society EHUD ALTMAN et al. PRX QUANTUM 2, 017003 (2021)

Quantum simulators are a promising technology on the spectrum of quantum devices from special- ized quantum experiments to universal quantum computers. These quantum devices utilize entanglement and many-particle behavior to explore and solve hard scientific, engineering, and computational prob- lems. Rapid development over the last two decades has produced more than 300 quantum simulators in operation worldwide using a wide variety of experimental platforms. Recent advances in several physical architectures promise a golden age of quantum simulators ranging from highly optimized special purpose simulators to flexible programmable devices. These developments have enabled a convergence of ideas drawn from fundamental physics, computer science, and device engineering. They have strong potential to address problems of societal importance, ranging from understanding vital chemical processes, to enabling the design of new materials with enhanced performance, to solving complex computational problems. It is the position of the community, as represented by participants of the National Science Foundation work- shop on “Programmable Quantum Simulators,” that investment in a national quantum simulator program is a high priority in order to accelerate the progress in this field and to result in the first practical applica- tions of quantum machines. Such a program should address two areas of emphasis: (1) support for creating quantum simulator prototypes usable by the broader scientific community, complementary to the present universal quantum computer effort in industry; and (2) support for fundamental research carried out by a blend of multi-investigator, multidisciplinary collaborations with resources for quantum simulator soft- ware, hardware, and education. This document is a summary from a U.S. National Science Foundation supported workshop held on 16–17 September 2019 in Alexandria, VA. Attendees were charged to identify the scientific and community needs, opportunities, and significant challenges for quantum simulators over the next 2–5 years.

DOI: 10.1103/PRXQuantum.2.017003

I. EXECUTIVE SUMMARY National leadership in quantum information science and engineering can be significantly bolstered by advanc- Recent technical advances have brought us closer to ing this technology toward platforms that tackle pressing realizing practical quantum simulators: engineered quan- fundamental and applied problems. We envision the cre- tum many-particle systems that can controllably simulate ation of a robust ecosystem in this area that spans all complex quantum phenomena. Quantum simulators can sectors. Academic researchers will excel at stimulating address questions across many domains of physics and technical and scientific breakthroughs, industry will lead scales of nature, from the behavior of solid-state mate- transitioning research to commercial-scale systems for rials and devices, to chemical and biochemical reaction widespread availability, while national laboratories will dynamics, to the extreme conditions of particle physics and contribute to shaping a large-scale research and develop- cosmology that cannot otherwise be readily probed in ter- ment effort, across the boundaries of traditional disciplines. restrial laboratories [1]. These state-of-the-art experiments Industry, universities, and national labs will collaborate involve the control of up to millions of quantum elements to focus on problems aligned with the long-term inter- and are implemented on a wide variety of atomic, molec- ests of end users and society. Successful realization of this ular, optical, and solid-state platforms. Each architecture unique opportunity requires a dedicated national quantum is characterized by strengths and weaknesses for solving simulator program. particular classes of quantum problems. Simulators run the gamut from special purpose to highly programmable We believe that realizing the ultimate potential of quan- devices. These systems have the potential to fill a critical tum simulators requires creating such a national pro- gap between conventional supercomputers—which cannot gram centered around two main pillars. (1) Early proto- efficiently simulate many-particle quantum systems—and type quantum simulators will support the development, fault-tolerant scalable digital quantum computers, which realization, and deployment of complementary quantum may be decades away. At the same time, there are sig- simulator prototypes. They will leverage—rather than nificant opportunities for codevelopment of the science duplicate—the substantial industrial investment in tech- and technology underlying both quantum simulators and nologies and software for digital quantum computing fault-tolerant quantum computers. toward realistic, near-term simulator machines. This strat- Many years of progress by single investigators have egy will promote and establish access to the most mature evolved the field to a tipping point where investing architectures, and the software to operate them, by the in programs that bring together experimental scientists, broader scientific community to foster and accelerate prac- theorists, computer scientists, and engineers will yield tical quantum simulations. (2) New, emerging quantum increasingly high returns and transformational outcomes. simulators will support creative, cutting-edge research

017003-2 QUANTUM SIMULATORS... PRX QUANTUM 2, 017003 (2021) in science and engineering to uncover new paradigms, environmental isolation are opening new directions of advance nascent hardware platforms, and develop new study in these systems, including far-from-equilibrium algorithms and applications for a new generation of quan- many-body physics and large-scale entanglement. For tum simulators. This effort will further support the devel- example, novel ordering of spins was observed in a col- opment of new materials and devices to help accelerate lection of over 50 Rydberg atoms held in optical tweez- the progress of new technologies and push them outside ers [12], a many-body order parameter was measured the research laboratory. Here we document the opportuni- with over 50 trapped atomic ions to show the behav- ties and challenges in quantum simulators and explain our ior of a dynamical phase transition [13], and there has vision for accelerating the evolution of and capitalizing been impressive progress toward demonstrating quantum on this promising quantum technology via this two-pillar advantage and supremacy in superconducting circuits [14]. approach. Quantum simulations with ultracold fermionic atoms in optical lattices simulate condensed matter Hubbard mod- els, and are shedding light onto pseudogap [15] and strange II. INTRODUCTION metal physics [16,17]. Meanwhile, novel quantum simula- Quantum simulators strive to solve scientific problems tor architectures—e.g., gated quantum dots and photonic that are not tractable by other means. For the purposes of arrays—are on the cusp of opening unique and important this article, we define a quantum simulator as “a quantum new areas of investigation, such as modeling many-body device that utilizes entanglement and other many-particle quantum transport in engineered reservoirs and predicting quantum phenomena to explore and solve hard scien- properties of quantum complex networks for a quantum tific, engineering, and computational problems.” Quantum internet [18,19]. simulators can be realized via different approaches, includ- Progress on advancing quantum simulation techniques ing highly tunable “analog” systems that naturally realize will be heralded by finer control over bulk systems and the physics problem of interest, or more digital methods scaling addressable systems to work with a larger num- that employ external control fields to produce non-native ber of particles. Both approaches have already established Hamiltonian evolution. Recent advances in several physi- a frontier: understanding quantum simulators even at the cal architectures promise a golden age ranging from highly 40–50 qubit scale is beyond direct brute-force diagonal- optimized special-purpose quantum simulators to flexible ization methods on classical computers. Scaling exist- and fully programmable devices. These developments are ing bottom-up quantum simulators to hundreds or even enabled by a convergence of ideas drawn from fundamen- thousands of interacting, entangled, and well-controlled tal physics, computer science, and device engineering. quantum elements is realistically within reach. Starting around 2002 [2], early implementations of Achieving more advanced quantum simulation tech- ultracold-atom-gas-based quantum simulators began to niques will impact a wide range of fundamental and shed light on a range of long-standing problems such applied science and engineering. Efforts to create new as quantum phase transitions, strongly interacting bosons materials by design will benefit from validated models and fermions [3], the quark-gluon plasma, neutron stars, of strongly correlated solids. New materials will offer and the only measured quantitative new predictions from potentially transformative properties, such as enhanced string theory (via holographic duality) [4]. Quantum simu- high-temperature superconductivity, topological excita- lators have led to discoveries of unanticipated dynamical tions, unprecedented functionality for energy transport and quantum many-body phenomena not governed by ther- storage, more efficient transistors, and advanced sens- modynamic laws [5], and even realized systems without ing technologies, as well as fundamentally new materials natural analogs such as hyperbolic spacetimes [6] and syn- possessing properties with yet-to-be-conceived applica- thetic dimensions [7,8]. Since many of these discoveries tions. Better understanding of nonequilibrium phenom- extend beyond what can be efficiently simulated exactly ena could lead to methods for generating light-induced on a classical computer, quantum simulators are believed topology and superconductivity, new techniques for con- to exhibit a form of “quantum advantage” for computation. trol over chemical reaction kinetics, novel approaches to Bulk-gas neutral atom experiments involving millions build robust quantum sensors for fundamental physics of particles [4,9], enabling precision thermodynamic mea- [20] and to enhance nonlinear optical response, a more surements, e.g., on strongly interacting fermionic matter complete theory of the quantum origin of thermody- [10,11], are complemented by more bottom-up approaches namics, and new insights into quantum gravity and with fully resolved control over smaller numbers of ele- lattice gauge theory. Applications to computer science ments. Highly coherent quantum systems consisting of could include hybrid digital-analog quantum comput- 50 or more individually addressed quantum elements ing, quantum approaches to combinatorial optimization have been created with superconducting circuits, trapped problems, and quantum machine learning [21]. Realizing ions, and atom arrays. Recent improvements in mate- this promise requires convergence of multidisciplinary rials, engineering, quantum control, measurement, and experimental theoretical work, including engineering

017003-3 EHUD ALTMAN et al. PRX QUANTUM 2, 017003 (2021) expertise throughout the design, implementation, and pro- developing new materials and device fabrication tech- cess deployment. niques to improve coherence, and work toward improving Fundamental research by single-investigator groups the programmability and scalability of quantum simulator continues to generate important advances in quantum sim- platforms. ulation. Given the diversity of possibilities, and unpre- dictable nature of how quantum simulation will advance, it is essential to foster such research. However, quickly tran- sitioning from fundamental research to mature develop- The remainder of this paper is organized as follows. In Sec. ments ready for widespread availability, while maintaining III we detail the opportunities and challenges for quantum alignment with the long-term interest of end users, requires simulators to explore a range of key scientific problems. In support and coordination best fueled by the creation of an Sec. IV we provide an overview of existing quantum sim- interdisciplinary, multiorganization, and multi-investigator ulator platform architectures. In Sec. V we address critical convergence accelerator program. Such a program will requirements to produce reliable simulators, particularly break down barriers among disciplines, achieve a cross tunability, programmability, and verifiability. In Sec. VI pollination of ideas, and provide a coordination of effort we describe the community structures that can take quan- that is essential for making rapid progress in the real- tum simulators to the next level, including the formation ization of practical simulators, especially those usable of a quantum hub internet resource for quantum simu- by the broader community outside of single-investigator lator hardware, software, and education. Conclusions are groups. provided in Sec. VII. We envision a convergence accelerator program sup- ported by two main pillars.

III. USING QUANTUM SIMULATORS TO (1) Early prototype quantum simulators focus on assist- INVESTIGATE FUNDAMENTAL SCIENCE AND ing the rapid development of practical (i.e., achievable BEYOND within 2–5 years) quantum simulator prototypes that can be made broadly available to the scientific community. Quantum simulators have the potential to solve a wide This effort will employ a systems engineering approach range of important outstanding scientific problems and dra- to advance the most mature technologies. Existing facili- matically impact technology development. They can tackle ties, commercially available quantum systems, and open- important models of quantum materials that defy under- source software will be used to accelerate the timeline standing despite decades of intensive research, promise to deployment. Key goals include making systems with breakthroughs in accurate simulation of chemical pro- improved flexibility for users and developing algorithms cesses far out of reach of even the most advanced super- to speed the initial practical applications of these quantum computers, and can access extreme conditions relevant machines. Success in this pillar requires focused, interdis- to high-energy particle physics and cosmology otherwise ciplinary collaborations including experimental and theo- impossible to create in the laboratory. Moreover, quantum retical physics, engineering, and computer science. Early simulators enable an unprecedented degree of spatiotem- engagement of industry and national laboratories is critical poral control and measurement detail and precision [22], to provide and manage access to existing systems for the offering deeper insights than previously accessible. broader scientific community. These stakeholders can also Near-term advantages will necessarily be realized with assist other technologies close to deployment readiness to systems that lack full error correction. The impact of become publicly available. imperfections such as noise and decoherence cannot be (2) New, emerging quantum simulators focus on accel- accurately modeled theoretically, and must be explored erated convergence of fundamental science and engineer- empirically by building and testing successively more ing to discover principles, devices, and new applications complex simulation platforms. Constant experimental that will lead to the next generation of simulators with advances will be required to reduce noise, increase the improved capabilities. Priorities include theoretical work number of interacting quantum elements, and improve in computer science and quantum many-body physics, the flexibility and programmability. Theoretical and algorith- development of new architectures and algorithms for quan- mic advances are required to extend the capabilities of tum simulators, novel classical methods to simulate many- quantum simulators, identify new directions for research, body systems informed by quantum simulator results, and analyze and interpret experimental results, and synthesize continued fundamental research that advances existing and outcomes from different platforms into a unified perspec- emerging quantum simulator platforms. This activity will tive. These challenges, detailed further below, highlight the require further work on experimental systems, classical need for cohesive collaborations between experiment and engineering for electronic and optical control systems, theory.

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A. Scientific opportunities for quantum simulators been made on simulating the interplay of molecular vibra- 1. Quantum materials simulation tions and electronic properties, and quantum simulations modeling phonon-assisted energy transfer have been car- Many deceptively simple models of correlated elec- ried out [30]. Extending these simulations will enable the tronic materials defy efficient simulation due to sign prob- identification of previously undiscovered electron-phonon lems associated with fermionic statistics, spin frustration, interactions. An alternative approach is hybrid quantum- or complex gauge fields. A paradigmatic example is the classical algorithms such as variational quantum eigen- Fermi-Hubbard model [23], which is commonly regarded solvers [31,32]. On a 2–5 year time scale a direct model of as a minimal microscopic starting point for describing the photosynthesis problem can be built on several quan- the physics of a host of solid-state materials, from high- tum simulator architectures to help resolve the ongoing temperature superconductors to frustrated quantum mag- controversy over the role of quantum coherence in exciton nets. Despite decades of theoretical and experimental transport and energy harvesting [33,34], with applications efforts, the physics of the Hubbard model and the mate- to a new generation of photovoltaics and many other rials it models are not fully understood. Spin and Bose- chemical problems such as multiscale enzyme reactions Hubbard systems have similar complexity in the presence [35]. The role of accessible prototypes to the chemistry of strong interactions and gauge fields or spin frustra- community under pillar (1) will greatly enhance such tion. Quantum simulators can implement these models and studies. explore exotic low-temperature phases and higher temper- ature regimes, including the famous pseudogap, strange metals, and the quantum critical fan [24]. Simulations of 3. Quantum devices and transport more complex features including heterostructures, artifi- Similar to constructing a direct model of quantum pro- cial lattice structures such as quantum spin ice [25], and cesses in complex molecules, quantum simulators admit quantum generalizations of soft matter such as the spin tunable models of quantum devices. Quantum simulators glass [26] are also achievable. Furthermore, quantum sim- can play a key role in understanding the transport of ulators allow more complete access to quantum states current, spin, heat, and information and the influence of and quantities difficult to access in conventional materials, coupling to gates and substrates in quantum devices. A including nonlocal observables, entanglement measures, general understanding of transport needs to be built beyond high-order correlators, and even full snapshots of the quan- semiclassical limits and linear response to include quan- tum wave functions. On the 2–5 year time scale a wide tized interactions and correlations. For example, a com- variety of such material simulations can be performed in plete quantum understanding of the basic building block a quantum simulation version of the materials genome ini- of central processing units (CPUs)—the field-effect tran- tiative, particularly as prototypes are made available to the sistor (FET)—may provide both fundamental insight and materials science community via pillar (1), and as multi- identify physical limits; quantum simulators are already investigator blended physics–materials-science teams are exploring this area [36]. Recent experiments are starting to formed in pillar (2). shed light on the transport properties of the Fermi-Hubbard model, believed to hold the key for the understanding of 2. Quantum chemistry high-temperature cuprate phenomenology [16,17]. Like- Chemistry problems such as calculating reaction rates wise, transport is essential to quantum-dot-based photo- and modeling catalysis are tantalizing topics with societal voltaics, quantum thermoelectrics, spintronics, and other importance, including more efficient nitrogen fixation [27] quantum entanglement-enhanced devices that tolerate or and making synthetic versions of light-harvesting photo- even prefer decoherence, rather than avoid it. The question synthetic complexes. Classical computation proves insuffi- of quantum thermoelectric effects and the quantum mean- cient in many areas, including reactions occurring through ing of heat transport ties in to nanothermodynamics more conical intersections, determining whether the reaction generally [37]. In this direction, creation of information- products are controllable by wave function manipulation based engines have been proposed, with initial demonstra- of the reactants, electron transport and energy harvest- tions of an information-based Carnot cycle [38], but a great ing in multiscale molecules and environments, and even deal of exploration is needed to unlock this field. Finally, many problems in bond energies and bulk properties in quantum complex networks can be realized in very recent modest-sized molecules. For example, accurately calculat- quantum simulator architectures, allowing one to predict ing molecular properties of a single Cr2 dimer from first and explore properties of future “quantum internet” chan- principles remains beyond the reach of current techniques nels and device elements. On the 2–5 year time scale, [28,29]. Quantum simulators can solve such problems by environment-enhanced quantum transport in a wide vari- directly emulating a model of such molecules or reactions ety of open quantum systems, quantum complex networks, and are not limited by the high overhead required by dig- and quantum nanothermodynamic devices can all be real- ital quantum computers. For example, recent progress has ized on several quantum simulator architectures. Progress

017003-5 EHUD ALTMAN et al. PRX QUANTUM 2, 017003 (2021) in this area will especially benefit from multidisciplinary enabling error-resilient storage and manipulation of quan- teams combining electrical engineers and physicists. tum information [44]. In thermalizing systems, quan- tum simulators can shed light on transport properties and nonlinear response, which are often poorly under- 4. Gravity, particle physics, and cosmology stood despite their critical importance for characteriz- Quantum simulators will serve as laboratory testbeds ing materials and designing electronic devices. Under- for nonterrestrial phenomena relevant to particle physics, standing nonequilibrium quantum many-body dynamics cosmology, and quantum gravity. Simulators can explore is perhaps the greatest strength of quantum simulators a wide range of phenomena, including lattice gauge the- and ties together all the topics of this section, falling ories [39], color superconductivity, cosmological defect squarely into the area of pillar (2) under fundamental production in inflating spacetimes and quantum effects research. in curved spacetimes. Investigations into the dynamics of thermalization have revealed striking and unantici- pated connections linking aspects of many-body quantum chaos, scrambling of quantum information theory, holo- B. Challenges and opportunities for theory graphic descriptions of black holes, and quantum gravity Theoretical work plays a critical role in designing quan- [40]. These conjectured links can be directly tested in tum simulators, interpreting the experimental data they quantum simulations, forging new connections between produce, and developing an overarching framework to these seemingly disparate disciplines. Entangled quan- apply lessons learned in quantum simulators to physical tum many-body systems constructed for simulation pur- systems of interest. The new theoretical ideas and meth- poses, combined with high-precision measurements, could ods needed to drive breakthroughs in quantum simulation even act as highly sensitive detectors to explore gravita- are possible only through a symbiotic relationship between tional effects. On the 2–5 year time scale, the question theoretical and experimental teams. of information scrambling in out-of-time-order correla- Advances in quantum simulators pose both challenges tors can be addressed on near-term quantum simulator and opportunities for theory. One key challenge is the architectures, particularly with the added benefit of multi- need to move beyond existing frameworks by investigating disciplinary supported collaboration between cosmologists new regimes of nonequilibrium dynamics not described by and string theorists together with quantum simulator the- standard statistical mechanics and capitalizing on access orists and experimentalists. A national quantum simula- to nonlocal observables such as entanglement [45], string tor program can also support joint programs in this area orders, snapshots of many-body wave functions [46], and (see Sec. VI). distribution functions. Standard theoretical approaches to many-body systems emphasizing two-point correlation functions of local observables and near-equilibrium lin- 5. Nonequilibrium quantum many-body dynamics ear response must be extended. Needed advances include Quantum simulators also enable access to fundamen- effective field theories, variational methods, and advanced tally new regimes of coherent, closed-system, and highly numerical techniques. excited dynamics previously inaccessible in conventional An opportunity for theory is the possibility for detailed materials [41,42]. This important problem spans all scales comparison of different model predictions against quan- of nature, from the formation of large-scale structures in tum simulation experiments, which will be fundamental to the universe to the response of semiconductor devices. extract lessons about the quantum problems at stake. For The potential impact of quantum simulators in this domain example, in the case of quantum materials, many classes of is high, since dynamics and excited states for multipar- theories have been proposed to explain competing orders, ticle interacting quantum systems are largely inacces- quantum criticality, and proximity to exotic fractional- sible to conventional computing. Furthermore, theoreti- ized phases in high-temperature superconductors. These cal tools for describing out-of-equilibrium behavior are theories can be used as a foundation for model-based anal- limited. Quantum simulators can access the full range ysis of the complex data sets from quantum simulation of many-body dynamics, including relaxation to ther- experiments. Such a program requires new methods to mal equilibrium in some closed systems, to nonther- translate the predictions from these models into the observ- malizing behavior in integrable and disordered systems ables from quantum simulators. Advances in data science [42]. Open challenges addressable by quantum simula- and machine-learning tools can also be used to compare tors include uncovering the universal organizing prin- theory and experiment and contrast different approximate ciples governing out-of-equilibrium and nonequilibrium theories. The same needs apply to other fields, such as quantum phenomena; understanding how time-dependent interpreting nuclear magnetic resonance (NMR) spectra control, driving, and engineered dissipation can be used in biomedical systems. Successes on quantum simulator to stabilize nonequilibrium quantum phases [43]; and problems can thus translate into understanding in other

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fields, such as NMR. Success calls for organizing multidis- quantum many-body states. Multiple platforms will ben- ciplinary collaborations between experts in data science, efit from new methods of state preparation, including new theoretical physics, chemistry, medicine, engineering, and cooling techniques, entropy redistribution via reservoir other fields of science. engineering, stabilization via a dissipative bath [47,48], and measurement-based state preparation. Alternatives to C. Challenges to building a large-scale quantum traditional adiabatic protocols include (i) autonomous error simulator mitigation for analog quantum simulators using engineered baths, e.g., in architectures A-7 (Rydberg atom arrays), The main technological challenges to leveraging the A-8 (superconducting quantum circuits), and A-10 (ultra- strengths and overcoming the weaknesses of quantum sim- cold neutral atoms); (ii) new tools for quantum state con- ulators are common across platforms and center around trol (see Sec. V); and (iii) optimizing state-preparation scalability, complexity, state preparation, control, and mea- protocols, cooling, and variational approaches in near- surement. term algorithms, including adaptive techniques [48]. These challenges present unique opportunities for disparate dis- 1. Scalability and complexity ciplines such as computer science, electrical engineering, The quantum simulator architectures, numbered A-1 materials science, and mathematics to contribute critical through A-11, are described in detail in Sec. IV. Some plat- insights making large-scale quantum simulation possible. forms, such as A-2 (color centers), A-3 (dopants in semi- conductors), A-4 (gate-defined quantum dots), and A-8 (superconducting quantum circuits), face the challenge of IV. QUANTUM SIMULATOR ARCHITECTURES variability, i.e., quantum devices with nominally identical Quantum simulators can be assembled from a wide vari- design rarely exhibit identical performance, are affected by ety of atomic, molecular, optical, and solid-state physical coupling to nearby environments or defects, and typically platforms. In the following, we summarize these platforms require time-intensive independent calibration. Addressing in alphabetical order. this issue will require better understanding of imperfec- tions and coupling to the environment; developing better techniques for placement and control of impurities, donor A-1: cold and ultracold molecules atoms, and vacancy centers that act as artificial atoms; and devising automated calibration processes to tune up a Polar molecules present a quantum element combin- large number of independent devices. Furthermore, many ing the strong, anisotropic electric dipolar interaction problems of interest require long-range connectivity that with one to hundreds of internal states with transitions typically cannot be easily achieved by physical wiring in at convenient frequencies [50–52]. They can be assem- planar devices. Implementing long-range interactions via bled from neutral atoms to reach Fermi degeneracy [53], swap networks is technically possible, but often incurs or be directly laser cooled [54]. Molecule-based quan- a large overhead. Progress is needed to enhance physi- tum technology will improve precision measurement [55] cal connectivity of devices, and devise better algorithmic and provide insights in molecular physics, chemistry, and methods to improve connectivity. Along with connectivity biology. Their range of frequencies, kilohertz to hun- comes cross talk or unwanted connections and interactions, dreds of terahertz, lends itself to efficient information as one finds natively in many of the other architectures, transduction across different platforms and the study of e.g., in A-1 (cold and ultracold molecules), A-6 (photons multiscale quantum physics, while combining with their and atoms in cavities), A-7 (Rydberg atom arrays), and intrinsic tunable interactions will allow them to reach high- A-9 (trapped atomic ions). A careful design of the sys- fidelity entanglement. Stacked multilayer fermionic polar tem architecture is required so that cross-talk errors do molecules [56] can simulate the extended-Hubbard and t-J not scale with the system size. As discussed below, as the models and topological phases, while different classes of system size grows, so does the complexity, not only for molecules can explore models difficult to access with other the physical architecture and the control and measurement platforms, e.g., exotic XYZ magnetism, and internal states hardware, but also for the quantum states involved and can provide a separately tunable reservoir for simulations their verification. of open quantum systems. Crucial challenges for lattice- based quantum simulators include cooling the system to the many-body ground state, obtaining more than about 2. State preparation and control 103 to 104 quantum elements, and extending the classes As quantum simulators approach ever larger scales and of molecules to simulate more models. Addressability at complexities, it becomes increasingly difficult to reach and the single molecule level is another key goal, as well as maintain the low entropy and low effective temperatures trapping and control of cold molecules in optical tweezers required to prepare and investigate strongly correlated [57,58].

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A-2: color centers Quantum dots offer the possibility of long-range interac- Color centers in wide band-gap semiconductors (dia- tions with controllable disorder for simulation of quan- mond, SiC, etc.) feature microwave transitions for control tum spin fluid formation, Wigner crystallization, Anderson and optical transitions for coupling to each other and to localization [73], and time crystals, as well as opportuni- cavities [59]. This system does not require high vacuum ties for reservoir engineering for open quantum systems. or particle trapping, and performs well at modest temper- Active areas of research include exploring material sci- atures (greater than 1.5 K) with coherence times ranging ence parameters to reduce interdevice variability, methods from hundreds of microseconds to minutes. Small quantum of using variability as a resource, modified measurement registers of up to ten fully connected qubits have recently schemes to improve speed and scalability, such as multi- been demonstrated [60]. Color centers are well suited for plexed dispersive readout, and automation of tuning and the study of open quantum systems [61]. Two quantum readout protocols. registers have been optically connected using nitrogen- vacancy centers in diamond [62]. Active areas of research A-5: photons in nanostructures to facilitate scalability include increasing the quality of Engineered nanophotonic structures coupled to strong optical interconnects through improved fabrication meth- nonlinearities offer a potential solution to realizing tunable ods and photonic optimization [63,64], exploration of new long-range interactions in two-dimensional lattices [74]. defects, integration of defects to photonics structures, and This will facilitate simulation of quantum spin fluid forma- precise control over defect placement. tion or Wigner crystallization, and Bose-Hubbard models [75]. Furthermore, the spectral or spatial inhomogeneity of the quantum emitters providing the nonlinearity also A-3: dopants in semiconductors acts as a disorder term, making these platforms well suited Dopant atoms have been integrated into gate-defined for implementation of disordered many-body systems with quantum-dot devices using deterministic ion implantation long-range interactions, challenging to investigate classi- [65], and have been placed with atomic precision into cally since the analytical tools used to study symmetric dopant-based devices using scanning probe fabrication. and translationally invariant systems break down in the Both single-qubit and two-qubit gates have been shown presence of disorder. Optimization techniques will play an using the electron spin bound to donor atoms [66]. Emer- important role in engineering of photonic structures [76]. gent many-body behavior has been seen in the transport Linear optics allows for simulation of the boson sampling through short one-dimensional chains of donors [67]. In problem [77]. general, dopants in semiconductors have many of the same opportunities and limitations of gate-defined quantum dots, A-6: photons and atoms in cavities with some notable differences. The nuclear spin provides Cavity quantum electrodynamics enables coupling of an additional degree of freedom that has very long coher- distant atoms through photon exchange via the mode of ence times, and can be coupled to bound electrons [68]. a cavity operating in the strong-coupling regime. These The main challenge of this platform is achieving tun- long-range interactions, which can include all-to-all con- able donor-donor coupling. Scaling to larger arrays also nectivity, allow simulation of exotic spin models [78–81]. requires managing the wiring for individual qubit control. Coupling to several cavity modes and/or Floquet driv- ing provides adjustable range, connectivity, and sign of the interactions, which in turn enables simulation of phe- A-4: gate-defined quantum dots nomena ranging from quantum spin glasses to information Spin qubits in gate-defined quantum dots offer a tun- scrambling in quantum black holes. Alternatively, these able, scalable platform with long spin coherence relative setups can be viewed as many-body systems of cav- to their gate time [69]. Advantages of this technology ity photons with strong photon-photon interactions medi- include the ability to scale to moderate numbers of qubits ated by atoms [82,83], and Laughlin states of light have using nanoscale lithographic patterning on high-quality recently been demonstrated [84]. In current experiments, semiconductor silicon, and silicon-germanium substrates. the cavity mode often couples collectively to large clusters 1D and 2D arrays of these structures have been demon- of atoms, which therefore behave as large semiclassi- strated with excellent control. Silicon quantum-dot plat- cal spins with cooperatively enhanced interactions. This forms have achieved single-qubit and two-qubit gate fideli- regime has allowed for deterministically generating many- ties of 99.9% [70] and 98% [71], respectively. Strong particle entangled states, including squeezed [85–88]and coupling between double quantum-dot qubits and super- W states [89]. In an opposite limit, cavity-mediated inter- conducting coplanar waveguide resonators has recently actions have enabled a two-qubit entangling gate [90]. been achieved. A Fermi-Hubbard model quantum sim- An important challenge for future experiments is to go ulator has been implemented with quantum dots [72]. deeper into the quantum regime in scalable many-body

017003-8 QUANTUM SIMULATORS... PRX QUANTUM 2, 017003 (2021) systems, by combining strong atom-light coupling with quantum control over more than tens of qubits, while main- local tunability of the interaction of individual atoms with taining and improving the coherence of individual circuit the cavity. elements.

A-7: Rydberg atom arrays A-9: trapped atomic ions Deterministically prepared, often reconfigurable 1D, Trapped atomic ions are among the most coherent and 2D, and 3D arrays of individually trapped cold neu- controllable of all quantum simulation platforms [103]. tral atoms with strong, long-range, coherent interactions The internal structure (spin) of atomic ions is not per- enabled by excitation to Rydberg states constitute a turbed by the external confinement forces. Trapped ion promising approach to realizing programmable quantum qubits can be localized, initialized, and measured with simulators. Recent experiments realized quantum spin high fidelity. Reconfigurable qubit couplings are medi- models using over 50 qubits with tunable interactions ated by the Coulomb interaction and controlled through [12], leading to the discovery of a new class of quantum state-dependent dipole forces realized with applied opti- many-body states that challenge traditional understand- cal or microwave fields. Qubits can be fully connected ing of thermalization in isolated quantum systems. The for modest system sizes. This allows the implementa- work also provided insights into quantum phase transi- tion of magnetic spin models with long-range and tunable tions in exotic, previously unexplored condensed matter interactions, and simulations of phase transitions and quan- models. Symmetry-protected topological phases of matter tum dynamical processes through adiabatic manipulations, have been realized using 2D atom arrays [91]. High- quantum quenches, and Hamiltonian modulation [104]. fidelity single-qubit rotations and multiparticle entangled Variational quantum eigensolver algorithms for quantum states, quantum state detection, and parallel quantum logic chemistry have also been demonstrated with this platform operations have been demonstrated, establishing neutral [105,106]. Current state-of-the-art trapped ion quantum atoms as a competitive platform for quantum informa- simulators involve more than 50 spins [13,107,108], with tion processing. Challenges include scaling to hundreds complete control and high fidelity up to a few tens of of entangled quantum elements and reproducing results on ions. The primary challenge to scaling ion traps is the similar or complementary platforms. systems-level engineering of optical controllers and elec- trode structures to connect groups of trapped ions through shuttling, as well as the integration of photonic intercon- A-8: superconducting quantum circuits nects for modular communication between trapped ion Superconducting circuits are a leading solid-state quan- qubit clusters. tum simulation platform with relatively long coherence times and strong, tunable interactions enabling fast, high- fidelity quantum logic gates. Relatively high-fidelity oper- A-10: ultracold neutral atoms ation and readout of more than 50 qubits is now achiev- Ultracold neutral atoms working with thousands to tens able [14,92]. A wide range of circuit topologies can be of millions of interacting fermionic or bosonic quantum lithographically defined, making superconducting circuits elements can simulate a wide variety of paradigmatic one of the most geometrically flexible simulator plat- quantum phases and phenomena because of their high forms [93]. Quantum elements include linear resonant degree of isolation, flexible geometry, interaction and spin elements operating as cavities or photon (bosonic) reser- control, and slow observable dynamics. Fermionic degrees voirs [94], and nonlinear elements operating as artificial of freedom can be natively realized. Quantum simulator multilevel atoms (qudits), two-level “atoms”, “spins”, or tools range from optical lattices [23,109] and Feshbach res- qubits [93,95]. Linear and nonlinear couplings between onances realizing strong interactions [3,110] to now arti- elements can provide tailor-made interactions [93,96,97] ficial gauge fields, arbitrary confining geometries, dipolar for investigating frustrated spin systems, photon-photon interactions, coupling to optical cavities, and individual interactions, or modeling phase transitions beyond mean- atom imaging and control in quantum gas microscopes field theory. This platform has been applied to digital [46,111], allowing one to directly sample the many-body simulation of spin models, fermionic dynamics, quantum wave function. Equilibrium quantum simulations acces- chemistry using variational quantum eigensolvers [94–96, sible to these devices include the Fermi-Hubbard model 98]; and machine learning for classification [97]. Analog (reducing temperature roughly fourfold may exhibit the simulation of strongly correlated quantum matter—such predicted d-wave superconductivity), quantum spin liq- as many-body localized states in disordered lattices and uids (using lattices with geometrical frustration), fractional the Mott insulating phase in the Bose-Hubbard model quantum Hall physics (using artificial gauge fields), and [102]—has recently been explored. Significant challenges even models from cosmology (using dynamical geome- in this platform include obtaining high fidelity and full try or interaction strengths). Nonequilibrium simulations

017003-9 EHUD ALTMAN et al. PRX QUANTUM 2, 017003 (2021) include the breakdown of thermalization in isolated inte- A. Digital, analog, or hybrid grable systems, the dynamics of many-body localization, While quantum simulators are traditionally classified as and high-order correlators, for example in atom interfer- analog or digital, actual realizations are more nuanced, ometry [112]. The unified approach of quantum simulation spanning the continuum between the two. Digital, i.e., and precision metrology [113,114] is leading a revolution gate-based quantum simulation, has the advantage of in our understanding of complex systems for applications versatility since, in principle, all Hamiltonians can be in measurement science. Floquet engineering on atomic effectively encoded into quantum circuits involving just quantum gases has already synthesized gauge fields rele- one- and two-qubit gates. However, the high coherence and vant to condensed matter, high-energy, particle, and grav- gate fidelity, along with error correction, required for deep itational physics. Challenges include the nonuniformity quantum circuits are likely unattainable in the next 2–5 inherent to many trapping scenarios, a variety of loss and years. Quantum simulators span the continuum between decoherence mechanisms from background vacuum gas to digital and analog and provide a more realistic path to trapping fields, and removing entropy to achieve ground solving scientifically pressing problems in the near term. states. Fully analog devices fix the Hamiltonian to mimic the problem exactly. Adding tunability allows broadening to a A-11: van der Waals heterostructures, Moiré class of problems rather than a fixed Hamiltonian. Addi- materials, and excitons tional capabilities such as single-qubit gates or single-site addressability provide added control and allow for an even Atomically thin 2D materials such as graphene and tran- larger class of problems to be tackled. On the other hand, sition metal dichalcogenides can be combined into layered in a model closer to the digital quantum computer, allow- heterostructures of great variety. These structures effec- ing for analog-like elements such as switching multiqubit tively simulate a highly tunable Hubbard model, analogous interactions on and off, rather than decomposing multi- to what occurs in complicated correlated materials, but on qubit gates in terms of two-qubit and single-qubit gates, a greatly expanded length scale. The relative importance of can lead to shorter depth circuits and the ability to sim- electronic tunneling and correlations can be continuously ulate more complex problems, despite limited coherence varied by tuning gate voltages, relative interlayer twist and gate fidelity. angles, strain, and dielectric environments, to explore a Hybrid models of simulation can also open new oppor- full phase diagram in a single material [115]. Moiré super- tunities. This can include either hybrid approaches involv- lattice structures of graphene have realized highly tunable ing different architectures from Sec. IV, or quantum- correlated insulators, magnets, and superconductors, and classical hybrid simulations, such as variational quantum future heterostructures will be able to simulate even more eigensolvers. In the former case, one approach is running complex correlated topologies, frustrated magnetism, and the same problem on different hardware to cross-check fractionalized spin liquids. Two-dimensional material het- and benchmark the results; another possibility is a phys- erostructures can also host high densities of long-lived ical connection between disparate systems via a quantum bosonic particles such as excitons and exciton-polaritons, channel [119]. For quantum-classical hybrid simulators, manipulable to produce highly tunable solid-state plat- the quantum system is used for encoding and evolving the forms to simulate bosonic many-particle systems, and quantum state as an ansatz, while the classical computer is to realize optoelectronic and thermoelectric applications used for optimization of its parameters. [116]. These architectures can be cooled more easily, rela- tive to the tunneling and superexchange energies, than for instance their counterparts in architectures A-1 (cold and B. Challenges and opportunities ultracold molecules) and A-10 (ultracold neutral atoms) to Before problems of practical importance can be tack- explore coherent spin physics, presenting both an exciting led, it is imperative to test the ability to accurately con- opportunity and a challenge. trol engineered quantum systems, verify that the results of the quantum simulators can be trusted, and quantify errors. Gate-based quantum simulators benefit from ver- V. PROGRAMMABILITY AND VERIFIABILITY ification and validation methods developed for quantum Quantum simulators can take many forms ranging from computing, such as randomized benchmarking [120]and completely analog to fully digital, with hybrid implemen- gate set tomography [121], to characterize system per- tations in between [117]. Having presented the scientific formance and diagnose errors. However, these tools have challenges and opportunities in Sec. III, and the archi- an intrinsic exponential scaling, limiting them to smaller tectures in Sec. IV, in this section we proceed to iden- systems. For analog quantum simulation, the theoretical tify opportunities and challenges in the programmability design of benchmarking and error-correction tools is in its and operation verification [118] of this large class of infancy. For example, what is the equivalent of a “quan- simulators. tum volume” [122,123] for quantum simulators that will

017003-10 QUANTUM SIMULATORS... PRX QUANTUM 2, 017003 (2021) enable comparison of the different architectures? There to both dephasing and environmental interactions. Well- is a broad opportunity for witness observables, akin to understood tools exist for characterizing and dissecting entanglement witnesses [124], to validate simulator oper- these errors in small-scale quantum circuits, such as ran- ation without a priori predictions for the outcome of the domized benchmarking, cross-entropy benchmarking, and complete simulation. In fact, we expect techniques for val- state and process tomographies. However, these tools idating, calibrating, and diagnosing quantum simulators become forbiddingly difficult to implement at the level of to be platform agnostic. Similarly, quantum error correc- 10 to 50 qubits, let alone for larger and more complex tion methods developed for universal quantum computers quantum elements [128]. Possible directions will involve provide high-level protocols transcending specific physical new benchmarking protocols to estimate the fidelity of architectures but require overheads too large for near-term quantum circuits without explicit reliance on classical cal- simulators. Uncovering new types of error correction and culations, and new measurement methodologies improving mitigation suitable for near-term simulators is an open upon the exponential or superexponential scaling behavior problem. in the number of quantum elements in the system. The use Furthermore, there is a natural trade-off between the of computer-science validation techniques will also prove coherence of a system and the degree of programmability crucial. For example, machine-learning-based techniques and tunability. Understanding and exploring this trade-off can be used to validate and reconstruct properties of large is important in developing quantum simulators. There is quantum hardware [129]. Success in any of these efforts, also an opportunity in the development of algorithms with even moderate, will have a profound impact on digital this trade-off in mind, leading naturally to the concept of quantum simulation and computation as a whole. codesign, i.e., developing applications for specific hard- ware and architectures. Such efforts will benefit from the 3. Comparison to classical calculations convergence of various areas of expertise, including exper- Comparison of experimental results with controlled imental physics, quantum control theory, computer science classical simulations of quantum systems plays an impor- and software, and engineering. tant role in the validation of quantum hardware. For small systems, brute-force classical simulations can still 1. Validating analog simulators be performed without essential approximations. At this Physical systems contain contributions to their Hamil- scale, systematic verification and comparison procedures tonian beyond the strict confines of the model that they can reveal flaws or neglected relevant perturbations in are designed to implement [125], representing a challenge microscopic models. For larger-scale quantum hardware, to analog quantum simulators. However, exact agreement comparing to classical simulation is more challenging between a simulator and its target model is not expected to but venues for benchmarking are still open. State-of- be necessary. Thanks to the universality of the low-energy the-art classical many-body techniques can be used to physics arising from collective behavior, often these addi- validate analog and digital quantum computers. For exam- tional terms or fluctuations will not affect the correctness ple, low-entangled states in one dimension are naturally of the simulation provided they are not too large. Current amenable to tensor-network simulations [130], whereas experiments show that good agreement with simple and sign-problem-free models can be effectively studied with tractable theoretical models can be achieved despite the stochastic quantum Monte Carlo techniques [131]. Com- presence of imperfections [126]. An immediate question is paring to classical simulations has a dual goal. First, whether it is possible to quantify the robustness of observ- it is crucial in understanding the microscopic details of ables to such perturbations. Classification of the relevance quantum hardware and better assessing its capabilities. of perturbations to the systems as relevant, marginally Second, experimentally accessing regimes beyond the cur- relevant, or irrelevant bear resemblance to classification rent applicability of many-body classical techniques can be schemes in renormalization group flows [127]. Methods to regarded as a way to benchmark and improve upon such determine how strongly observables are affected by small techniques. perturbations and to derive reliable error bounds are desir- able. This presents remarkable research opportunities to 4. Verification of simulators quantify uncertainties in systems without a priori known Given that many problems are well suited to implemen- behavior. tation on multiple platforms, comparison of simulations of the same Hamiltonian using different technologies can 2. Validating digital simulators verify the outcome or reveal unexpected interactions in Digital quantum simulation suffers from several inher- the simulators. Alternatively, one can use self-verification, ent sources of errors, including digitization errors arising where the simulator is run forward and then backward, test- from an insufficient number of Trotterization steps, con- ing that the state at the midpoint has the desired properties trol errors on the gate unitaries, and decoherence due of the simulation and that the inversion of the evolution

017003-11 EHUD ALTMAN et al. PRX QUANTUM 2, 017003 (2021) returns to the same initial state. A more complex self- introduce hard models; computer scientists and systems verification will generate the same Hamiltonian through engineers who ensure that the simulator is appropriately two different physical processes to compare outcomes. tunable, reliable, and usable; and quantum experimental- ists who implement and run the device and extract the 5. Error correction and mitigation for quantum data. There are common techniques among multiple physi- simulators cal architectures, from manipulating individual photons, to trapping and interrogating atoms and molecules, to con- The type of quantum simulator hardware determines the trolling decoherence in quantum circuits and materials. impact and types of imperfections affecting the system. There are also common analysis techniques and theoretical Decoherence and unwanted interactions have a different tools behind the identification of models and their rela- physical origin depending on the platform. The central tion to the native interactions in the quantum hardware. A challenge is to identify and correct for these unwanted successful quantum simulator program will streamline the interactions. To date, the most successful approach is to use of such common tools by establishing standards and address every imperfection individually by careful engi- encouraging the sharing of resources between all scientific neering and ingenuity. A methodology is needed for quan- groups, including software and theoretical computational tum simulators that, similar to quantum error correction, tools, schematics for control systems used across many is able to mitigate the effect of errors and offer a high architectures, and the practical details of building quan- degree of portability across different architectures. Because tum simulators on specific architectures that often prove quantum simulators do not demand the same flexibility as surprisingly useful on different platforms. universal quantum computers, they open up the possibil- Operating different platforms requires different equip- ity to devise error mitigation schemes that are targeted at ment. For example, trapped atoms or ions and supercon- special purpose simulations with near-term devices [132– ducting quantum circuits are, at first sight, quite distinct. 135]. More research is needed to explore opportunities to However, they have directly benefited from each other, apply methods derived from quantum error correction and for example in applying concepts of quantum trajecto- mitigation to analog simulators. ries from quantum optics [136] to superconducting cir- cuits [137,138]. In fact, experimental technologies, spe- 6. Mesoscopic metrics of quantum complexity cific techniques, physical models, system Hamiltonians, Most models of computational complexity are based on and quantum operations can all be very similar. Dedi- the asymptotic limit of computation, an approach that is cated funding support for establishing and promoting these relevant for large systems. This is a poor model for quan- interdisciplinary collaborations will have a high impact. In tum simulators, which possess both limited control and particular, to create the necessary synergy among laborato- limited components. Developing a complexity theory of ries, we envision a mixture of two approaches: vertical and quantum simulation that is more relevant to medium-scale horizontal. In the vertically integrated approach, a single systems is an open problem that will impact the further experimental quantum simulator platform is implemented design of these platforms. by a team of principal investigators with different exper- tise. In the horizontally integrated approach, teams employ VI. FOSTERING COLLABORATION AND multiple platforms to study the same problem or model. SHARED RESOURCES Ultimately, the goals of pillar (1) (to create a transition of mature quantum simulator architectures from laboratory B. Academic, national laboratory, and industry demonstrations to prototypes to end-user products accessi- cooperation and mutual benefit ble by the broader scientific community) and pillar (2) (to The success of these vertical and horizontal approaches bring less well-developed platforms up to that point and requires continued maturation of key supporting subsys- perform fundamental research) require a multifaceted pro- tems, including atomic sources, integrated optical systems, gram to support multidisciplinary team formation beyond optomechanical assemblies, quantum-limited amplifiers, the present predominantly single-investigator level. In the and high-speed field-programmable gate array control sys- following, we describe our vision of community support tems. Given the significant challenges to maturation for for such a national quantum simulator program. It is the quantum systems engineering, we see a substantial oppor- position of the community that this approach is necessary tunity to inspire and push for industrial development of to succeed on a 2–5 year time scale. these new tools for a broad user community through strate- gic and deliberately coordinated partnerships between aca- A. Horizontally and vertically integrated teams demic, national lab, and industrial developers. The design and operation of a quantum simulator Collaborations between universities, national labs, and involve a high level of collaboration between theorists who industry to improve existing technologies will also be

017003-12 QUANTUM SIMULATORS... PRX QUANTUM 2, 017003 (2021) vital to accelerating the development of quantum simu- computer science student projects (e.g., as a supplement lators as deployable devices. Advancements on this front to a funded project) to design and benchmark a modular can be spurred by supporting academic access to national hardware or software component. Funding such projects, lab and industrial systems. Dedicated or priority access at possibly coadvised, will provide a pathway to transfer- multiple levels—e.g., high-level software and application ring critical engineering expertise into groups working on programming interface (API) and low-level qubit and con- quantum simulator research. Information shared on the trol hardware—will help enable researchers to understand repository will also help identify current and future engi- the entire system and develop new protocols that will lead neering needs for quantum simulators, which will help to improved and larger-scale quantum simulations. All par- nucleate these student projects and activities. ties can also provide open-source code, building features The hub will also provide a centralized location to curate that the community identifies as being beneficial for the and promote existing open-source software tools, similar advancement of their work. to the highly successful nanoHUB [140]. Funding agencies We therefore envision a student- and postdoc-exchange can incentivize and encourage groups to post capabilities program that will encourage cross pollination of ideas at to this hub. Discussion forums will also provide a central- multiple levels. First, we emphasize the need for direct ized online communication network, allowing individuals interactions between researchers in experiment and the- from across physics, computer science, and engineering to ory. Theory students or postdocs will spend time at communicate and grow collaborations involving expertise different institutions collaborating with experimentalists from different areas. Forum discussions will cover capa- in their labs and vice versa. Second, students or post- bilities of experimental platforms and theoretical methods, docs from one architecture will visit labs from another motivating problems in physics, chemistry, computer sci- to share common strategies that exist between differ- ence, and other fields, and their connections to different ent platforms. Third, we suggest fellowships and other hardware systems. funding opportunities be created for students and post- Creating such a forum and ensuring that it reaches crit- docs to work in academia-national lab-industry partner- ical mass—like the mathematics, computer science, and ships. quantum information stack exchanges—will require a con- It is imperative and timely to prepare students with certed effort and leadership from the community. Time and a broad, cross-cutting educational experience spanning effort from experts in the field will be required to ini- architectures—e.g., neutral atoms and superconducting tiate and moderate discussions and establish a tradition quantum circuits—and sectors, e.g., academia and national of collaboration and communication. Resources will be labs. This approach will best position the future workforce required to enable principal investigators, postdocs, senior to develop and deploy the prototypes needed to solve the students, and dedicated engineers to devote time to devel- scientifically pressing questions described in Sec. III and oping the hub so that it can grow into a valuable tool for the practical problems highlighted in Sec. V. fostering collaboration, communication, and connections beyond a select few groups across the quantum simulator community. C. National quantum repository and information We note that the success of the hub to accelerate the exchange hub development of quantum technology hardware will depend Technical expertise in academia is typically siloed in critically on sustained and centralized support. This chal- individual groups and can be difficult to share due to a lack lenge provides an opportunity for the community to work of documentation, software robustness, and instrument with permanent partners such as national labs to establish compatibility. Strong collaborations and greater exchanges such a critical resource. of technical expertise between research groups and exper- In addition to a virtual hub, other approaches to a quan- imental and theory programs, encouraged by dedicated tum simulator hub were discussed by workshop partic- funding, will strongly facilitate progress. For larger-scale ipants. Inspired by the LIGO-style-focused collaborative exchanges, we recommend establishing a national quan- effort, and motivated by potentially strong opportunities to tum repository and information exchange hub in the bring revolutionary impacts to science and technology, a form of an internet resource for technical information quantum simulator hub could include experimental scien- and common basic subsystems. An organized, searchable tists, engineers, theoretical physicists, and computer scien- repository of schematics, technical drawings, and publica- tists all working together toward selected grand challenge tions similar to the LIGO portal [139] will be maintained goals. Such a hub could utilize several complimentary plat- as part of the quantum hub. forms, both advanced and emerging, aiming to address A key challenge to this plan is that physics research key scientific and engineering challenges to produce prac- groups are typically not motivated to develop robust tically useful simulators for scientific application. It would and well-documented hardware solutions. A potential complement individual investigators’ efforts and could workaround to this problem is to fund engineering and include robust community outreach efforts to enable access

017003-13 EHUD ALTMAN et al. PRX QUANTUM 2, 017003 (2021) to most advanced platforms and to disseminate technology. recent related National Science Foundation accelera- It is also in the spirit of the National Quantum Initia- tor workshops—“Quantum Interconnects” and “Quantum tive that a quantum simulator hub of this form would Computers” [119,141]. include strong partnerships with industry and national labs. ACKNOWLEDGMENTS This material is based upon work supported by the VII. CONCLUSIONS National Science Foundation under Grant No. OIA- 1945947. Any subjective views or opinions that might Despite advances in high-performance conventional be expressed in the paper do not necessarily represent computing, machine learning, and artificial intelligence, the views of the U.S. Department of Commerce, the U.S. simulations on classical hardware remain unable to address Department of Energy, or the United States Government. many key scientific problems. Universal digital quantum computers have been proposed to solve many of these outstanding problems, with very exciting recent progress toward quantum advantage and supremacy [14]. How- [1] I. M. Georgescu, S. Ashhab, and Franco Nori, Quantum ever, achieving a sufficient number of well-controlled simulation, Rev. Mod. Phys. 86, 153 (2014). error-corrected qubits of large enough quantum volume [2] Markus Greiner, Olaf Mandel, Tilman Esslinger, Theodor [122] to broadly realize impactful use cases—i.e., the W. Hänsch, and Immanuel Bloch, Quantum phase tran- “killer app”—is likely decades away. An alternative, sition from a superfluid to a Mott insulator in a gas of nonuniversal approach for certain applications are quan- ultracold atoms, Nature 415, 39 (2002). tum simulators. These devices are already being built on [3] M. Inguscio, W. Ketterle, and C. 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