1
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Bluvstein D, Evered SJ, Geim AA, Li SH, Zhou H, Manovitz T, Ebadi S, Cain M, Kalinowski M, Hangleiter D, Bonilla Ataides JP, Maskara N, Cong I, Gao X, Sales Rodriguez P, Karolyshyn T, Semeghini G, Gullans MJ, Greiner M, Vuletić V, Lukin MD. Logical quantum processor based on reconfigurable atom arrays. Nature 2024; 626:58-65. [PMID: 38056497 PMCID: PMC10830422 DOI: 10.1038/s41586-023-06927-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2023] [Accepted: 12/01/2023] [Indexed: 12/08/2023]
Abstract
Suppressing errors is the central challenge for useful quantum computing1, requiring quantum error correction (QEC)2-6 for large-scale processing. However, the overhead in the realization of error-corrected 'logical' qubits, in which information is encoded across many physical qubits for redundancy2-4, poses substantial challenges to large-scale logical quantum computing. Here we report the realization of a programmable quantum processor based on encoded logical qubits operating with up to 280 physical qubits. Using logical-level control and a zoned architecture in reconfigurable neutral-atom arrays7, our system combines high two-qubit gate fidelities8, arbitrary connectivity7,9, as well as fully programmable single-qubit rotations and mid-circuit readout10-15. Operating this logical processor with various types of encoding, we demonstrate improvement of a two-qubit logic gate by scaling surface-code6 distance from d = 3 to d = 7, preparation of colour-code qubits with break-even fidelities5, fault-tolerant creation of logical Greenberger-Horne-Zeilinger (GHZ) states and feedforward entanglement teleportation, as well as operation of 40 colour-code qubits. Finally, using 3D [[8,3,2]] code blocks16,17, we realize computationally complex sampling circuits18 with up to 48 logical qubits entangled with hypercube connectivity19 with 228 logical two-qubit gates and 48 logical CCZ gates20. We find that this logical encoding substantially improves algorithmic performance with error detection, outperforming physical-qubit fidelities at both cross-entropy benchmarking and quantum simulations of fast scrambling21,22. These results herald the advent of early error-corrected quantum computation and chart a path towards large-scale logical processors.
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Affiliation(s)
- Dolev Bluvstein
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Simon J Evered
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Sophie H Li
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Hengyun Zhou
- Department of Physics, Harvard University, Cambridge, MA, USA
- QuEra Computing Inc., Boston, MA, USA
| | - Tom Manovitz
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Sepehr Ebadi
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Madelyn Cain
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Dominik Hangleiter
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, MD, USA
| | | | - Nishad Maskara
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Iris Cong
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Xun Gao
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | | | - Giulia Semeghini
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
| | - Michael J Gullans
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, MD, USA
| | - Markus Greiner
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Vladan Vuletić
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Mikhail D Lukin
- Department of Physics, Harvard University, Cambridge, MA, USA.
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2
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Evered SJ, Bluvstein D, Kalinowski M, Ebadi S, Manovitz T, Zhou H, Li SH, Geim AA, Wang TT, Maskara N, Levine H, Semeghini G, Greiner M, Vuletić V, Lukin MD. High-fidelity parallel entangling gates on a neutral-atom quantum computer. Nature 2023; 622:268-272. [PMID: 37821591 PMCID: PMC10567572 DOI: 10.1038/s41586-023-06481-y] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Accepted: 07/25/2023] [Indexed: 10/13/2023]
Abstract
The ability to perform entangling quantum operations with low error rates in a scalable fashion is a central element of useful quantum information processing1. Neutral-atom arrays have recently emerged as a promising quantum computing platform, featuring coherent control over hundreds of qubits2,3 and any-to-any gate connectivity in a flexible, dynamically reconfigurable architecture4. The main outstanding challenge has been to reduce errors in entangling operations mediated through Rydberg interactions5. Here we report the realization of two-qubit entangling gates with 99.5% fidelity on up to 60 atoms in parallel, surpassing the surface-code threshold for error correction6,7. Our method uses fast, single-pulse gates based on optimal control8, atomic dark states to reduce scattering9 and improvements to Rydberg excitation and atom cooling. We benchmark fidelity using several methods based on repeated gate applications10,11, characterize the physical error sources and outline future improvements. Finally, we generalize our method to design entangling gates involving a higher number of qubits, which we demonstrate by realizing low-error three-qubit gates12,13. By enabling high-fidelity operation in a scalable, highly connected system, these advances lay the groundwork for large-scale implementation of quantum algorithms14, error-corrected circuits7 and digital simulations15.
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Affiliation(s)
- Simon J Evered
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Dolev Bluvstein
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Sepehr Ebadi
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Tom Manovitz
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Hengyun Zhou
- Department of Physics, Harvard University, Cambridge, MA, USA
- QuEra Computing Inc., Boston, MA, USA
| | - Sophie H Li
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Tout T Wang
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Nishad Maskara
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Harry Levine
- Department of Physics, Harvard University, Cambridge, MA, USA
- AWS Center for Quantum Computing, Pasadena, CA, USA
| | - Giulia Semeghini
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
| | - Markus Greiner
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Vladan Vuletić
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Mikhail D Lukin
- Department of Physics, Harvard University, Cambridge, MA, USA.
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3
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Su L, Douglas A, Szurek M, Groth R, Ozturk SF, Krahn A, Hébert AH, Phelps GA, Ebadi S, Dickerson S, Ferlaino F, Marković O, Greiner M. Dipolar quantum solids emerging in a Hubbard quantum simulator. Nature 2023; 622:724-729. [PMID: 37880438 DOI: 10.1038/s41586-023-06614-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2023] [Accepted: 09/05/2023] [Indexed: 10/27/2023]
Abstract
In quantum mechanical many-body systems, long-range and anisotropic interactions promote rich spatial structure and can lead to quantum frustration, giving rise to a wealth of complex, strongly correlated quantum phases1. Long-range interactions play an important role in nature; however, quantum simulations of lattice systems have largely not been able to realize such interactions. A wide range of efforts are underway to explore long-range interacting lattice systems using polar molecules2-5, Rydberg atoms2,6-8, optical cavities9-11 or magnetic atoms12-15. Here we realize novel quantum phases in a strongly correlated lattice system with long-range dipolar interactions using ultracold magnetic erbium atoms. As we tune the dipolar interaction to be the dominant energy scale in our system, we observe quantum phase transitions from a superfluid into dipolar quantum solids, which we directly detect using quantum gas microscopy with accordion lattices. Controlling the interaction anisotropy by orienting the dipoles enables us to realize a variety of stripe-ordered states. Furthermore, by transitioning non-adiabatically through the strongly correlated regime, we observe the emergence of a range of metastable stripe-ordered states. This work demonstrates that novel strongly correlated quantum phases can be realized using long-range dipolar interactions in optical lattices, opening the door to quantum simulations of a wide range of lattice models with long-range and anisotropic interactions.
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Affiliation(s)
- Lin Su
- Department of Physics, Harvard University, Cambridge, MA, USA.
| | | | - Michal Szurek
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Robin Groth
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - S Furkan Ozturk
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Aaron Krahn
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Anne H Hébert
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Sepehr Ebadi
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Francesca Ferlaino
- Institut für Experimentalphysik, Universität Innsbruck, Innsbruck, Austria
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Innsbruck, Austria
| | - Ognjen Marković
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Markus Greiner
- Department of Physics, Harvard University, Cambridge, MA, USA.
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4
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Ebadi S, Keesling A, Cain M, Wang TT, Levine H, Bluvstein D, Semeghini G, Omran A, Liu JG, Samajdar R, Luo XZ, Nash B, Gao X, Barak B, Farhi E, Sachdev S, Gemelke N, Zhou L, Choi S, Pichler H, Wang ST, Greiner M, Vuletic V, Lukin MD. Quantum optimization of maximum independent set using Rydberg atom arrays. Science 2022; 376:1209-1215. [PMID: 35511943 DOI: 10.1126/science.abo6587] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Realizing quantum speedup for practically relevant, computationally hard problems is a central challenge in quantum information science. Using Rydberg atom arrays with up to 289 qubits in two spatial dimensions, we experimentally investigate quantum algorithms for solving the Maximum Independent Set problem. We use a hardware-efficient encoding associated with Rydberg blockade, realize closed-loop optimization to test several variational algorithms, and subsequently apply them to systematically explore a class of graphs with programmable connectivity. We find the problem hardness is controlled by the solution degeneracy and number of local minima, and experimentally benchmark the quantum algorithm's performance against classical simulated annealing. On the hardest graphs, we observe a superlinear quantum speedup in finding exact solutions in the deep circuit regime and analyze its origins.
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Affiliation(s)
- S Ebadi
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Keesling
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing Inc., Boston, MA 02135, USA
| | - M Cain
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - T T Wang
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - H Levine
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - D Bluvstein
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - G Semeghini
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Omran
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing Inc., Boston, MA 02135, USA
| | - J-G Liu
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing Inc., Boston, MA 02135, USA
| | - R Samajdar
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - X-Z Luo
- QuEra Computing Inc., Boston, MA 02135, USA.,Department of Physics and Astronomy, University of Waterloo, Waterloo N2L 3G1, Canada.,Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
| | - B Nash
- School of Engineering and Applied Science, Harvard University, Cambridge, MA 02138, USA
| | - X Gao
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - B Barak
- School of Engineering and Applied Science, Harvard University, Cambridge, MA 02138, USA
| | - E Farhi
- Google Quantum AI, Venice, CA 90291, USA.,Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - S Sachdev
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA
| | - N Gemelke
- QuEra Computing Inc., Boston, MA 02135, USA
| | - L Zhou
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125, USA
| | - S Choi
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - H Pichler
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria.,Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - S-T Wang
- QuEra Computing Inc., Boston, MA 02135, USA
| | - M Greiner
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | | | - M D Lukin
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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5
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Bluvstein D, Levine H, Semeghini G, Wang TT, Ebadi S, Kalinowski M, Keesling A, Maskara N, Pichler H, Greiner M, Vuletić V, Lukin MD. A quantum processor based on coherent transport of entangled atom arrays. Nature 2022; 604:451-456. [PMID: 35444318 PMCID: PMC9021024 DOI: 10.1038/s41586-022-04592-6] [Citation(s) in RCA: 54] [Impact Index Per Article: 27.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2021] [Accepted: 02/28/2022] [Indexed: 11/23/2022]
Abstract
The ability to engineer parallel, programmable operations between desired qubits within a quantum processor is key for building scalable quantum information systems1,2. In most state-of-the-art approaches, qubits interact locally, constrained by the connectivity associated with their fixed spatial layout. Here we demonstrate a quantum processor with dynamic, non-local connectivity, in which entangled qubits are coherently transported in a highly parallel manner across two spatial dimensions, between layers of single- and two-qubit operations. Our approach makes use of neutral atom arrays trapped and transported by optical tweezers; hyperfine states are used for robust quantum information storage, and excitation into Rydberg states is used for entanglement generation3–5. We use this architecture to realize programmable generation of entangled graph states, such as cluster states and a seven-qubit Steane code state6,7. Furthermore, we shuttle entangled ancilla arrays to realize a surface code state with thirteen data and six ancillary qubits8 and a toric code state on a torus with sixteen data and eight ancillary qubits9. Finally, we use this architecture to realize a hybrid analogue–digital evolution2 and use it for measuring entanglement entropy in quantum simulations10–12, experimentally observing non-monotonic entanglement dynamics associated with quantum many-body scars13,14. Realizing a long-standing goal, these results provide a route towards scalable quantum processing and enable applications ranging from simulation to metrology. A quantum processer is realized using arrays of neutral atoms that are transported in a parallel manner by optical tweezers during computations, and used for quantum error correction and simulations.
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Affiliation(s)
- Dolev Bluvstein
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Harry Levine
- Department of Physics, Harvard University, Cambridge, MA, USA.,AWS Center for Quantum Computing, Pasadena, CA, USA
| | | | - Tout T Wang
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Sepehr Ebadi
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Alexander Keesling
- Department of Physics, Harvard University, Cambridge, MA, USA.,QuEra Computing Inc., Boston, MA, USA
| | - Nishad Maskara
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Hannes Pichler
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck, Austria.,Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck, Austria
| | - Markus Greiner
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Vladan Vuletić
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Mikhail D Lukin
- Department of Physics, Harvard University, Cambridge, MA, USA.
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6
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Semeghini G, Levine H, Keesling A, Ebadi S, Wang TT, Bluvstein D, Verresen R, Pichler H, Kalinowski M, Samajdar R, Omran A, Sachdev S, Vishwanath A, Greiner M, Vuletić V, Lukin MD. Probing topological spin liquids on a programmable quantum simulator. Science 2021; 374:1242-1247. [PMID: 34855494 DOI: 10.1126/science.abi8794] [Citation(s) in RCA: 77] [Impact Index Per Article: 25.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
[Figure: see text].
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Affiliation(s)
- G Semeghini
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - H Levine
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Keesling
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing, Boston, MA 02135, USA
| | - S Ebadi
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - T T Wang
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - D Bluvstein
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - R Verresen
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - H Pichler
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria.,Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - M Kalinowski
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - R Samajdar
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Omran
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing, Boston, MA 02135, USA
| | - S Sachdev
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA
| | - A Vishwanath
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - M Greiner
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - V Vuletić
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - M D Lukin
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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7
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Bluvstein D, Omran A, Levine H, Keesling A, Semeghini G, Ebadi S, Wang TT, Michailidis AA, Maskara N, Ho WW, Choi S, Serbyn M, Greiner M, Vuletić V, Lukin MD. Controlling quantum many-body dynamics in driven Rydberg atom arrays. Science 2021; 371:1355-1359. [PMID: 33632894 DOI: 10.1126/science.abg2530] [Citation(s) in RCA: 46] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2020] [Accepted: 02/12/2021] [Indexed: 11/02/2022]
Abstract
The control of nonequilibrium quantum dynamics in many-body systems is challenging because interactions typically lead to thermalization and a chaotic spreading throughout Hilbert space. We investigate nonequilibrium dynamics after rapid quenches in a many-body system composed of 3 to 200 strongly interacting qubits in one and two spatial dimensions. Using a programmable quantum simulator based on Rydberg atom arrays, we show that coherent revivals associated with so-called quantum many-body scars can be stabilized by periodic driving, which generates a robust subharmonic response akin to discrete time-crystalline order. We map Hilbert space dynamics, geometry dependence, phase diagrams, and system-size dependence of this emergent phenomenon, demonstrating new ways to steer complex dynamics in many-body systems and enabling potential applications in quantum information science.
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Affiliation(s)
- D Bluvstein
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Omran
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing Inc., Boston, MA 02135, USA
| | - H Levine
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Keesling
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - G Semeghini
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - S Ebadi
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - T T Wang
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | | | - N Maskara
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - W W Ho
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,Department of Physics, Stanford University, Stanford, CA 94305, USA
| | - S Choi
- Department of Physics, University of California Berkeley, Berkeley, CA 94720, USA
| | - M Serbyn
- IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - M Greiner
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - V Vuletić
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - M D Lukin
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.
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8
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Omran A, Levine H, Keesling A, Semeghini G, Wang TT, Ebadi S, Bernien H, Zibrov AS, Pichler H, Choi S, Cui J, Rossignolo M, Rembold P, Montangero S, Calarco T, Endres M, Greiner M, Vuletić V, Lukin MD. Generation and manipulation of Schrödinger cat states in Rydberg atom arrays. Science 2020; 365:570-574. [PMID: 31395778 DOI: 10.1126/science.aax9743] [Citation(s) in RCA: 89] [Impact Index Per Article: 22.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2019] [Accepted: 07/08/2019] [Indexed: 11/03/2022]
Abstract
Quantum entanglement involving coherent superpositions of macroscopically distinct states is among the most striking features of quantum theory, but its realization is challenging because such states are extremely fragile. Using a programmable quantum simulator based on neutral atom arrays with interactions mediated by Rydberg states, we demonstrate the creation of "Schrödinger cat" states of the Greenberger-Horne-Zeilinger (GHZ) type with up to 20 qubits. Our approach is based on engineering the energy spectrum and using optimal control of the many-body system. We further demonstrate entanglement manipulation by using GHZ states to distribute entanglement to distant sites in the array, establishing important ingredients for quantum information processing and quantum metrology.
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Affiliation(s)
- A Omran
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - H Levine
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Keesling
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - G Semeghini
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - T T Wang
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,Department of Physics, Gordon College, Wenham, MA 01984, USA
| | - S Ebadi
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - H Bernien
- Institute for Molecular Engineering, University of Chicago, Chicago, IL 60637, USA
| | - A S Zibrov
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - H Pichler
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,Institute for Theoretical Atomic Molecular and Optical Physics (ITAMP), Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA
| | - S Choi
- Department of Physics, University of California, Berkeley, Berkeley, CA 94720, USA
| | - J Cui
- Forschungszentrum Jülich, Institute of Quantum Control (PGI-8), D-52425 Jülich, Germany
| | - M Rossignolo
- Institute for Quantum Optics and Center of Integrated Quantum Science and Technology (IQST), Universität Ulm, D-89081 Ulm, Germany
| | - P Rembold
- Forschungszentrum Jülich, Institute of Quantum Control (PGI-8), D-52425 Jülich, Germany
| | - S Montangero
- Dipartimento di Fisica e Astronomia "G. Galilei," Università degli Studi di Padova and Istituto Nazionale di Fisica Nucleare (INFN), I-35131 Padova, Italy
| | - T Calarco
- Forschungszentrum Jülich, Institute of Quantum Control (PGI-8), D-52425 Jülich, Germany.,Institute for Theoretical Physics, University of Cologne, D-50937 Cologne, Germany
| | - M Endres
- Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA 91125, USA
| | - M Greiner
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - V Vuletić
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - M D Lukin
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.
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9
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Levine H, Keesling A, Semeghini G, Omran A, Wang TT, Ebadi S, Bernien H, Greiner M, Vuletić V, Pichler H, Lukin MD. Parallel Implementation of High-Fidelity Multiqubit Gates with Neutral Atoms. Phys Rev Lett 2019; 123:170503. [PMID: 31702233 DOI: 10.1103/physrevlett.123.170503] [Citation(s) in RCA: 64] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2019] [Indexed: 06/10/2023]
Abstract
We report the implementation of universal two- and three-qubit entangling gates on neutral-atom qubits encoded in long-lived hyperfine ground states. The gates are mediated by excitation to strongly interacting Rydberg states and are implemented in parallel on several clusters of atoms in a one-dimensional array of optical tweezers. Specifically, we realize the controlled-phase gate, enacted by a novel, fast protocol involving only global coupling of two qubits to Rydberg states. We benchmark this operation by preparing Bell states with fidelity F≥95.0(2)%, and extract gate fidelity ≥97.4(3)%, averaged across five atom pairs. In addition, we report a proof-of-principle implementation of the three-qubit Toffoli gate, in which two control atoms simultaneously constrain the behavior of one target atom. These experiments demonstrate key ingredients for high-fidelity quantum information processing in a scalable neutral-atom platform.
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Affiliation(s)
- Harry Levine
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Alexander Keesling
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Giulia Semeghini
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Ahmed Omran
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Tout T Wang
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Department of Physics, Gordon College, Wenham, Massachusetts 01984, USA
| | - Sepehr Ebadi
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Hannes Bernien
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Markus Greiner
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Vladan Vuletić
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Hannes Pichler
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
| | - Mikhail D Lukin
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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Rvachov TM, Son H, Park JJ, Ebadi S, Zwierlein MW, Ketterle W, Jamison AO. Two-photon spectroscopy of the NaLi triplet ground state. Phys Chem Chem Phys 2018; 20:4739-4745. [PMID: 29379932 DOI: 10.1039/c7cp08481a] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
We employ two-photon spectroscopy to study the vibrational states of the triplet ground state potential (a3Σ+) of the 23Na6Li molecule. Pairs of Na and Li atoms in an ultracold mixture are photoassociated into an excited triplet molecular state, which in turn is coupled to vibrational states of the triplet ground potential. Vibrational state binding energies, line strengths, and potential fitting parameters for the triplet ground a3Σ+ potential are reported. We also observe rotational splitting in the lowest vibrational state.
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Affiliation(s)
- Timur M Rvachov
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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11
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Rvachov TM, Son H, Sommer AT, Ebadi S, Park JJ, Zwierlein MW, Ketterle W, Jamison AO. Long-Lived Ultracold Molecules with Electric and Magnetic Dipole Moments. Phys Rev Lett 2017; 119:143001. [PMID: 29053331 DOI: 10.1103/physrevlett.119.143001] [Citation(s) in RCA: 65] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2017] [Indexed: 06/07/2023]
Abstract
We create fermionic dipolar ^{23}Na^{6}Li molecules in their triplet ground state from an ultracold mixture of ^{23}Na and ^{6}Li. Using magnetoassociation across a narrow Feshbach resonance followed by a two-photon stimulated Raman adiabatic passage to the triplet ground state, we produce 3×10^{4} ground state molecules in a spin-polarized state. We observe a lifetime of 4.6 s in an isolated molecular sample, approaching the p-wave universal rate limit. Electron spin resonance spectroscopy of the triplet state was used to determine the hyperfine structure of this previously unobserved molecular state.
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Affiliation(s)
- Timur M Rvachov
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Hyungmok Son
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Ariel T Sommer
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Sepehr Ebadi
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada
| | - Juliana J Park
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Martin W Zwierlein
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Wolfgang Ketterle
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Alan O Jamison
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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12
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Ebadi H, Siddiqui H, Ebadi S, Ngo M, Breiner A, Bril V. Peripheral Nerve Ultrasound in Small Fiber Polyneuropathy. Ultrasound Med Biol 2015; 41:2820-2826. [PMID: 26318562 DOI: 10.1016/j.ultrasmedbio.2015.06.011] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2014] [Revised: 06/11/2015] [Accepted: 06/16/2015] [Indexed: 06/04/2023]
Abstract
Routine nerve conduction studies are normal in patients with small fiber neuropathy (SFN), and a definitive diagnosis is based on skin biopsy revealing reduced intra-epidermal nerve fiber density (IENFD). In large fiber polyneuropathy, ultrasound (US) parameters indicate enlargement in cross-sectional area (CSA). This study was aimed at determining if similar changes in large fibers on US are apparent in patients with SFN. Twenty-five patients with SFN diagnosed by reduced IENFD and 25 age- and body mass index (BMI)-matched healthy controls underwent US studies of sural and superficial peroneal sensory nerves. The mean CSA of the sural nerve in SFN patients was 3.2 ± 0.8 mm(2), and in controls, 2.7 ± 0.6 mm(2) (p < 0.0070), and this was independent of sex. There was no difference in the thickness-to-width ratio or echogenicity of the nerves. US of the sural nerve in patients diagnosed with small fiber neuropathy reveals an enlarged cross-sectional area similar to that in large fiber polyneuropathy.
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Affiliation(s)
- Hamid Ebadi
- Department of Clinical Neurosciences, University of Calgary, Calgary, Alberta, Canada
| | - Hafsah Siddiqui
- Division of Neurology, Department of Medicine, University of Toronto, Toronto, Ontario, Canada
| | - Sepehr Ebadi
- Division of Engineering Science, Faculty of Applied Sciences and Engineering, University of Toronto, Toronto, Ontario, Canada
| | - MyLan Ngo
- Division of Neurology, Department of Medicine, University of Toronto, Toronto, Ontario, Canada
| | - Ari Breiner
- Division of Neurology, Department of Medicine, University of Toronto, Toronto, Ontario, Canada
| | - Vera Bril
- Division of Neurology, Department of Medicine, University of Toronto, Toronto, Ontario, Canada.
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Ansari NN, Ebadi S, Talebian S, Naghdi S, Mazaheri H, Olyaei G, Jalaie S. A randomized, single blind placebo controlled clinical trial on the effect of continuous ultrasound on low back pain. Electromyogr Clin Neurophysiol 2006; 46:329-36. [PMID: 17147074 DOI: pmid/17147074] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
Low back pain (LBP) is a very common problem in primary care and a major cause of disability. There is no evidence for the efficacy of therapeutic modalities such as ultrasound in LBP In a randomized, single blind placebo controlled clinical trial, we aimed to evaluate the effect of continuous ultrasound (US) in patients with non specific LBP Of the fifty eight patients recruited, 10 patients (8 women and 2 men) randomly allocated to ultrasound (n=5) or placebo controlled (n=5) groups. The patients were treated by either US or sham-US for ten sessions, three days per week, every other day. The outcome measures were Functional Rating Index (FRI), Hmax/Mmax ratio and range of motion (ROM), which were measured at baseline, after 5 treatment sessions and at the end of treatment. To analyze the data, The Mann Whitney U test and Wilcoxon Signed Rank test were used. After treatment, both US and placebo groups showed statistically significant decrease in FRI scores indicating improvement in functional ability (p = 0.042 and p = 0.043, respectively). The mean changes of FRI during the second five treatment sessions and after the end of treatment was significantly better in the US group than in the placebo group (p = 0.016 and p = 0.032, respectively). Before and after treatment, the mean H reflex latency and Hmax/Mmax ratio, right and left side were similar in the groups (p > 0.05), and no significant changes were observed in the treatment groups (p > 0.05). After treatment, the extension and lateral flexion range of motion significantly increased in the US group (p = 0.04), but the back movements in the placebo group did not show significant changes (p > 0.05). The present study supports the significant effect of US on LBP, and suggests that US may improve the functional ability of patients with non specific low back pain.
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Affiliation(s)
- N N Ansari
- Rehabilitation Faculty, Tehran University of Medical Sciences, Iran.
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