Cited by 144Quantum Computing Algorithms and ArchitectureQuantum Information and CryptographyCold Atom Physics and Bose-Einstein Condensates

Hardware-Efficient, Fault-Tolerant Quantum Computation with Rydberg Atoms

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Cong, Iris, Levine, Harry, Keesling, Alexander, Bluvstein, Dolev, Wang, Sheng-Tao, Lukin, Mikhail D.·2022·Physical Review X

Abstract

Neutral-atom arrays have recently emerged as a promising platform for quantum information processing.One important remaining roadblock for the large-scale application of these systems is the ability to perform error-corrected quantum operations.To entangle the qubits in these systems, atoms are typically excited to Rydberg states, which could decay or give rise to various correlated errors that cannot be addressed directly through traditional methods of fault-tolerant quantum computation.In this work, we provide the first complete characterization of these sources of error in a neutral-atom quantum computer and propose hardware-efficient, fault-tolerant quantum computation schemes that mitigate them.Notably, we develop a novel and distinctly efficient method to address the most important errors associated with the decay of atomic qubits to states outside of the computational subspace.These advances allow us to significantly reduce the resource cost for fault-tolerant quantum computation compared to existing, general-purpose schemes.Our protocols can be implemented in the near term using state-of-the-art neutral-atom platforms with qubits encoded in both alkali and alkaline-earth atoms.

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  • Mid-circuit readout is enabled by moving selected qubits about 100 μm away to a readout zone and illuminating with a focused imaging beam, resulting in high-fidelity imaging and negligible decoherence on stored qubits.

    “Mid-circuit readout is enabled by moving selected qubits about 100 μm away to a readout zone and illuminating with a focused imaging beam7,35, resulting in high-fidelity imaging, as well as negligible decoherence on stored qubits (Fig. 1c and Extended Data Fig. 3).”

    From Logical quantum processor based on reconfigurable atom arrays (2024) · cites this paper as [35]

    In “Measurements and feed-forward corrections” (page unavailable), the paper proposes moving selected ancilla atoms to a distant detection zone and detecting scattered photons. It estimates displacements greater than 50 μm and predicts negligible crosstalk on data qubits. It does not specify a focused imaging beam or establish high-fidelity imaging and negligible decoherence of stored qubits as observed results. (LLM, conf=0.86)

    Experimental — accuracy not yet measured
  • Finite lifetime of an atom in the Rydberg state can give rise to correlated errors that are difficult to address by standard error correction methods.

    “Another important challenge is the finite lifetime of an atom in the Rydberg state, which can give rise to different kinds of correlated errors that are difficult to address by standard error correction methods [40].”
  • Those errors have been addressed recently by a hardware-efficient, fault-tolerant error correction scheme, making use of the specific properties of Rydberg atoms.

    “Those have been addressed recently by a hardwareefficient, fault-tolerant error correction scheme, making use of the specific properties of Rydberg atoms [62].”

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  1. D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Cote, and M. D. Lukin, Fast Quantum Gates for Neutral Atoms, Phys. Rev. Lett. 85, 2208 (2000). · DOI · Paper page
  2. M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, Dipole Blockade and Quantum Information Processing in Mesoscopic Atomic Ensembles, Phys. Rev. Lett. 87, 037901 (2001). · DOI
  3. M. Saffman, T. G. Walker, and K. Mølmer, Quantum Information with Rydberg Atoms, Rev. Mod. Phys. 82, 2313 (2010). · DOI
  4. D. Barredo, S. de Léséleuc, V. Lienhard, T. Lahaye, and A. Browaeys, An Atom-by-Atom Assembler of Defect-Free Two- Dimensional Atomic Arrays, Science 354, 1021 (2016). · DOI
  5. D. Barredo, V. Lienhard, S. de Léséleuc, T. Lahaye, and A. Browaeys, Synthetic Three-Dimensional Atomic Structures Assembled Atom by Atom, Nature (London) 561, 79 (2018). · DOI · Paper page
  6. D. Barredo, V. Lienhard, P. Scholl, S. de Léséleuc, T. Boulier, A. Browaeys, and T. Lahaye, Three-Dimensional Trapping of Individual Rydberg Atoms in Ponderomotive Bottle Beam Traps, Phys. Rev. Lett. 124, 023201 (2020). · DOI
  7. H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin, High-Fidelity Control and Entanglement of Rydberg Atom Qubits, Phys. Rev. Lett. 121, 123603 (2018). · DOI
  8. H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, M. Macri, T. Lahaye, and A. Browaeys, Tunable Two-Dimensional Arrays of Single Rydberg Atoms for Realizing Quantum Ising Models, Nature (London) 534, 667 (2016). · DOI
  9. K. M. Maller, M. T. Lichtman, T. Xia, Y. Sun, M. J. Piotrowicz, A. W. Carr, L. Isenhower, and M. Saffman, Rydberg-Blockade Controlled-NOT Gate and Entanglement in a Two-Dimensional Array of Neutral-Atom Qubits, Phys. Rev. A 92, 022336 (2015). · DOI
  10. H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletic, H. Pichler, and M. D. Lukin, Parallel Implementation of High- Fidelity Multiqubit Gates with Neutral Atoms, Phys. Rev. Lett. 123, 170503 (2019). · DOI · Paper page
  11. H. Kim, Y. J. Park, K. Kim, H.-S. Sim, and J. Ahn, Detailed Balance of Thermalization Dynamics in Rydberg-Atom Quantum Simulators, Phys. Rev. Lett. 120, 180502 (2018). · DOI
  12. A. Keesling, A. Omran, H. Levine, H. Bernien, H. Pichler, S. Choi, R. Samajdar, S. Schwartz, P. Silvi, S. Sachdev, P. Zoller, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin, Quantum Kibble-Zurek Mechanism and Critical Dynamics on a Programmable Rydberg Simulator, Nature (London) 568, 207 (2019). · DOI · Paper page
  13. A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin, Generation and Manipulation of Schrödinger Cat States in Rydberg Atom Arrays, Science 365, 570 (2019). · DOI · Paper page
  14. G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kalinowski, R. Samajdar, A. Omran, S. Sachdev, A. Vishwanath, M. Greiner, V. Vuletić, and M. D. Lukin, Probing Topological Spin Liquids on a Programmable Quantum Simulator, Science 374, 1242 (2021). · DOI · Paper page
  15. D. Bluvstein, H. Levine, G. Semeghini, T. T. Wang, S. Ebadi, M. Kalinowski, A. Keesling, N. Maskara, H. Pichler, M. Greiner, V. Vuletic, and M. D. Lukin, A Quantum Processor Based on Coherent Transport of Entangled Atom Arrays, arXiv:2112.03923. · arXiv
  16. M. A. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).
  17. P. W. Shor, in Proceedings of the 37th Conference on Foundations of Computer Science (IEEE, New York, 1996), pp. 56-65.
  18. A. Y. Kitaev, Fault-Tolerant Quantum Computation by Anyons, Ann. Phys. (Amsterdam) 303, 2 (2003). · DOI · Paper page
  19. D. Gottesman, Proceedings of the Symposium in Applied Mathematics Quantum Information Science and Its Contributions to Mathematics (American Mathematical Society, Providence, 2010), pp. 13-56.
  20. T. J. Yoder and I. H. Kim, The Surface Code with a Twist, Quantum 1, 2 (2017). · DOI
  21. R. Chao and B. W. Reichardt, Quantum Error Correction with Only Two Extra Qubits, Phys. Rev. Lett. 121, 050502 (2018). · DOI
  22. R. Chao and B. W. Reichardt, Fault-Tolerant Quantum Computation with Few Qubits, npj Quantum Inf. 4, 42 (2018). · DOI · Paper page
  23. B. W. Reichardt, Fault-Tolerant Quantum Error Correction for Steane's Seven-Qubit Color Code with Few or No Extra Qubits, Quantum Sci. Technol. 6, 015007 (2021). · DOI
  24. C. Chamberland and M. E. Beverland, Flag Fault-Tolerant Error Correction with Arbitrary Distance Codes, Quantum 2, 53 (2018). · DOI · Paper page
  25. R. Chao and B. W. Reichardt, Flag Fault-Tolerant Error Correction for Any Stabilizer Code, PRX Quantum 1, 010302 (2020). · DOI · Paper page
  26. M. H. Michael, M. Silveri, R. T. Brierley, V. V. Albert, J. Salmilehto, L. Jiang, and S. M. Girvin, New Class of Quantum Error-Correcting Codes for a Bosonic Mode, Phys. Rev. X 6, 031006 (2016). · DOI
  27. C. Chamberland, K. Noh, P. Arrangoiz-Arriola, E. T. Campbell, C. T. Hann, J. Iverson, H. Putterman, T. C. Bohdanowicz, S. T. Flammia, A. Keller, G. Refael, J. Preskill, L. Jiang, A. H. Safavi-Naeini, O. Painter, and F. G. S. L. Brando, Building a Fault-Tolerant Quantum Computer Using Concatenated Cat Codes, PRX Quantum 3, 010329 (2022). · DOI · Paper page
  28. T. J. Yoder, R. Takagi, and I. L. Chuang, Universal Fault- Tolerant Gates on Concatenated Stabilizer Codes, Phys. Rev. X 6, 031039 (2016). · DOI
  29. D. Nigg, M. Müller, E. A. Martinez, P. Schindler, M. Hennrich, T. Monz, M. A. Martin-Delgado, and R. Blatt, Quantum Computations on a Topologically Encoded Qubit, Science 345, 302 (2014). · DOI · Paper page
  30. S. Rosenblum, P. Reinhold, M. Mirrahimi, L. Jiang, L. Frunzio, and R. J. Schoelkopf, Fault-Tolerant Detection of a Quantum Error, Science 361, 266 (2018). · DOI
  31. P. Campagne-Ibarcq, A. Eickbusch, S. Touzard, E. Zalys- Geller, N. E. Frattini, V. V. Sivak, P. Reinhold, S. Puri, S. Shankar, R. J. Schoelkopf et al., Quantum Error Correction of a Qubit Encoded in Grid States of an Oscillator, Nature (London) 584, 368 (2020). · DOI · Paper page
  32. B. de Neeve, T. L. Nguyen, T. Behrle, and J. Home, Error Correction of a Logical Grid State Qubit by Dissipative Pumping, arXiv:2010.09681. · arXiv
  33. L. Egan, D. M. Debroy, C. Noel, A. Risinger, D. Zhu, D. Biswas, M. Newman, M. Li, K. R. Brown, M. Cetina, and C. Monroe, Fault-Tolerant Operation of a Quantum Error- Correction Code, arXiv:2009.11482. · arXiv
  34. A. Steane, Multiple-Particle Interference and Quantum Error Correction, Proc. R. Soc. A 452, 2551 (1996). · DOI · Paper page
  35. L. Isenhower, M. Saffman, and K. Mølmer, Multibit C k NOT Quantum Gates via Rydberg Blockade, Quantum Inf. Process. 10, 755 (2011). · DOI
  36. J. M. Auger, S. Bergamini, and D. E. Browne, Blueprint for Fault-Tolerant Quantum Computation with Rydberg Atoms, Phys. Rev. A 96, 052320 (2017). · DOI
  37. Y. Shi, Both Toffoli and Controlled-NOT Need Little Help To Do Universal Quantum Computation, Quantum Inf. Comput. 3, 84 (2003). · DOI · Paper page
  38. J. Guillaud and M. Mirrahimi, Repetition Cat Qubits for Fault-Tolerant Quantum Computation, Phys. Rev. X 9, 041053 (2019). · DOI · Paper page
  39. Y. Zeng, P. Xu, X. He, Y. Liu, M. Liu, J. Wang, D. J. Papoular, G. V. Shlyapnikov, and M. Zhan, Entangling Two Individual Atoms of Different Isotopes via Rydberg Blockade, Phys. Rev. Lett. 119, 160502 (2017). · DOI
  40. K. Singh, S. Anand, A. Pocklington, J. T. Kemp, and H. Bernien, Dual-Element, Two-Dimensional Atom Array with Continuous-Mode Operation, Phys. Rev. X 12, 011040 (2022). · DOI
  41. I. S. Madjarov, J. P. Covey, A. L. Shaw, J. Choi, A. Kale, A. Cooper, H. Picher, V. Schkolnik, J. R. Williams, and M. Endres, High-Fidelity Entanglement and Detection of Alkaline-Earth Rydberg Atoms, Nat. Phys. 16, 857 (2020). · DOI
  42. J. Wilson, S. Saskin, Y. Meng, S. Ma, R. Dilip, A. Burgers, and J. Thompson, Trapping Alkaline-Earth-Metal Rydberg Atom Optical Tweezer Arrays, Phys. Rev. Lett. 128, 033201 (2022). · DOI
  43. L. M. K. Vandersypen and I. L. Chuang, NMR Techniques for Quantum Control and Computation, Rev. Mod. Phys. 76, 1037 (2005). · DOI · Paper page
  44. I. I. Beterov, I. I. Ryabtsev, D. B. Tretyakov, and V. M. Entin, Quasiclassical Calculations of Blackbody- Radiation-Induced Depopulation Rates and Effective Life- times of Rydberg ns, np, and nd Alkali-Metal Atoms with n ≤ 80, Phys. Rev. A 79, 052504 (2009). · DOI
  45. H. J. Carmichael, An Open Systems Approach to Quantum Optics (Springer, New York, 1993).
  46. J. Preskill, Quantum Information and Computation, Lecture Notes for Physics Vol. 229 (California Institute of Technology, Pasadena, 1998).
  47. W. E. Cooke and T. F. Gallagher, Effects of Blackbody Radiation on Highly Excited Atoms, Phys. Rev. A 21, 588 (1980). · DOI
  48. R. Löw, H. Weimer, J. Nipper, J. B. Balewski, B. Butscher, H. P. Büchler, and T. Pfau, An Experimental and Theoretical Guide to Strongly Interacting Rydberg Gases, J. Phys. B 45, 113001 (2012). · DOI
  49. Y. Wu, S. Kolkowitz, S. Puri, and J. D. Thompson, Erasure Conversion for Fault-Tolerant Quantum Computing in Alkaline Earth Rydberg Atom Arrays, arXiv:2201.03540. · arXiv
  50. P. Wang, C.-Y. Luan, M. Qiao, M. Um, J. Zhang, Y. Wang, X. Yuan, M. Gu, J. Zhang, and K. Kim, Single Ion Qubit with Estimated Coherence Time Exceeding One Hour, Nat. Commun. 12, 1 (2021). · DOI · Paper page
  51. J. S. Cohen, Effect of Tunneling on Ionization of Rydberg States in Intense Fields: Hydrogenic Atoms, Phys. Rev. A 68, 033409 (2003). · DOI
  52. L. Beguin, Measurement of the van der Waals Interaction between Two Rydberg Atoms, Ph.D. thesis, Institut d'Optique Graduate School, 2013.
  53. S. Puri, L. St-Jean, J. A. Gross, A. Grimm, N. E. Frattini, P. S. Iyer, A. Krishna, S. Touzard, L. Jiang, A. Blais, S. T. Flammia, and S. M. Girvin, Bias-Preserving Gates with Stabilized Cat Qubits, Sci. Adv. 6, aay5901 (2020). · DOI · Paper page
  54. D. Bluvstein, A. Omran, H. Levine, A. Keesling, G. Semeghini, S. Ebadi, T. T. Wang, A. A. Michailidis, N. Maskara, W. W. Ho, S. Choi, M. Serbyn, M. Greiner, V. Vuletic, and M. D. Lukin, Controlling Quantum Many-Body Dynamics in Driven Rydberg Atom Arrays, Science 371, 1355 (2021). · DOI
  55. A. Bergschneider, V. M. Klinkhamer, J. H. Becher, R. Klemt, G. Zürn, P. M. Preiss, and S. Jochim, Spin-Resolved Single-Atom Imaging of 6 Li in Free Space, Phys. Rev. A 97, 063613 (2018). · DOI
  56. P. Carruthers and M. M. Nieto, Coherent States and the Forced Quantum Oscillator, Am. J. Phys. 33, 537 (1965). · DOI
  57. M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. Blatt, T. Zanon-Willette, S. M. Foreman, and J. Ye, Nuclear Spin Effects in Optical Lattice Clocks, Phys. Rev. A 76, 022510 (2007). · DOI · Paper page
  58. D. Hayes, D. Stack, B. Bjork, A. C. Potter, C. H. Baldwin, and R. P. Stutz, Eliminating Leakage Errors in Hyperfine Qubits, Phys. Rev. Lett. 124, 170501 (2020). · DOI
  59. S. B. Bravyi and A. Y. Kitaev, Quantum Codes on a Lattice with Boundary, arXiv:quant-ph/9811052. · arXiv
  60. H. Bombin and M. A. Martin-Delgado, Topological Quantum Distillation, Phys. Rev. Lett. 97, 180501 (2006). · DOI · Paper page
  61. H. Bombin and M. A. Martin-Delgado, Topological Computation without Braiding, Phys. Rev. Lett. 98, 160502 (2007). · DOI
  62. D. K. Tuckett, S. D. Bartlett, and S. T. Flammia, Ultrahigh Error Threshold for Surface Codes with Biased Noise, Phys. Rev. Lett. 120, 050505 (2018). · DOI · Paper page
  63. B. Kaulakys, Consistent Analytical Approach for the Quasi- classical Radial Dipole Matrix Elements, J. Phys. B 28, 4963 (1995). · DOI
  64. G. Lagmago Kamta, S. G. Nana Engo, M. G. Kwato Njock, and B. Oumarou, Consistent Description of Klein-Gordon Dipole Matrix Elements, J. Phys. B 31, 963 (1998). · DOI

Cited by

Sorted by citations

Authors
Cong, I., Levine, H., Keesling, A., Bluvstein, D., Wang, S.-T., & Lukin, M. D.
Affiliations
  • Harvard University (US)
  • QuEra Computing (United States) (US)
Venue
Physical Review X
Published
2022-06-01
Volume
12
Issue
2
ISSN
2160-3308 (ISSN-L)
OpenAlex
W3168728763
Cited by
144
References
8
Citations by year
2026: 16 · 2025: 39 · 2024: 39 · 2023: 37 · 2022: 11 · 2021: 2
FWCI
10.36
Type
journal article
Language
en
Open access
Locations
  • Physical Review X (publishedVersion, cc-by)
  • arXiv (Cornell University) (acceptedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
  • arXiv (Cornell University) (cc-by)
Funders
  • Center for Ultracold Atoms, Massachusetts Institute of Technology
  • National Science Foundation (DGE1745303)
  • U.S. Department of Energy (DE-SC0021013)
  • Lawrence Berkeley National Laboratory
  • Army Research Office
  • Defense Advanced Research Projects Agency
  • Hertz Foundation
  • Paul and Daisy Soros Fellowships for New Americans
  • Amazon Web Services
  • U.S. Department of Defense
  • National Defense Science and Engineering Graduate
  • QuEra Computing
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
Keywords
fault-tolerant quantum computing, Rydberg atoms, neutral atom quantum computing, error mitigation, correlated errors, alkali atoms, alkaline-earth atoms, qubit entanglement

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