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Practical quantum advantage in quantum simulation

Nature volume 607, pages 667–676 (2022)Cite this article

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Abstract

The development of quantum computing across several technologies and platforms has reached the point of having an advantage over classical computers for an artificial problem, a point known as ‘quantum advantage’. As a next step along the development of this technology, it is now important to discuss ‘practical quantum advantage’, the point at which quantum devices will solve problems of practical interest that are not tractable for traditional supercomputers. Many of the most promising short-term applications of quantum computers fall under the umbrella of quantum simulation: modelling the quantum properties of microscopic particles that are directly relevant to modern materials science, high-energy physics and quantum chemistry. This would impact several important real-world applications, such as developing materials for batteries, industrial catalysis or nitrogen fixing. Much as aerodynamics can be studied either through simulations on a digital computer or in a wind tunnel, quantum simulation can be performed not only on future fault-tolerant digital quantum computers but also already today through special-purpose analogue quantum simulators. Here we overview the state of the art and future perspectives for quantum simulation, arguing that a first practical quantum advantage already exists in the case of specialized applications of analogue devices, and that fully digital devices open a full range of applications but require further development of fault-tolerant hardware. Hybrid digital–analogue devices that exist today already promise substantial flexibility in near-term applications.

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Fig. 1: Overview of quantum simulators.
Fig. 2: Quantum advantage of quantum simulators over classical simulation.

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References

  1. Ladd, T. D. et al. Quantum computers. Nature 464, 45–53 (2010).

    Article  CAS  PubMed  ADS  Google Scholar 

  2. Grumbling, E. & Horowitz, M. (eds) Quantum Computing: Progress and Prospects (National Academies Press, 2019).

  3. Deutsch, I. H. Harnessing the power of the second quantum revolution. PRX Quantum 1, 020101 (2020).

    Article  Google Scholar 

  4. Nielsen, M. & Chuang, I. Quantum Computation and Quantum Information 10th anniversary edn (Cambridge Univ. Press, 2010).

  5. Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982).

    Article  MathSciNet  Google Scholar 

  6. Montanaro, A. Quantum algorithms: an overview. npj Quantum Inf. 2, 15023 (2016).

    Article  ADS  Google Scholar 

  7. Aramon, M. et al. Physics-inspired optimization for quadratic unconstrained problems using a digital annealer. Front. Phys. 7, 48 (2019).

  8. Gibney, E. Hello quantum world! Google publishes landmark quantum supremacy claim. Nature 574, 461–462 (2019).

    Article  CAS  PubMed  ADS  Google Scholar 

  9. Arute, F. et al. Quantum supremacy using a programmable superconducting processor. Nature 574, 505–510 (2019). This article reports the demonstration of a quantum advantage with verification for a mathematical problem designed to test the quantum hardware.

    Article  CAS  PubMed  ADS  Google Scholar 

  10. Zhong, H.-S. et al. Quantum computational advantage using photons. Science 370, 1460–1463 (2020).

    Article  CAS  PubMed  ADS  Google Scholar 

  11. Cirac, J. I. & Zoller, P. Goals and opportunities in quantum simulation. Nat. Phys. 8, 264–266 (2012).

    Article  CAS  Google Scholar 

  12. Georgescu, I. M., Ashhab, S. & Nori, F. Quantum simulation. Rev. Mod. Phys. 86, 153–185 (2014).

    Article  ADS  Google Scholar 

  13. Reiher, M., Wiebe, N., Svore, K. M., Wecker, D. & Troyer, M. Elucidating reaction mechanisms on quantum computers. Proc. Natl Acad. Sci. USA 114, 7555–7560 (2017).

    Article  CAS  PubMed  PubMed Central  ADS  Google Scholar 

  14. Quintanilla, J. & Hooley, C. The strong-correlations puzzle. Phys. World 22, 32–37 (2009).

    Article  Google Scholar 

  15. Childs, A. M., Maslov, D., Nam, Y., Ross, N. J. & Su, Y. Toward the first quantum simulation with quantum speedup. Proc. Natl Acad. Sci. USA 115, 9456–9461 (2018).

    Article  MathSciNet  CAS  PubMed  PubMed Central  MATH  ADS  Google Scholar 

  16. Lloyd, S. Universal quantum simulators. Science 273, 1073–1078 (1996). This article discusses in detail how digital quantum simulation could be implemented on quantum computers, and forms the basis for the fault-tolerant quantum simulation protocols discussed here.

    Article  MathSciNet  CAS  PubMed  MATH  ADS  Google Scholar 

  17. Roffe, J. Quantum error correction: an introductory guide. Contemp. Phys. 60, 226–245 (2019).

    Article  ADS  Google Scholar 

  18. Preskill, J. Quantum computing in the NISQ era and beyond. Quantum 2, 79 (2018).

    Article  Google Scholar 

  19. Buluta, I. & Nori, F. Quantum simulators. Science 326, 108–111 (2009).

    Article  CAS  PubMed  ADS  Google Scholar 

  20. Browaeys, A. & Lahaye, T. Many-body physics with individually controlled Rydberg atoms. Nat. Phys. 16, 132–142 (2020).

    Article  CAS  Google Scholar 

  21. Gross, C. & Bloch, I. Quantum simulations with ultracold atoms in optical lattices. Science 357, 995–1001 (2017).

    Article  CAS  PubMed  ADS  Google Scholar 

  22. Greiner, M., Mandel, O., Esslinger, T., Hänsch, T. W. & Bloch, I. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39–44 (2002). This article demonstrates the first analogue quantum simulation of a strongly correlated quantum system, making use of cold atoms in optical lattices.

    Article  CAS  PubMed  ADS  Google Scholar 

  23. Houck, A. A., Türeci, H. E. & Koch, J. On-chip quantum simulation with superconducting circuits. Nat. Phys. 8, 292–299 (2012).

    Article  CAS  Google Scholar 

  24. Hartmann, M. J. Quantum simulation with interacting photons. J. Opt. 18, 104005 (2016).

    Article  ADS  Google Scholar 

  25. Blatt, R. & Roos, C. F. Quantum simulations with trapped ions. Nat. Phys. 8, 277–284 (2012).

    Article  CAS  Google Scholar 

  26. Monroe, C. et al. Programmable quantum simulations of spin systems with trapped ions. Rev. Mod. Phys. 93, 025001 (2021).

    Article  MathSciNet  CAS  ADS  Google Scholar 

  27. Aspuru-Guzik, A. & Walther, P. Photonic quantum simulators. Nat. Phys. 8, 285–291 (2012).

    Article  CAS  Google Scholar 

  28. White, A. G. Photonic quantum simulation. In 2014 OptoElectronics and Communication Conference and Australian Conference on Optical Fibre Technology 660–661 (Optica Publishing Group, 2014).

  29. Choi, J.-y et al. Exploring the many-body localization transition in two dimensions. Science 352, 1547–1552 (2016). This paper provides an important recent demonstration of the use of analogue quantum simulators with cold atoms in optical lattices to explore the dynamics of interacting particles in a disordered system, which is intractable to classical computation.

    Article  MathSciNet  CAS  PubMed  MATH  ADS  Google Scholar 

  30. Chiu, C. S. et al. String patterns in the doped Hubbard model. Science 365, 251–256 (2019).

    Article  MathSciNet  CAS  PubMed  MATH  ADS  Google Scholar 

  31. Koepsell, J. et al. Imaging magnetic polarons in the doped Fermi–Hubbard model. Nature 572, 358–362 (2019).

    Article  CAS  PubMed  ADS  Google Scholar 

  32. Semeghini, G. et al. Probing topological spin liquids on a programmable quantum simulator. Science 374, 1242–1247 (2021).

  33. Satzinger, K. J. et al. Realizing topologically ordered states on a quantum processor. Science374, 1237–1241 (2021).

  34. Bluvstein, D. et al. Controlling quantum many-body dynamics in driven Rydberg atom arrays. Science 371, 1355–1359 (2021). This article demonstrates the state of the art for observing many-body dynamics in an analogue quantum simulator with neutral atom arrays and Rydberg excitations.

    Article  MathSciNet  CAS  PubMed  MATH  ADS  Google Scholar 

  35. Scholl, P. et al. Quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms. Nature 595, 233–238 (2021). This article demonstrates analogue quantum simulation of dynamics with 196 spins using neutral atoms in tweezer arrays.

    Article  CAS  PubMed  ADS  Google Scholar 

  36. Zhang, J. et al. Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator. Nature 551, 601–604 (2017).

    Article  CAS  PubMed  PubMed Central  ADS  Google Scholar 

  37. Zhang, J. et al. Observation of a discrete time crystal. Nature 543, 217–220 (2017).

    Article  CAS  PubMed  ADS  Google Scholar 

  38. Barreiro, J. T. et al. An open-system quantum simulator with trapped ions. Nature 470, 486–491 (2011).

    Article  CAS  PubMed  ADS  Google Scholar 

  39. Altman, E. et al. Quantum simulators: architectures and opportunities. PRX Quantum 2, 017003 (2021).

    Article  Google Scholar 

  40. LeBlanc, J. P. F. et al. Solutions of the two-dimensional Hubbard model: benchmarks and results from a wide range of numerical algorithms. Phys. Rev. X 5, 041041 (2015).

    Google Scholar 

  41. Zheng, B.-X. et al. Stripe order in the underdoped region of the two-dimensional Hubbard model. Science 358, 1155–1160 (2017).

    Article  MathSciNet  CAS  PubMed  MATH  ADS  Google Scholar 

  42. Bauer, B. et al. The ALPS project release 2.0: open source software for strongly correlated systems. J. Stat. Mech. 2011, P05001 (2011).

    Google Scholar 

  43. Becca, F. & Sorella, S. Quantum Monte Carlo Approaches for Correlated Systems (Cambridge Univ. Press, 2017).

  44. Werner, P., Oka, T. & Millis, A. J. Diagrammatic Monte Carlo simulation of nonequilibrium systems. Phys. Rev. B 79, 035320 (2009).

    Article  ADS  CAS  Google Scholar 

  45. Troyer, M. & Wiese, U.-J. Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations. Phys. Rev. Lett. 94, 170201 (2005).

    Article  PubMed  ADS  CAS  Google Scholar 

  46. Eisert, J. Entangling power and quantum circuit complexity. Phys. Rev. Lett.127, 020501 (2021).

  47. Swingle, B., Bentsen, G., Schleier-Smith, M. & Hayden, P. Measuring the scrambling of quantum information. Phys. Rev. A 94, 040302 (2016).

    Article  MathSciNet  ADS  Google Scholar 

  48. Hatano, N. & Suzuki, M. in Quantum Annealing and Other Optimization Methods (eds Das, A. & Chakrabarti, B. K.) 37–68 (Lecture Notes in Physics, Springer, 2005).

  49. Childs, A. M., Su, Y., Tran, M. C., Wiebe, N. & Zhu, S. Theory of Trotter error with commutator scaling. Phys. Rev. X 11, 011020 (2021).

    CAS  Google Scholar 

  50. Heyl, M., Hauke, P. & Zoller, P. Quantum localization bounds trotter errors in digital quantum simulation. Sci. Adv. 5, eaau8342 (2019).

    Article  PubMed  PubMed Central  ADS  Google Scholar 

  51. Wecker, D., Bauer, B., Clark, B. K., Hastings, M. B. & Troyer, M. Gate-count estimates for performing quantum chemistry on small quantum computers. Phys. Rev. A 90, 022305 (2014).

    Article  ADS  CAS  Google Scholar 

  52. Wecker, D. et al. Solving strongly correlated electron models on a quantum computer. Phys. Rev. A 92, 062318 (2015).

    Article  ADS  CAS  Google Scholar 

  53. Kliesch, M., Gogolin, C. & Eisert, J. Lieb–Robinson Bounds and the Simulation of Time-Evolution of Local Observables in Lattice Systems 301–318 (Springer, 2014).

  54. Schollwöck, U. The density-matrix renormalization group in the age of matrix product states. Ann. Phys. 326, 96–192 (2011).

    Article  MathSciNet  MATH  ADS  CAS  Google Scholar 

  55. Verstraete, F., Murg, V. & Cirac, J. I. Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems. Adv. Phys. 57, 143–224 (2008).

    Article  ADS  Google Scholar 

  56. Vidal, G. Efficient simulation of one-dimensional quantum many-body systems. Phys. Rev. Lett. 93, 040502 (2004). This article introduced classical simulation of one-dimensional many-body systems using matrix product states, which provide the present state of the art in classical simulation of quench dynamics in strongly interacting systems.

    Article  PubMed  ADS  CAS  Google Scholar 

  57. Amico, L., Fazio, R., Osterloh, A. & Vedral, V. Entanglement in many-body systems. Rev. Mod. Phys. 80, 517–576 (2008).

    Article  MathSciNet  CAS  MATH  ADS  Google Scholar 

  58. Albash, T. & Lidar, D. A. Adiabatic quantum computation. Rev. Mod. Phys. 90, 015002 (2018).

    Article  MathSciNet  ADS  Google Scholar 

  59. Kempe, J., Kitaev, A. & Regev, O. The complexity of the local Hamiltonian problem. SIAM J. Comput. 35, 1070–1097 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  60. Poggi, P. M., Lysne, N. K., Kuper, K. W., Deutsch, I. H. & Jessen, P. S. Quantifying the sensitivity to errors in analog quantum simulation. PRX Quantum 1, 020308 (2020).

    Article  Google Scholar 

  61. Lanyon, B. P. et al. Universal digital quantum simulation with trapped ions. Science 334, 57–61 (2011).

    Article  CAS  PubMed  ADS  Google Scholar 

  62. Martinez, E. A. et al. Real-time dynamics of lattice gauge theories with a few-qubit quantum computer. Nature 534, 516–519 (2016).

    Article  CAS  PubMed  ADS  Google Scholar 

  63. Berry, D. W., Childs, A. M., Cleve, R., Kothari, R. & Somma, R. D. Simulating Hamiltonian dynamics with a truncated taylor series. Phys. Rev. Lett. 114, 090502 (2015).

    Article  PubMed  ADS  CAS  Google Scholar 

  64. Haah, J., Hastings, M. B., Kothari, R. & Low, G. H. Quantum algorithm for simulating real time evolution of lattice Hamiltonians. SIAM J. Comput. FOCS18-250-FOCS18-284 (2021).

  65. Aharonov, D. & Ta-Shma, A. Adiabatic quantum state generation and statistical zero knowledge. In Proc. Thirty-Fifth Annual ACM Symposium on Theory of Computing, STOC ’03 20–29 (Association for Computing Machinery, 2003).

  66. Low, G. H. & Chuang, I. L. Hamiltonian simulation by qubitization. Quantum 3, 163 (2019).

    Article  Google Scholar 

  67. Flannigan, S. et al. Propagation of errors and quantitative quantum simulation with quantum advantage. Preprint at https://arxiv.org/abs/2204.13644 (2022).

  68. Morgado, M. & Whitlock, S. Quantum simulation and computing with rydberg-interacting qubits. AVS Quantum Sci. 3, 023501 (2021).

    Article  CAS  ADS  Google Scholar 

  69. Poulin, D. et al. The Trotter step size required for accurate quantum simulation of quantum chemistry. Quantum Inf. Comput. 15, 361–384 (2015).

    MathSciNet  CAS  Google Scholar 

  70. Sornborger, A. T. & Stewart, E. D. Higher-order methods for simulations on quantum computers. Phys. Rev. A 60, 1956–1965 (1999).

    Article  CAS  ADS  Google Scholar 

  71. Hastings, M. B., Wecker, D., Bauer, B. & Troyer, M. Improving quantum algorithms for quantum chemistry. Quantum Inf. Comput. 15, 1–21 (2015).

    MathSciNet  CAS  Google Scholar 

  72. Bocharov, A., Roetteler, M. & Svore, K. M. Efficient synthesis of universal repeat-until-success quantum circuits. Phys. Rev. Lett. 114, 080502 (2015).

    Article  PubMed  ADS  CAS  Google Scholar 

  73. Gidney, C. Halving the cost of quantum addition. Quantum 2, 74 (2018).

    Article  Google Scholar 

  74. Carrasco, J., Elben, A., Kokail, C., Kraus, B. & Zoller, P. Theoretical and experimental perspectives of quantum verification. PRX Quantum 2, 010102 (2021).

    Article  Google Scholar 

  75. Eisert, J. et al. Quantum certification and benchmarking. Nat. Rev. Phys. 2, 382–390 (2020).

    Article  Google Scholar 

  76. Elben, A. et al. Cross-platform verification of intermediate scale quantum devices. Phys. Rev. Lett. 124, 010504 (2020).

    Article  CAS  PubMed  ADS  Google Scholar 

  77. Bairey, E., Arad, I. & Lindner, N. H. Learning a local Hamiltonian from local measurements. Phys. Rev. Lett. 122, 020504 (2019).

    Article  CAS  PubMed  ADS  Google Scholar 

  78. Evans, T. J., Harper, R. & Flammia, S. T. Scalable Bayesian Hamiltonian learning. Preprint at https://arxiv.org/abs/1912.07636 (2019).

  79. Li, Z., Zou, L. & Hsieh, T. H. Hamiltonian tomography via quantum quench. Phys. Rev. Lett. 124, 160502 (2020).

    Article  CAS  PubMed  ADS  Google Scholar 

  80. Valenti, A., van Nieuwenburg, E., Huber, S. & Greplova, E. Hamiltonian learning for quantum error correction. Phys. Rev. Res. 1, 033092 (2019).

    Article  CAS  Google Scholar 

  81. Wang, J. et al. Experimental quantum Hamiltonian learning. Nat. Phys. 13, 551–555 (2017).

    Article  CAS  Google Scholar 

  82. Abanin, D. A., Altman, E., Bloch, I. & Serbyn, M. Colloquium: Many-body localization, thermalization, and entanglement. Rev. Mod. Phys. 91, 021001 (2019).

    Article  MathSciNet  CAS  ADS  Google Scholar 

  83. Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91, 015006 (2019).

    Article  MathSciNet  CAS  ADS  Google Scholar 

  84. Turner, C. J., Michailidis, A. A., Abanin, D. A., Serbyn, M. & Papić, Z. Weak ergodicity breaking from quantum many-body scars. Nat. Phys. 14, 745–749 (2018).

    Article  CAS  Google Scholar 

  85. Bañuls, M. C. et al. Simulating lattice gauge theories within quantum technologies. Eur. Phys. J. D 74, 165 (2020).

    Article  ADS  CAS  Google Scholar 

  86. Bentsen, G. et al. Treelike interactions and fast scrambling with cold atoms. Phys. Rev. Lett. 123, 130601 (2019).

    Article  CAS  PubMed  ADS  Google Scholar 

  87. Periwal, A. et al. Programmable interactions and emergent geometry in an atomic array. Nature 600, 630–635 (2021).

  88. Argüello-Luengo, J., González-Tudela, A., Shi, T., Zoller, P. & Cirac, J. I. Analogue quantum chemistry simulation. Nature 574, 215–218 (2019).

    Article  PubMed  ADS  CAS  Google Scholar 

  89. Cubitt, T., Montanaro, A. & Piddock, S. Universal quantum Hamiltonians. Proc. Natl Acad. Sci. USA 115, 9497–9502 (2018).

  90. Zhou, L. & Aharonov, D. Strongly universal Hamiltonian simulators. Preprint at https://arxiv.org/abs/2102.02991 (2021).

  91. Kaubruegger, R. et al. Variational spin-squeezing algorithms on programmable quantum sensors. Phys. Rev. Lett. 123, 260505 (2019).

    Article  CAS  PubMed  ADS  Google Scholar 

  92. Liu, H. et al. Prospects of quantum computing for molecular sciences. Mater. Theory 6, 11 (2022).

  93. Bassman, L. et al. Simulating quantum materials with digital quantum computers. Quant. Sci. Technol. 6, 043002 (2021).

  94. Ma, H., Govoni, M. & Galli, G. Quantum simulations of materials on near-term quantum computers. npj Comput. Mater. 6, 85 (2020).

    Article  ADS  Google Scholar 

  95. Rieger, H. in Quantum Annealing and Other Optimization Methods (eds Das, A. & Chakrabarti, B. K.) 299–324 (Lecture Notes in Physics, Springer, 2005).

  96. Hauke, P., Katzgraber, H. G., Lechner, W., Nishimori, H. & Oliver, W. D. Perspectives of quantum annealing: methods and implementations. Rep. Prog. Phys. 83, 054401 (2020).

    Article  CAS  PubMed  ADS  Google Scholar 

  97. Lamata, L., Parra-Rodriguez, A., Sanz, M. & Solano, E. Digital-analog quantum simulations with superconducting circuits. Adv. Phys. X 3, 1457981 (2018).

    Google Scholar 

  98. Brydges, T. et al. Probing Rényi entanglement entropy via randomized measurements. Science 364, 260–263 (2019).

    Article  CAS  PubMed  ADS  Google Scholar 

  99. Kokail, C. et al. Self-verifying variational quantum simulation of lattice models. Nature 569, 355–360 (2019). This article reports the demonstration of an analogue quantum simulator being used for variational quantum simulation, demonstrating a self-verified solution to a model from high-energy physics.

    Article  CAS  PubMed  ADS  Google Scholar 

  100. Babukhin, D. V., Zhukov, A. A. & Pogosov, W. V. Hybrid digital-analog simulation of many-body dynamics with superconducting qubits. Phys. Rev. A 101, 052337 (2020).

    Article  CAS  ADS  Google Scholar 

  101. Arrazola, I., Pedernales, J. S., Lamata, L. & Solano, E. Digital-analog quantum simulation of spin models in trapped ions. Sci. Rep. 6, 30534 (2016).

    Article  CAS  PubMed  PubMed Central  ADS  Google Scholar 

  102. Kokail, C., van Bijnen, R., Elben, A., Vermersch, B. & Zoller, P. Entanglement Hamiltonian tomography in quantum simulation. Nat. Phys. 17, 936–942 (2021).

  103. Joshi, M. K. et al. Quantum information scrambling in a trapped-ion quantum simulator with tunable range interactions. Phys. Rev. Lett. 124, 240505 (2020).

    Article  CAS  PubMed  ADS  Google Scholar 

  104. Henriet, L. et al. Quantum computing with neutral atoms. Quantum 4, 327 (2020).

    Article  Google Scholar 

  105. Cerezo, M. et al. Variational quantum algorithms. Nat. Rev. Phys. 3, 625–644 (2021).

  106. Zhou, L., Wang, S.-T., Choi, S., Pichler, H. & Lukin, M. D. Quantum approximate optimization algorithm: performance, mechanism, and implementation on near-term devices. Phys. Rev. X 10, 021067 (2020).

    CAS  Google Scholar 

  107. Biamonte, J. et al. Quantum machine learning. Nature 549, 195–202 (2017).

    Article  CAS  PubMed  ADS  Google Scholar 

  108. Huang, H.-Y. et al. Power of data in quantum machine learning. Nat. Commun. 12, 2631 (2021).

  109. Bloch, I., Dalibard, J. & Nascimbène, S. Quantum simulations with ultracold quantum gases. Nat. Phys. 8, 267–276 (2012).

    Article  CAS  Google Scholar 

  110. Schäfer, F., Fukuhara, T., Sugawa, S., Takasu, Y. & Takahashi, Y. Tools for quantum simulation with ultracold atoms in optical lattices. Nat. Rev. Phys. 2, 411–425 (2020).

    Article  CAS  Google Scholar 

  111. The Hubbard model at half a century. Nat. Phys. 9, 523 (2013).

  112. Essler, F. H. L., Frahm, H., Göhmann, F., Klümper, A. & Korepin, V. E. The One-Dimensional Hubbard Model (Cambridge Univ. Press, 2005).

  113. Lee, P. A., Nagaosa, N. & Wen, X.-G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006).

    Article  CAS  ADS  Google Scholar 

  114. von Burg, V. et al. Quantum computing enhanced computational catalysis. Phys. Rev. Res. 3, 033055 (2021).

    Article  Google Scholar 

  115. Bauer, B., Bravyi, S., Motta, M. & Chan, G. K.-L. Quantum algorithms for quantum chemistry and quantum materials science. Chem. Rev. 120, 12685–12717 (2020).

    Article  CAS  PubMed  Google Scholar 

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Acknowledgements

We acknowledge discussions with B. Kraus and G. H. Low. This work was supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement number 817482 PASQuanS. Work at the University of Strathclyde was supported by the EPSRC Programme Grant DesOEQ (EP/P009565/1), the EPSRC Hub in Quantum Computing and simulation (EP/T001062/1) and AFOSR grant number FA9550-18-1-0064.

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Authors and Affiliations

  1. Department of Physics and SUPA, University of Strathclyde, Glasgow, UK

    Andrew J. Daley, Stuart Flannigan & Natalie Pearson

  2. Max Planck Institute of Quantum Optics, Garching, Germany

    Immanuel Bloch

  3. Ludwig Maximilians University, Munich, Germany

    Immanuel Bloch

  4. Munich Center for Quantum Science and Technology, Munich, Germany

    Immanuel Bloch

  5. Universität Innsbruck, Innsbruck, Austria

    Christian Kokail & Peter Zoller

  6. Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck, Austria

    Christian Kokail & Peter Zoller

  7. Microsoft Corporation, Redmond, WA, USA

    Matthias Troyer

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All authors discussed the topics addressed in this Perspective, wrote the article and agreed on the final text. The example of Fig. 2 was produced by S.F. and A.J.D., the digital gate count example was produced by N.P. and M.T., and the Box 3 example was produced by C.K. and P.Z., in discussion with all authors.

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Correspondence to Andrew J. Daley.

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M.T. notes that Microsoft is developing digital quantum computers and offers quantum computers and simulators in Azure. The other authors declare no competing interests.

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Daley, A.J., Bloch, I., Kokail, C. et al. Practical quantum advantage in quantum simulation. Nature 607, 667–676 (2022). https://doi.org/10.1038/s41586-022-04940-6

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