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Computer-inspired quantum experiments

Abstract

The design of new devices and experiments has historically relied on the intuition of human experts. Now, design inspirations from computers are increasingly augmenting the capability of scientists. We briefly overview different fields of physics that rely on computer-inspired designs using a variety of computational approaches based on topological optimization, evolutionary strategies, deep learning, reinforcement learning or automated reasoning. Then we focus specifically on quantum physics. When designing new quantum experiments, there are two challenges: quantum phenomena are unintuitive, and the number of possible configurations of quantum experiments explodes exponentially. These challenges can be overcome by using computer-designed quantum experiments. We focus on the most mature and practical approaches to find new complex quantum experiments, which have subsequently been realized in the lab. These methods rely on a highly efficient topological search, which can inspire new scientific ideas. We review several extensions and alternatives based on various optimization and machine learning techniques. Finally, we discuss what can be learned from the different approaches and outline several future directions.

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Fig. 1: Algorithms for designing quantum experiments.
Fig. 2: Concept of the class III algorithm for computer-inspired experiments, MELVIN.
Fig. 3: The complexity of computer-inspired quantum experiments.
Fig. 4: Concrete example of how a computer-discovered outlier can inspire new ideas, concepts or technology in experimental quantum optics.
Fig. 5: Example of a class IIa algorithm.
Fig. 6: Examples of class I algorithms for computer-inspired quantum experiments using various optimization and machine learning techniques.

Code availability

Example codes both for Wolfram Mathematica and for Python (using SymPy) can be found at https://github.com/XuemeiGu/MelvinPython/.

References

  1. 1.

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

    Google Scholar 

  2. 2.

    Gentile, A. A. et al. Learning models of quantum systems from experiments. Preprint at https://arxiv.org/abs/2002.06169 (2020).

  3. 3.

    Torlai, G. et al. Neural-network quantum state tomography. Nat. Phys. 14, 447–450 (2018).

    Google Scholar 

  4. 4.

    Palmieri, A. M. et al. Experimental neural network enhanced quantum tomography. npj Quantum Inf. 6, 20 (2020).

    ADS  Google Scholar 

  5. 5.

    Gebhart, V. & Bohmann, M. Neural-network approach for identifying nonclassicality from click-counting data. Phys. Rev. Res. 2, 023150 (2020).

    Google Scholar 

  6. 6.

    Weidner, C. & Anderson, D. Z. Experimental demonstration of shaken-lattice interferometry. Phys. Rev. Lett. 120, 263201 (2018).

    ADS  Google Scholar 

  7. 7.

    Cimini, V. et al. Calibration of quantum sensors by neural networks. Phys. Rev. Lett. 123, 230502 (2019).

    ADS  Google Scholar 

  8. 8.

    Youssry, A., Chapman, R. J., Peruzzo, A., Ferrie, C. & Tomamichel, M. Modeling and control of a reconfigurable photonic circuit using deep learning. Quantum Sci. Technol. 5, 025001 (2020).

    ADS  Google Scholar 

  9. 9.

    You, C. et al. Identification of light sources using machine learning. Appl. Phys. Rev. 7, 021404 (2020).

    ADS  Google Scholar 

  10. 10.

    Carleo, G. et al. Machine learning and the physical sciences. Rev. Mod. Phys. 91, 045002 (2019).

    ADS  Google Scholar 

  11. 11.

    Dunjko, V. & Briegel, H. J. Machine learning & artificial intelligence in the quantum domain: a review of recent progress. Rep. Prog. Phys. 81, 074001 (2018).

    ADS  MathSciNet  Google Scholar 

  12. 12.

    Lamata, L. Quantum machine learning and quantum biomimetics: a perspective. Mach. Learn. Sci. Technol. 1, 033002 (2020).

    Google Scholar 

  13. 13.

    Fasoli, A. et al. Computational challenges in magnetic-confinement fusion physics. Nat. Phys. 12, 411 (2016).

    Google Scholar 

  14. 14.

    Helander, P. Theory of plasma confinement in non-axisymmetric magnetic fields. Rep. Prog. Phys. 77, 087001 (2014).

    ADS  Google Scholar 

  15. 15.

    Pedersen, T. S. et al. Confirmation of the topology of the Wendelstein 7-X magnetic field to better than 1: 100,000. Nat. Commun. 7, 13493 (2016).

    ADS  Google Scholar 

  16. 16.

    Wolf, R. et al. Major results from the first plasma campaign of the Wendelstein 7-X stellarator. Nucl. Fusion 57, 102020 (2017).

    ADS  Google Scholar 

  17. 17.

    Hofler, A. et al. Innovative applications of genetic algorithms to problems in accelerator physics. Phys. Rev. Spec. Top. Accel. Beams 16, 010101 (2013).

    ADS  Google Scholar 

  18. 18.

    Li, Y., Cheng, W., Yu, L. H. & Rainer, R. Genetic algorithm enhanced by machine learning in dynamic aperture optimization. Phys. Rev. Accel. Beams 21, 054601 (2018).

    ADS  Google Scholar 

  19. 19.

    Appel, S. et al. Optimization of heavy-ion synchrotrons using nature-inspired algorithms and machine learning. In 13th International Computational Accelerator Physics Conference (ICAP’18) 15–21 (JACOW, 2019).

  20. 20.

    Pierrick, H., Juliette, P., Claude, M. & Franck, P. Klystron efficiency optimization based on a genetic algorithm. In 2019 International Vacuum Electronics Conference (IVEC) 1–2 (IEEE, 2019).

  21. 21.

    Bentley, P. Evolutionary Design by Computers (Morgan Kaufmann, 1999).

  22. 22.

    Bendsøe, M. P. Topology Optimization (Springer, 2009).

  23. 23.

    van Dijk, N. P., Maute, K., Langelaar, M. & Van Keulen, F. Level-set methods for structural topology optimization: a review. Struct. Multidiscipl. Optim. 48, 437–472 (2013).

    MathSciNet  Google Scholar 

  24. 24.

    Sigmund, O. On the usefulness of non-gradient approaches in topology optimization. Struct. Multidiscipl. Optim. 43, 589–596 (2011).

    MathSciNet  MATH  Google Scholar 

  25. 25.

    Bendsøe, M. P. & Kikuchi, N. Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Eng. 71, 197–224 (1988).

    ADS  MathSciNet  MATH  Google Scholar 

  26. 26.

    Xie, Y. M. & Steven, G. P. A simple evolutionary procedure for structural optimization. Comput. Struct. 49, 885–896 (1993).

    Google Scholar 

  27. 27.

    Aage, N., Andreassen, E., Lazarov, B. S. & Sigmund, O. Giga-voxel computational morphogenesis for structural design. Nature 550, 84–86 (2017).

    ADS  Google Scholar 

  28. 28.

    Molesky, S. et al. Inverse design in nanophotonics. Nat. Photon. 12, 659–670 (2018).

    ADS  Google Scholar 

  29. 29.

    Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019).

    Google Scholar 

  30. 30.

    Shen, B., Wang, P., Polson, R. & Menon, R. Integrated metamaterials for efficient and compact free-space-to-waveguide coupling. Opt. Express 22, 27175–27182 (2014).

    ADS  Google Scholar 

  31. 31.

    Su, L., Piggott, A. Y., Sapra, N. V., Petykiewicz, J. & Vuckovic, J. Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer. ACS Photon. 5, 301–305 (2017).

    Google Scholar 

  32. 32.

    Dory, C. et al. Inverse-designed diamond photonics. Nat. Commun. 10, 3309 (2019).

    ADS  Google Scholar 

  33. 33.

    Peano, V., Sapper, F. & Marquardt, F. Rapid exploration of topological band structures using deep learning. Preprint at https://arxiv.org/abs/1912.03296 (2019).

  34. 34.

    Sapra, N. V. et al. On-chip integrated laser-driven particle accelerator. Science 367, 79–83 (2020).

    ADS  Google Scholar 

  35. 35.

    Sheeran, M., Singh, S. & Stålmarck, G. Checking safety properties using induction and a SAT-solver. In International Conference on Formal Methods in Computer-aided Design (eds Hunt Jr, W. A. & Johnson, S. D.) 127–144 (Springer, 2000).

  36. 36.

    Saeedi, M. & Markov, I. L. Synthesis and optimization of reversible circuits–a survey. ACM Comput. Surv. 45, 21 (2013).

    MATH  Google Scholar 

  37. 37.

    Dawson, C. M. & Nielsen, M. A. The Solovay–Kitaev algorithm. https://arxiv.org/abs/quant-ph/0505030 (2005).

  38. 38.

    Maslov, D., Dueck, G. W., Miller, D. M. & Negrevergne, C. Quantum circuit simplification and level compaction. IEEE Trans. Comput. Des. Integr. Circuits Syst. 27, 436–444 (2008).

    Google Scholar 

  39. 39.

    Bocharov, A., Roetteler, M. & Svore, K. M. Efficient synthesis of probabilistic quantum circuits with fallback. Phys. Rev. A 91, 052317 (2015).

    ADS  Google Scholar 

  40. 40.

    Nam, Y., Ross, N. J., Su, Y., Childs, A. M. & Maslov, D. Automated optimization of large quantum circuits with continuous parameters. npj Quantum Inf. 4, 23 (2018).

    Google Scholar 

  41. 41.

    Martinez, E. A., Monz, T., Nigg, D., Schindler, P. & Blatt, R. Compiling quantum algorithms for architectures with multi-qubit gates. New J. Phys. 18, 063029 (2016).

    ADS  Google Scholar 

  42. 42.

    Maslov, D. Basic circuit compilation techniques for an ion-trap quantum machine. New J. Phys. 19, 023035 (2017).

    ADS  Google Scholar 

  43. 43.

    Peruzzo, A. et al. A variational eigenvalue solver on a photonic quantum processor. Nat. Commun. 5, 4213 (2014).

    ADS  Google Scholar 

  44. 44.

    McClean, J. R., Romero, J., Babbush, R. & Aspuru-Guzik, A. The theory of variational hybrid quantum-classical algorithms. New J. Phys. 18, 023023 (2016).

    ADS  Google Scholar 

  45. 45.

    Farhi, E., Goldstone, J. & Gutmann, S. A quantum approximate optimization algorithm. Preprint at https://arxiv.org/abs/1411.4028 (2014).

  46. 46.

    McClean, J. R., Boixo, S., Smelyanskiy, V. N., Babbush, R. & Neven, H. Barren plateaus in quantum neural network training landscapes. Nat. Commun. 9, 4812 (2018).

    ADS  Google Scholar 

  47. 47.

    Sim, S., Johnson, P. D. & Aspuru-Guzik, A. Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms. Adv. Quantum Technol. 2, 1900070 (2019).

    Google Scholar 

  48. 48.

    Rattew, A. G., Hu, S., Pistoia, M., Chen, R. & Wood, S. A domain-agnostic, noise-resistant evolutionary variational quantum eigensolver for hardware-efficient optimization in the Hilbert space. Preprint at https://arxiv.org/abs/1910.09694 (2019).

  49. 49.

    Fösel, T., Tighineanu, P., Weiss, T. & Marquardt, F. Reinforcement learning with neural networks for quantum feedback. Phys. Rev. X 8, 031084 (2018).

    Google Scholar 

  50. 50.

    Friis, N., Melnikov, A. A., Kirchmair, G. & Briegel, H. J. Coherent controlization using superconducting qubits. Sci. Rep. 5, 18036 (2015).

    ADS  Google Scholar 

  51. 51.

    Bukov, M. et al. Reinforcement learning in different phases of quantum control. Phys. Rev. X 8, 031086 (2018).

    Google Scholar 

  52. 52.

    Fösel, T., Krastanov, S., Marquardt, F. & Jiang, L. Efficient cavity control with SNAP gates. Preprint at https://arxiv.org/abs/2004.14256 (2020).

  53. 53.

    Brakensiek, J., Heule, M., Mackey, J. & Narváez, D. The resolution of Keller’s conjecture. In International Joint Conference on Automated Reasoning (eds Peltier, N. & Sofronie-Stokkermans, V.) 48–65 (Springer, 2020).

  54. 54.

    Wille, R., Przigoda, N. & Drechsler, R. A compact and efficient SAT encoding for quantum circuits. In 2013 Africon 1–6 (IEEE, 2013).

  55. 55.

    Meuli, G., Soeken, M. & De Micheli, G. SAT-based CNOT, T quantum circuit synthesis. In International Conference on Reversible Computation (eds Kari, J. & Ulidowski, I.) 175–188 (Springer, 2018).

  56. 56.

    Wille, R., Burgholzer, L. & Zulehner, A. Mapping quantum circuits to IBM QX architectures using the minimal number of SWAP and H operations. In Proc. 56th Annual Design Automation Conference 2019 142 (ACM, 2019).

  57. 57.

    Menke, T. et al. Automated discovery of superconducting circuits and its application to 4-local coupler design. Preprint at https://arxiv.org/abs/1912.03322 (2019).

  58. 58.

    Sanchez-Lengeling, B. & Aspuru-Guzik, A. Inverse molecular design using machine learning: generative models for matter engineering. Science 361, 360–365 (2018).

    ADS  Google Scholar 

  59. 59.

    Gromski, P. S., Henson, A. B., Granda, J. M. & Cronin, L. How to explore chemical space using algorithms and automation. Nat. Rev. Chem. 3, 119–128 (2019).

    Google Scholar 

  60. 60.

    Virshup, A. M., Contreras-García, J., Wipf, P., Yang, W. & Beratan, D. N. Stochastic voyages into uncharted chemical space produce a representative library of all possible drug-like compounds. J. Am. Chem. Soc. 135, 7296–7303 (2013).

    Google Scholar 

  61. 61.

    Robbins, D. W. & Hartwig, J. F. A simple, multidimensional approach to high-throughput discovery of catalytic reactions. Science 333, 1423–1427 (2011).

    ADS  Google Scholar 

  62. 62.

    Gómez-Bombarelli, R. et al. Design of efficient molecular organic light-emitting diodes by a high-throughput virtual screening and experimental approach. Nat. Mater. 15, 1120–1127 (2016).

    ADS  Google Scholar 

  63. 63.

    Lyu, J. et al. Ultra-large library docking for discovering new chemotypes. Nature 566, 224–229 (2019).

    ADS  Google Scholar 

  64. 64.

    O’Boyle, N. M., Campbell, C. M. & Hutchison, G. R. Computational design and selection of optimal organic photovoltaic materials. J. Phys. Chem. C 115, 16200–16210 (2011).

    Google Scholar 

  65. 65.

    Chen, X., Du, W., Qi, R., Qian, F. & Tianfield, H. Hybrid gradient particle swarm optimization for dynamic optimization problems of chemical processes. Asia Pac. J. Chem. Eng. 8, 708–720 (2013).

    Google Scholar 

  66. 66.

    Jensen, J. H. A graph-based genetic algorithm and generative model/Monte Carlo tree search for the exploration of chemical space. Chem. Sci. 10, 3567–3572 (2019).

    Google Scholar 

  67. 67.

    Nigam, A., Friederich, P., Krenn, M. & Aspuru-Guzik, A. Augmenting genetic algorithms with deep neural networks for exploring the chemical space. Preprint at https://arxiv.org/abs/1909.11655 (2020).

  68. 68.

    Gómez-Bombarelli, R. et al. Automatic chemical design using a data-driven continuous representation of molecules. ACS Cent. Sci. 4, 268–276 (2018).

    Google Scholar 

  69. 69.

    Coello, C. A. C. et al. Evolutionary Algorithms for Solving Multi-objective Problems Vol. 5 (Springer, 2007).

  70. 70.

    Coello, C. A. C. List of references on evolutionary multiobjective optimization. Delta http://delta.cs.cinvestav.mx/~ccoello/EMOO/emoopage.html (2017).

  71. 71.

    Pan, J.-W. et al. Multiphoton entanglement and interferometry. Rev. Mod. Phys. 84, 777–838 (2012).

    ADS  Google Scholar 

  72. 72.

    Flamini, F., Spagnolo, N. & Sciarrino, F. Photonic quantum information processing: a review. Rep. Prog. Phys. 82, 016001 (2018).

    ADS  Google Scholar 

  73. 73.

    Graffitti, F., Kundys, D., Reid, D. T., Brańczyk, A. M. & Fedrizzi, A. Pure down-conversion photons through sub-coherence-length domain engineering. Quantum Sci. Technol. 2, 035001 (2017).

    ADS  Google Scholar 

  74. 74.

    Lenzini, F. et al. Active demultiplexing of single photons from a solid-state source. Laser Photon. Rev. 11, 1600297 (2017).

    ADS  Google Scholar 

  75. 75.

    Wang, X.-L. et al. 18-qubit entanglement with six photons’ three degrees of freedom. Phys. Rev. Lett. 120, 260502 (2018).

    ADS  Google Scholar 

  76. 76.

    Luo, Y.-H. et al. Quantum teleportation in high dimensions. Phys. Rev. Lett. 123, 070505 (2019).

    ADS  Google Scholar 

  77. 77.

    Bornman, N. et al. Ghost imaging using entanglement-swapped photons. npj Quantum Inf. 5, 63 (2019).

    ADS  Google Scholar 

  78. 78.

    Wang, H. et al. Boson sampling with 20 input photons and a 60-mode interferometer in a 1014-dimensional Hilbert space. Phys. Rev. Lett. 123, 250503 (2019).

    ADS  Google Scholar 

  79. 79.

    Hu, X.-M. et al. Experimental multi-level quantum teleportation. Preprint at https://arxiv.org/abs/1904.12249 (2019).

  80. 80.

    Llewellyn, D. et al. Chip-to-chip quantum teleportation and multi-photon entanglement in silicon. Nat. Phys. 16, 148–153 (2020).

    Google Scholar 

  81. 81.

    Bavaresco, J. et al. Measurements in two bases are sufficient for certifying high-dimensional entanglement. Nat. Phys. 14, 1032–1037 (2018).

    Google Scholar 

  82. 82.

    Ahn, D. et al. Adaptive compressive tomography with no a priori information. Phys. Rev. Lett. 122, 100404 (2019).

    ADS  Google Scholar 

  83. 83.

    Krenn, M., Malik, M., Fickler, R., Lapkiewicz, R. & Zeilinger, A. Automated search for new quantum experiments. Phys. Rev. Lett. 116, 090405 (2016).

    ADS  Google Scholar 

  84. 84.

    Gao, X., Krenn, M., Kysela, J. & Zeilinger, A. Arbitrary d-dimensional Pauli X gates of a flying qudit. Phys. Rev. A 99, 023825 (2019).

    ADS  Google Scholar 

  85. 85.

    Malik, M. et al. Multi-photon entanglement in high dimensions. Nat. Photon. 10, 248–252 (2016).

    ADS  Google Scholar 

  86. 86.

    Schlederer, F., Krenn, M., Fickler, R., Malik, M. & Zeilinger, A. Cyclic transformation of orbital angular momentum modes. New J. Phys. 18, 043019 (2016).

    ADS  Google Scholar 

  87. 87.

    Wang, F. et al. Generation of the complete four-dimensional bell basis. Optica 4, 1462–1467 (2017).

    ADS  Google Scholar 

  88. 88.

    Babazadeh, A. et al. High-dimensional single-photon quantum gates: concepts and experiments. Phys. Rev. Lett. 119, 180510 (2017).

    ADS  Google Scholar 

  89. 89.

    Erhard, M., Malik, M., Krenn, M. & Zeilinger, A. Experimental Greenberger–Horne–Zeilinger entanglement beyond qubits. Nat. Photon. 12, 759–764 (2018).

    ADS  Google Scholar 

  90. 90.

    Kysela, J., Erhard, M., Hochrainer, A., Krenn, M. & Zeilinger, A. Experimental high-dimensional entanglement by path identity. Proc. Natl Acad. Sci. USA (in the press).

  91. 91.

    Krenn, M., Hochrainer, A., Lahiri, M. & Zeilinger, A. Entanglement by path identity. Phys. Rev. Lett. 118, 080401 (2017).

    ADS  MathSciNet  Google Scholar 

  92. 92.

    Krenn, M., Gu, X. & Zeilinger, A. Quantum experiments and graphs: multiparty states as coherent superpositions of perfect matchings. Phys. Rev. Lett. 119, 240403 (2017).

    ADS  Google Scholar 

  93. 93.

    Gao, X., Erhard, M., Zeilinger, A. & Krenn, M. Computer-inspired concept for high-dimensional multipartite quantum gates. Phys. Rev. Lett. 125, 050501 (2020).

    ADS  MathSciNet  Google Scholar 

  94. 94.

    Wang, X.-L. et al. Quantum teleportation of multiple degrees of freedom of a single photon. Nature 518, 516–519 (2015).

    ADS  Google Scholar 

  95. 95.

    Anwer, H., Nawareg, M., Cabello, A. & Bourennane, M. Experimental test of maximal tripartite nonlocality using an entangled state and local measurements that are maximally incompatible. Phys. Rev. A 100, 022104 (2019).

    ADS  Google Scholar 

  96. 96.

    Leach, J., Padgett, M. J., Barnett, S. M., Franke-Arnold, S. & Courtial, J. Measuring the orbital angular momentum of a single photon. Phys. Rev. Lett. 88, 257901 (2002).

    ADS  Google Scholar 

  97. 97.

    Huber, M. & de Vicente, J. I. Structure of multidimensional entanglement in multipartite systems. Phys. Rev. Lett. 110, 030501 (2013).

    ADS  Google Scholar 

  98. 98.

    Huber, M., Perarnau-Llobet, M. & de Vicente, J. I. Entropy vector formalism and the structure of multidimensional entanglement in multipartite systems. Phys. Rev. A 88, 042328 (2013).

    ADS  Google Scholar 

  99. 99.

    Ryu, J. et al. Multisetting Greenberger–Horne–Zeilinger theorem. Phys. Rev. A 89, 024103 (2014).

    ADS  Google Scholar 

  100. 100.

    Lawrence, J. Rotational covariance and Greenberger–Horne–Zeilinger theorems for three or more particles of any dimension. Phys. Rev. A 89, 012105 (2014).

    ADS  Google Scholar 

  101. 101.

    Lawrence, J. Many-qutrit Mermin inequalities with three measurement bases. Preprint at https://arxiv.org/abs/1910.05869 (2019).

  102. 102.

    Zou, X., Wang, L. J. & Mandel, L. Induced coherence and indistinguishability in optical interference. Phys. Rev. Lett. 67, 318–321 (1991).

    ADS  Google Scholar 

  103. 103.

    Gu, X., Erhard, M., Zeilinger, A. & Krenn, M. Quantum experiments and graphs II: quantum interference, computation, and state generation. Proc. Natl Acad. Sci. USA 116, 4147–4155 (2019).

    ADS  MathSciNet  MATH  Google Scholar 

  104. 104.

    Gu, X., Chen, L., Zeilinger, A. & Krenn, M. Quantum experiments and graphs. III. High-dimensional and multiparticle entanglement. Phys. Rev. A 99, 032338 (2019).

    ADS  Google Scholar 

  105. 105.

    Krenn, M., Gu, X. & Soltész, D. Questions on the structure of perfect matchings inspired by quantum physics. In Proc. 2nd Croatian Combinatorial Days (eds Došlić, T. & Martinjak, I) 57–70 (Faculty of Civil Engineering, University of Zagreb, 2019).

  106. 106.

    Lehman, J. et al. The surprising creativity of digital evolution: a collection of anecdotes from the evolutionary computation and artificial life research communities. Artif. Life 26, 274–306 (2020).

    Google Scholar 

  107. 107.

    Wang, J., Sciarrino, F., Laing, A. & Thompson, M. G. Integrated photonic quantum technologies. Nat. Photon. 14, 273–284 (2020).

    ADS  Google Scholar 

  108. 108.

    Feng, L.-T., Guo, G.-C. & Ren, X.-F. Progress on integrated quantum photonic sources with silicon. Adv. Quantum Technol. 3, 1900058 (2020).

    Google Scholar 

  109. 109.

    Slussarenko, S. & Pryde, G. J. Photonic quantum information processing: a concise review. Appl. Phys. Rev. 6, 041303 (2019).

    ADS  Google Scholar 

  110. 110.

    Reck, M., Zeilinger, A., Bernstein, H. J. & Bertani, P. Experimental realization of any discrete unitary operator. Phys. Rev. Lett. 73, 58–61 (1994).

    ADS  Google Scholar 

  111. 111.

    Clements, W. R., Humphreys, P. C., Metcalf, B. J., Kolthammer, W. S. & Walmsley, I. A. Optimal design for universal multiport interferometers. Optica 3, 1460–1465 (2016).

    ADS  Google Scholar 

  112. 112.

    Tischler, N., Rockstuhl, C. & Słowik, K. Quantum optical realization of arbitrary linear transformations allowing for loss and gain. Phys. Rev. X 8, 021017 (2018).

    Google Scholar 

  113. 113.

    Xiao, L. et al. Observation of critical phenomena in parity-time-symmetric quantum dynamics. Phys. Rev. Lett. 123, 230401 (2019).

    ADS  Google Scholar 

  114. 114.

    Zhan, X. et al. Experimental quantum cloning in a pseudo-unitary system. Phys. Rev. A 101, R010302 (2020).

    ADS  Google Scholar 

  115. 115.

    Krenn, M., Kottmann, J., Tischler, N. & Aspuru-Guzik, A. Conceptual understanding through efficient inverse-design of quantum optical experiments. Preprint at https://arxiv.org/abs/2005.06443 (2020).

  116. 116.

    Giovannetti, V., Lloyd, S. & Maccone, L. Advances in quantum metrology. Nat. Photon. 5, 222–229 (2011).

    ADS  Google Scholar 

  117. 117.

    Knott, P. A search algorithm for quantum state engineering and metrology. New J. Phys. 18, 073033 (2016).

    ADS  Google Scholar 

  118. 118.

    Salimans, T., Ho, J., Chen, X., Sidor, S. & Sutskever, I. Evolution strategies as a scalable alternative to reinforcement learning. Preprint at https://arxiv.org/abs/1703.03864 (2017).

  119. 119.

    O’Driscoll, L., Nichols, R. & Knott, P. A hybrid machine learning algorithm for designing quantum experiments. Quantum Mach. Intell. 1, 5–15 (2019).

    Google Scholar 

  120. 120.

    Nichols, R., Mineh, L., Rubio, J., Matthews, J. C. & Knott, P. A. Designing quantum experiments with a genetic algorithm. Quantum Sci. Technol. 4, 045012 (2019).

    ADS  Google Scholar 

  121. 121.

    Melnikov, A. A. et al. Active learning machine learns to create new quantum experiments. Proc. Natl Acad. Sci. USA 115, 1221–1226 (2018).

    ADS  Google Scholar 

  122. 122.

    Briegel, H. J. & De las Cuevas, G. Projective simulation for artificial intelligence. Sci. Rep. 2, 400 (2012).

    Google Scholar 

  123. 123.

    Briegel, H. J. On creative machines and the physical origins of freedom. Sci. Rep. 2, 522 (2012).

    ADS  Google Scholar 

  124. 124.

    Wallnöfer, J., Melnikov, A. A., Dür, W. & Briegel, H. J. Machine learning for long-distance quantum communication. PRX Quantum 1, 010301 (2020).

    Google Scholar 

  125. 125.

    Adler, T. et al. Quantum optical experiments modeled by long short-term memory. Preprint at https://arxiv.org/abs/1910.13804 (2019).

  126. 126.

    Hochreiter, S. & Schmidhuber, J. Long short-term memory. Neural Comput. 9, 1735–1780 (1997).

    Google Scholar 

  127. 127.

    Qiang, X. et al. Large-scale silicon quantum photonics implementing arbitrary two-qubit processing. Nat. Photon. 12, 534–539 (2018).

    ADS  Google Scholar 

  128. 128.

    Wang, J. et al. Multidimensional quantum entanglement with large-scale integrated optics. Science 360, 285–291 (2018).

    ADS  MathSciNet  MATH  Google Scholar 

  129. 129.

    Lu, L. et al. Three-dimensional entanglement on a silicon chip. npj Quantum Inf. 6, 30 (2020).

    ADS  Google Scholar 

  130. 130.

    Weedbrook, C. et al. Gaussian quantum information. Rev. Mod. Phys. 84, 621–669 (2012).

    ADS  Google Scholar 

  131. 131.

    Lenzini, F. et al. Integrated photonic platform for quantum information with continuous variables. Sci. Adv. 4, eaat9331 (2018).

    ADS  Google Scholar 

  132. 132.

    Zhang, G. et al. An integrated silicon photonic chip platform for continuous-variable quantum key distribution. Nat. Photon. 13, 839–842 (2019).

    ADS  Google Scholar 

  133. 133.

    Arrazola, J. M., et al. Machine learning method for state preparation and gate synthesis on photonic quantum computers. Quantum Sci. Technol. 4, 024004 (2019).

    ADS  Google Scholar 

  134. 134.

    Killoran, N. et al. Continuous-variable quantum neural networks. Phys. Rev. Res. 1, 033063 (2019).

    Google Scholar 

  135. 135.

    Menicucci, N. C. Fault-tolerant measurement-based quantum computing with continuous-variable cluster states. Phys. Rev. Lett. 112, 120504 (2014).

    ADS  Google Scholar 

  136. 136.

    Killoran, N. et al. Strawberry fields: a software platform for photonic quantum computing. Quantum 3, 129 (2019).

    Google Scholar 

  137. 137.

    Sabapathy, K. K., Qi, H., Izaac, J. & Weedbrook, C. Production of photonic universal quantum gates enhanced by machine learning. Phys. Rev. A 100, 012326 (2019).

    ADS  Google Scholar 

  138. 138.

    Gimeno-Segovia, M., Shadbolt, P., Browne, D. E. & Rudolph, T. From three-photon Greenberger–Horne–Zeilinger states to ballistic universal quantum computation. Phys. Rev. Lett. 115, 020502 (2015).

    ADS  Google Scholar 

  139. 139.

    Zaidi, H. A., Dawson, C., van Loock, P. & Rudolph, T. Near-deterministic creation of universal cluster states with probabilistic Bell measurements and three-qubit resource states. Phys. Rev. A 91, 042301 (2015).

    ADS  Google Scholar 

  140. 140.

    Gubarev, F. et al. Improved heralded schemes to generate entangled states from single photons. Preprint at https://arxiv.org/abs/2004.02691 (2020).

  141. 141.

    Wang, H. et al. On-demand semiconductor source of entangled photons which simultaneously has high fidelity, efficiency, and indistinguishability. Phys. Rev. Lett. 122, 113602 (2019).

    ADS  Google Scholar 

  142. 142.

    Morizur, J.-F. et al. Programmable unitary spatial mode manipulation. J. Opt. Soc. A 27, 2524–2531 (2010).

    ADS  Google Scholar 

  143. 143.

    Fontaine, N. K. et al. Laguerre–Gaussian mode sorter. Nat. Commun. 10, 1865 (2019).

    ADS  Google Scholar 

  144. 144.

    Brandt, F., Hiekkamäki, M., Bouchard, F., Huber, M. & Fickler, R. High-dimensional quantum gates using full-field spatial modes of photons. Optica 7, 98–107 (2020).

    ADS  Google Scholar 

  145. 145.

    Rotter, S. & Gigan, S. Light fields in complex media: mesoscopic scattering meets wave control. Rev. Mod. Phys. 89, 015005 (2017).

    ADS  Google Scholar 

  146. 146.

    Fickler, R., Ginoya, M. & Boyd, R. W. Custom-tailored spatial mode sorting by controlled random scattering. Phys. Rev. B 95, 161108 (2017).

    ADS  Google Scholar 

  147. 147.

    Leedumrongwatthanakun, S. et al. Programmable linear quantum networks with a multimode fibre. Nat. Photon. 14, 139–142 (2020).

    ADS  Google Scholar 

  148. 148.

    Krenn, M., Häse, F., Nigam, A., Friederich, P. & Aspuru-Guzik, A. SELFIES: a robust representation of semantically constrained graphs with an example application in chemistry. MLST (in the press).

  149. 149.

    Heule, M. J., Kullmann, O. & Marek, V. W. Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In International Conference on Theory and Applications of Satisfiability Testing (eds Creignou, N. & Le Berre, D.) 228–245 (Springer, 2016).

  150. 150.

    Heule, M. J. & Kullmann, O. The science of brute force. Commun. ACM 60, 70–79 (2017).

    Google Scholar 

  151. 151.

    Higgins, I. et al. beta-VAE: learning basic visual concepts with a constrained variational framework. In ICLR 2017 (2017).

  152. 152.

    Chen, T. Q., Li, X., Grosse, R. B. & Duvenaud, D. K. Isolating sources of disentanglement in variational autoencoders. Adv. Neural Inf. Process. Syst. 21, 2610–2620 (2018).

    Google Scholar 

  153. 153.

    Lusch, B., Kutz, J. N. & Brunton, S. L. Deep learning for universal linear embeddings of nonlinear dynamics. Nat. Commun. 9, 4950 (2018).

    ADS  Google Scholar 

  154. 154.

    Roscher, R., Bohn, B., Duarte, M. F. & Garcke, J. Explainable machine learning for scientific insights and discoveries. IEEE Access 8, 42200–42216 (2020).

    Google Scholar 

  155. 155.

    Iten, R., Metger, T., Wilming, H., Del Rio, L. & Renner, R. Discovering physical concepts with neural networks. Phys. Rev. Lett. 124, 010508 (2020).

    ADS  Google Scholar 

  156. 156.

    Nautrup, H. P. et al. Operationally meaningful representations of physical systems in neural networks. Preprint at https://arxiv.org/abs/2001.00593 (2020).

  157. 157.

    Lehman, J. et al. The surprising creativity of digital evolution: a collection of anecdotes from the evolutionary computation and artificial life research communities. Artif. Life 26, 274–306 (2020).

    Google Scholar 

  158. 158.

    Pavičić, M., Waegell, M., Megill, N. D. & Aravind, P. Automated generation of Kochen–Specker sets. Sci. Rep. 9, 6765 (2019).

    ADS  MATH  Google Scholar 

  159. 159.

    Goyeneche, D., Alsina, D., Latorre, J. I., Riera, A. & Życzkowski, K. Absolutely maximally entangled states, combinatorial designs, and multiunitary matrices. Phys. Rev. A 92, 032316 (2015).

    ADS  Google Scholar 

  160. 160.

    Bengtsson, I. & Życzkowski, K. Geometry of Quantum States: An Introduction to Quantum Entanglement (Cambridge Univ. Press, 2017).

  161. 161.

    Horodecki, P., Rudnicki, L. & Zyczkowski, K. Five open problems in quantum information. Preprint at https://arxiv.org/abs/2002.03233 (2020).

  162. 162.

    Bharti, K., Haug, T., Vedral, V. & Kwek, L.-C. Machine learning meets quantum foundations: a brief survey. Preprint at https://arxiv.org/abs/2003.11224 (2020).

  163. 163.

    Mnih, V. et al. Human-level control through deep reinforcement learning. Nature 518, 529–533 (2015).

    ADS  Google Scholar 

  164. 164.

    Vinyals, O. et al. Grandmaster level in StarCraft II using multi-agent reinforcement learning. Nature 575, 350–354 (2019).

    ADS  Google Scholar 

  165. 165.

    Jaderberg, M. et al. Human-level performance in 3D multiplayer games with population-based reinforcement learning. Science 364, 859–865 (2019).

    ADS  MathSciNet  Google Scholar 

  166. 166.

    Pathak, D., Agrawal, P., Efros, A. A. & Darrell, T. Curiosity-driven exploration by self-supervised prediction. In Proc. IEEE Conference on Computer Vision and Pattern Recognition Workshops 16–17 (IEEE, 2017).

  167. 167.

    Burda, Y. et al. Large-scale study of curiosity-driven learning. Preprint at https://arxiv.org/abs/1808.04355 (2019).

  168. 168.

    Silver, D. et al. A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play. Science 362, 1140–1144 (2018).

    ADS  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by the Austrian Academy of Sciences (ÖAW), University of Vienna via the project QUESS and the Austrian Science Fund (FWF) with SFB F40 (FOQUS). M.E. acknowledges support from FWF project W 1210-N25 (CoQuS). M.K. acknowledges support from the FWF via the Erwin Schrödinger fellowship number J4309.

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Correspondence to Mario Krenn, Manuel Erhard or Anton Zeilinger.

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Krenn, M., Erhard, M. & Zeilinger, A. Computer-inspired quantum experiments. Nat Rev Phys 2, 649–661 (2020). https://doi.org/10.1038/s42254-020-0230-4

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