A hybrid machine learning algorithm for designing quantum experiments

Springer Science and Business Media LLC - Tập 1 - Trang 5-15 - 2019
L. O’Driscoll1, R. Nichols1, P. A. Knott1
1Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems (CQNE), School of Mathematical Sciences, University of Nottingham, Nottingham, UK

Tóm tắt

We introduce a hybrid machine learning algorithm for designing quantum optics experiments to produce specific quantum states. Our algorithm successfully found experimental schemes to produce all 5 states we asked it to, including Schrödinger cat states and cubic phase states, all to a fidelity of over 96%. Here, we specifically focus on designing realistic experiments, and hence all of the algorithm’s designs only contain experimental elements that are available with current technology. The core of our algorithm is a genetic algorithm that searches for optimal arrangements of the experimental elements, but to speed up the initial search, we incorporate a neural network that classifies quantum states. The latter is of independent interest, as it quickly learned to accurately classify quantum states given their photon number distributions.

Tài liệu tham khảo

Abadi M, Barham P, Chen J, Chen Z, Davis A, Dean J, Devin M, Ghemawat S, Irving G, Isard M et al (2016) Tensorflow: a system for large-scale machine learning. OSDI 16:265–283 AdaQuantum is available and free to use on GitHub. https://github.com/paulk444/AdaQuantum, (2019) Arrazola JM, Bromley TR, Izaac J, Myers CR, Brádler K, Killoran N (2019) Machine learning method for state preparation and gate synthesis on photonic quantum computers. Quantum Science and Technology 4:024004 Barnett SM, Radmore PM (2002) Methods in Theoretical Quantum Optics, vol 15. Oxford University Press, Oxford Bartley TJ, Donati G, Spring JB, Jin X-M, Barbieri M, Datta A, Smith BJ, Walmsley IA (2012) Multiphoton state engineering by heralded interference between single photons and coherent states. Phys Rev A 86(4):043820 Biamonte J, Wittek P, Pancotti N, Rebentrost P, Wiebe N, Lloyd S (2017) Quantum machine learning. Nature 549(7671):195 Claudon J, Bleuse J, Malik NS, Bazin M, Jaffrennou P, Gregersen N, Sauvan C, Lalanne P, Gérard J (2010) A highly efficient single-photon source based on a quantum dot in a photonic nanowire. Nature Photon 4(3):174–177 Deep K, Thakur M (2007) A new mutation operator for real coded genetic algorithms. Appl Math Comput 193(1):211–230 Dunjko V, Briegel HJ (2017) Machine learning and artificial intelligence in the quantum domain. arXiv:1709.02779 Etesse J, Bouillard M, Kanseri B, Tualle-Brouri R (2015) Experimental generation of squeezed cat states with an operation allowing iterative growth. Phys Rev Lett 114(19):193602 Gerrits T, Glancy S, Clement TS, Calkins B, Lita AE, Miller AJ, Migdall AL, Nam SW, Mirin RP, Knill E (2010) Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum. Phys Rev A 82(3):031802 Ghose S, Sanders BC (2007) Non-gaussian ancilla states for continuous variable quantum computation via gaussian maps. J Mod Opt 54(6):855–869 Gottesman D, Kitaev A, Preskill J (2001) Encoding a qubit in an oscillator. Phys Rev A 64(1):012310 Gu M, Weedbrook C, Menicucci NC, Ralph TC, van Loock P (2009) Quantum computing with continuous-variable clusters. Phys Rev A 79(6):062318 Hall MJW, Wiseman HM (2012) Heisenberg-style bounds for arbitrary estimates of shift parameters including prior information. New J Phys 14(3):033040 Hall MJW, Berry DW, Zwierz M, Wiseman HM (2012) Universality of the Heisenberg limit for estimates of random phase shifts. Phys Rev A 85(4):041802 Huang K (2015) Optical Hybrid Architectures for Quantum Information Processing. PhD thesis l’École Normale supérieure de Paris and East China Normal University. Huang K, Le Jeannic H, Ruaudel J, Verma VB, Shaw MD, Marsili F, Nam SW, Wu E, Zeng H, Jeong Y-C et al (2015) Optical synthesis of large-amplitude squeezed coherent-state superpositions with minimal resources. Phys Rev Lett 115(2):023602 Humphreys PC, Metcalf BJ, Gerrits T, Hiemstra T, Lita AE, Nunn J, Nam SW, Datta A, Kolthammer WS, Walmsley IA (2015) Tomography of photon-number resolving continuous-output detectors. arXiv:1502.07649 Jiang L-y, Guo Q, Xu X-x, Cai M, Yuan W, Duan Z-l (2016) Dynamics and nonclassical properties of an opto-mechanical system prepared in four-headed cat state and number state. Opt Commun 369:179–188 Jin Y (2011) Surrogate-assisted evolutionary computation: Recent advances and future challenges. Swarm Evol Comput 1(2):61–70 Kingma DP, Ba J (2014) Adam: A Method for Stochastic Optimization. arXiv:1412.6980 [cs.LG], 12 Knott P, Proctor T, Hayes A, Cooling J, Dunningham J (2016) Practical quantum metrology with large precision gains in the low-photon-number regime. Phys. Rev. A 93(3):033859 Knott PA (2016) A search algorithm for quantum state engineering and metrology. New J Phys 18(7):073033 Kok P, Lovett BW (2010) Introduction to Optical Quantum Information Processing. Cambridge University Press, Cambridge Krenn M, Malik M, Fickler R, Lapkiewicz R, Zeilinger A (2016) Automated search for new quantum experiments. Phys Rev Lett 116(9):090405 Lee S-Y, Lee C-W, Lee J, Nha H (2015) Quantum phase estimation using a class of entangled states: NOON-type states. arXiv:1505.06000 Lee S-Y, Lee C-W, Nha H, Kaszlikowski D (2015) Quantum phase estimation using a multi-headed cat state. JOSA B 32(6):1186–1192 Mehmet M, Ast S, Eberle T, Steinlechner S, Vahlbruch H, Schnabel R (2011) Squeezed light at 1550 nm with a quantum noise reduction of 12.3 db. Opt Express 19(25):25763–25772 Melnikov AA, Nautrup HP, Krenn M, Dunjko V, Tiersch M, Zeilinger A, Briegel HJ (2018) Active learning machine learns to create new quantum experiments. In: Proceedings of the National Academy of Sciences, p 201714936 Morin O, D’Auria V, Fabre C, Laurat J (2012) High-fidelity single-photon source based on a type II optical parametric oscillator. Opt Lett 37(17):3738–3740 Müller K, Rundquist A, Fischer KA, Sarmiento T, Lagoudakis KG, Kelaita YA, Sanchez Muñoz C, del Valle E, Laussy FP, Vučković J (2015) Coherent generation of nonclassical light on chip via detuned photon blockade. Phys Rev Lett 114(23):233601 Nichols R, Mineh L, Rubio J, Matthews JCF, Knott PA (2018) Designing quantum experiments with a genetic algorithm. arXiv:1812.01032 Nielsen MA, Chuang IL (2010) Quantum Computation and Quantum Information. Cambridge University Press, Cambridge Our DNN and quantum-state generator on GitHub. https://github.com/lewis-od/Quantum-Optics, (2018) Ourjoumtsev A, Tualle-brouri R, Grangier P (2006) Quantum homodyne tomography of a two-photon Fock state. Phys Rev Lett 96(21):213601 Ourjoumtsev A, Jeong H, Tualle-Brouri R, Grangier P (2007) Generation of optical ’schrödinger cats’ from photon number states. Nature 448(7155):784 Paris MGA (1996) Displacement operator by beam splitter. Phys Lett A 217(2):78–80 Rivas A, Luis A (2012) Sub-heisenberg estimation of non-random phase shifts. New J Phys 14(9):093052 Rubio J, Knott P, Dunningham J (2018) Non-asymptotic analysis of quantum metrology protocols beyond the Cramér–rao bound. Journal of Physics Communications 2(1):015027 Sabapathy KK, Qi H, Izaac J, Weedbrook C (2018) Near-deterministic production of universal quantum photonic gates enhanced by machine learning. arXiv:1809.04680 Sabapathy KK, Weedbrook C (2018) On states as resource units for universal quantum computation with photonic architectures. Phys Rev A 97(6):062315 Schrödinger E (1935) Die gegenwärtige situation in der quantenmechanik. Naturwissenschaften 23(49):823–828 Schuld M, Sinayskiy I, Petruccione F (2015) An introduction to quantum machine learning. Contemp Phys 56(2):172–185 Takagi R, Zhuang Q (2018) Convex resource theory of non-gaussianity. Phys Rev A 97:062337 T M Inc., Global optimization toolbox: user’s guide (r2018a). https://uk.mathworks.com/help/gads/index.htmlhttps://uk.mathworks.com/help/gads/index.html. Last accessed 2018-07-17