Learning an unknown transformation via a genetic approach

Recent developments in integrated photonics technology are opening the way to the fabrication of complex linear optical interferometers. The application of this platform is ubiquitous in quantum information science, from quantum simulation to quantum metrology, including the quest for quantum supremacy via the boson sampling problem. Within these contexts, the capability to learn efficiently the unitary operation of the implemented interferometers becomes a crucial requirement. In this letter we develop a reconstruction algorithm based on a genetic approach, which can be adopted as a tool to characterize an unknown linear optical network. We report an experimental test of the described method by performing the reconstruction of a 7-mode interferometer implemented via the femtosecond laser writing technique. Further applications of genetic approaches can be found in other contexts, such as quantum metrology or learning unknown general Hamiltonian evolutions.

[1]  Anthony Laing,et al.  Direct dialling of Haar random unitary matrices , 2015, 1506.06220.

[2]  A. Crespi,et al.  Integrated multimode interferometers with arbitrary designs for photonic boson sampling , 2013, Nature Photonics.

[3]  T. Ralph,et al.  Quantum process tomography of a controlled-NOT gate. , 2004, Physical review letters.

[4]  Jeongho Bang,et al.  A strategy for quantum algorithm design assisted by machine learning , 2013, 1301.1132.

[5]  Kompa,et al.  Whither the future of controlling quantum phenomena? , 2000, Science.

[6]  A Schreiber,et al.  Decoherence and disorder in quantum walks: from ballistic spread to localization. , 2011, Physical review letters.

[7]  Roberto Morandotti,et al.  Realization of quantum walks with negligible decoherence in waveguide lattices. , 2007, Physical review letters.

[8]  C. Eisenhardt,et al.  Photoionization and dissociation of BF3·((CH3)2O)n mixed aggregates (n=1, 2) studied by mass spectrometry and ab initio calculations , 1997 .

[9]  A. Politi,et al.  Multimode quantum interference of photons in multiport integrated devices , 2010, Nature communications.

[10]  A. G. White,et al.  Ancilla-assisted quantum process tomography. , 2003, Physical review letters.

[11]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[12]  Nathan Wiebe,et al.  Robust online Hamiltonian learning , 2012, TQC.

[13]  A. Crespi,et al.  Anderson localization of entangled photons in an integrated quantum walk , 2013, Nature Photonics.

[14]  Philip Walther,et al.  On unitary reconstruction of linear optical networks , 2015, 1512.04769.

[15]  Thomas Bäck,et al.  Theory of Genetic Algorithms , 2001, Current Trends in Theoretical Computer Science.

[16]  G. D’Ariano,et al.  Optimal quantum learning of a unitary transformation , 2009, 0903.0543.

[17]  M. Mohseni,et al.  Direct characterization of quantum dynamics. , 2006, Physical review letters.

[18]  M Sanz,et al.  Genetic Algorithms for Digital Quantum Simulations. , 2015, Physical review letters.

[19]  W. Marsden.  I and J , 2012 .

[20]  J. O'Brien,et al.  On the experimental verification of quantum complexity in linear optics , 2013, Nature Photonics.

[21]  Nicolò Spagnolo,et al.  General rules for bosonic bunching in multimode interferometers. , 2013, Physical review letters.

[22]  Marco Barbieri,et al.  Heralded processes on continuous-variable spaces as quantum maps , 2012, 1205.6195.

[23]  L. G. Helt,et al.  Tunable quantum interference in a 3D integrated circuit , 2014, Scientific Reports.

[24]  Philip Walther,et al.  Experimental boson sampling , 2012, Nature Photonics.

[25]  Darrell Whitley,et al.  A genetic algorithm tutorial , 1994, Statistics and Computing.

[26]  E. Mazur,et al.  Femtosecond laser micromachining in transparent materials , 2008 .

[27]  Marcus Huber,et al.  A composite parameterization of unitary groups, density matrices and subspaces , 2010, 1004.5252.

[28]  Augusto Smerzi,et al.  Quantum-enhanced multiparameter estimation in multiarm interferometers , 2015, Scientific Reports.

[29]  Andrew G. White,et al.  Photonic Boson Sampling in a Tunable Circuit , 2012, Science.

[30]  Barry C. Sanders,et al.  Accurate and precise characterization of linear optical interferometers , 2015, 1508.00283.

[31]  F. Petruccione,et al.  An introduction to quantum machine learning , 2014, Contemporary Physics.

[32]  Andrew G. White,et al.  Observation of topologically protected bound states in photonic quantum walks , 2011, Nature Communications.

[33]  A. Politi,et al.  Quantum Walks of Correlated Photons , 2010, Science.

[34]  A. Schreiber,et al.  A 2D Quantum Walk Simulation of Two-Particle Dynamics , 2012, Science.

[35]  Nicolò Spagnolo,et al.  Experimental validation of photonic boson sampling , 2014, Nature Photonics.

[36]  B. J. Metcalf,et al.  Boson Sampling on a Photonic Chip , 2012, Science.

[37]  T.C. Ralph,et al.  Quantum gate characterization in an extended Hilbert space , 2005, 2005 Quantum Electronics and Laser Science Conference.

[38]  Nicolò Spagnolo,et al.  Quantum interferometry with three-dimensional geometry , 2012, Scientific Reports.

[39]  A Aspuru-Guzik,et al.  Discrete single-photon quantum walks with tunable decoherence. , 2010, Physical review letters.

[40]  Jeongho Bang,et al.  A genetic-algorithm-based method to find unitary transformations for any desired quantum computation and application to a one-bit oracle decision problem , 2014, 1403.2827.

[41]  G. Vallone,et al.  Two-particle bosonic-fermionic quantum walk via integrated photonics. , 2011, Physical review letters.

[42]  Barry C Sanders,et al.  Complete Characterization of Quantum-Optical Processes , 2008, Science.

[43]  M. J. Withford,et al.  Two-photon quantum walks in an elliptical direct-write waveguide array , 2011, 1103.0604.

[44]  Vladislav V. Yakovlev,et al.  Feedback quantum control of molecular electronic population transfer , 1997 .

[45]  Reck,et al.  Experimental realization of any discrete unitary operator. , 1994, Physical review letters.

[46]  Gerber,et al.  Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses , 1998, Science.

[47]  Hong,et al.  Measurement of subpicosecond time intervals between two photons by interference. , 1987, Physical review letters.

[48]  Roberto Osellame,et al.  Micromachining of photonic devices by femtosecond laser pulses , 2008 .

[49]  G. Vallone,et al.  Experimental quantum process tomography of non-trace-preserving maps , 2010, 1008.5334.

[50]  Nicolò Spagnolo,et al.  Experimental scattershot boson sampling , 2015, Science Advances.

[51]  Andrew G. White,et al.  Direct characterization of linear-optical networks. , 2012, Optics express.

[52]  Daniel A. Lidar,et al.  Quantum Process Tomography: Resource Analysis of Different Strategies , 2007, quant-ph/0702131.

[53]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.