References and further reading

Further reading

For more details and further information on continuous-variable quantum computation and Gaussian quantum information, please see the following:

[FR1]Christian Weedbrook, Stefano Pirandola, Raúl García-Patrón, Nicolas J. Cerf, Timothy C. Ralph, Jeffrey H. Shapiro, and Seth Lloyd. Gaussian quantum information. Reviews of Modern Physics, 84(2):621–669, May 2012. arXiv:1110.3234, doi:10.1103/revmodphys.84.621.
[FR2]Gerardo Adesso, Sammy Ragy, and Antony R. Lee. Continuous variable quantum information: gaussian states and beyond. Open Systems & Information Dynamics, 21(01n02):1440001, Jun 2014. doi:10.1142/s1230161214400010.
[FR3]Alessio Serafini. Quantum Continuous Variables: A Primer of Theoretical Methods. CRC Press, 2017.
[FR4]Alessandro Ferraro, Stefano Olivares, and Matteo GA Paris. Gaussian states in continuous variable quantum information. arXiv, 2005. arXiv:quant-ph/0503237.

References

[1]M.A. Nielsen and I.L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2010. ISBN 9780511992773. URL: https://books.google.ca/books?id=JRz3jgEACAAJ.
[2]Scott Aaronson and Alex Arkhipov. The computational complexity of linear optics. Theory of Computing, 9(1):143–252, 2013. doi:10.4086/toc.2013.v009a004.
[3]Max Tillmann, Borivoje Dakić, René Heilmann, Stefan Nolte, Alexander Szameit, and Philip Walther. Experimental boson sampling. Nature Photonics, 7(7):540–544, May 2013. doi:10.1038/nphoton.2013.102.
[4]L.G. Valiant. The complexity of computing the permanent. Theoretical Computer Science, 8(2):189–201, 1979. doi:10.1016/0304-3975(79)90044-6.
[5]Michael Reck, Anton Zeilinger, Herbert J. Bernstein, and Philip Bertani. Experimental realization of any discrete unitary operator. Physical Review Letters, 73(1):58–61, Jul 1994. doi:10.1103/physrevlett.73.58.
[6]William R Clements, Peter C Humphreys, Benjamin J Metcalf, W Steven Kolthammer, and Ian A Walsmley. Optimal design for universal multiport interferometers. Optica, 3(12):1460–1465, 2016. doi:10.1364/OPTICA.3.001460.
[7]A. Furusawa and P. van Loock. Quantum Teleportation and Entanglement: A Hybrid Approach to Optical Quantum Information Processing. Wiley, 2011. ISBN 9783527635290. URL: https://books.google.ca/books?id=eKxHZ0UHEU4C.
[8]D. Gottesman and I. L. Chuang. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature, 402:390–393, Nov 1999. arXiv:quant-ph/9908010, doi:10.1038/46503.
[9]Mile Gu, Christian Weedbrook, Nicolas C. Menicucci, Timothy C. Ralph, and Peter van Loock. Quantum computing with continuous-variable clusters. Physical Review A, 79:062318, Jun 2009. doi:10.1103/PhysRevA.79.062318.
[10]Stephen D. Bartlett and William J. Munro. Quantum teleportation of optical quantum gates. Physical Review Letters, 90:117901, Mar 2003. doi:10.1103/PhysRevLett.90.117901.
[11]Peter van Loock. Examples of gaussian cluster computation. Journal of the Optical Society of America B, 24(2):340–346, Feb 2007. doi:10.1364/JOSAB.24.000340.
[12]A. P. Lund, A. Laing, S. Rahimi-Keshari, T. Rudolph, J. L. O’Brien, and T. C. Ralph. Boson sampling from a gaussian state. Physical Review Letters, 113:100502, Sep 2014. doi:10.1103/PhysRevLett.113.100502.
[13]Craig S. Hamilton, Regina Kruse, Linda Sansoni, Sonja Barkhofen, Christine Silberhorn, and Igor Jex. Gaussian boson sampling. Physical Review Letters, 119:170501, Oct 2017. arXiv:1612.01199, doi:10.1103/PhysRevLett.119.170501.
[14]P. van Loock and Samuel L. Braunstein. Telecloning of continuous quantum variables. Physical Review Letters, Nov 2001. doi:10.1103/physrevlett.87.247901.
[15]W. K. Wootters and W. H. Zurek. A single quantum cannot be cloned. Nature, 299(5886):802–803, Oct 1982. doi:10.1038/299802a0.
[16]D. Dieks. Communication by EPR devices. Physics Letters A, 92(6):271–272, Nov 1982. doi:10.1016/0375-9601(82)90084-6.
[17]V. Bužek and M. Hillery. Quantum copying: beyond the no-cloning theorem. Physical Review A, 54(3):1844–1852, Sep 1996. doi:10.1103/physreva.54.1844.
[18]N. J. Cerf, A. Ipe, and X. Rottenberg. Cloning of continuous quantum variables. Physical Review Letters, 85(8):1754–1757, Aug 2000. doi:10.1103/physrevlett.85.1754.
[19]Ulrik L. Andersen, Vincent Josse, and Gerd Leuchs. Unconditional quantum cloning of coherent states with linear optics. Physical Review Letters, Jun 2005. doi:10.1103/physrevlett.94.240503.
[20]Stefano Olivares, Matteo G. A. Paris, and Ulrik L. Andersen. Cloning of gaussian states by linear optics. Physical Review A, Jun 2006. doi:10.1103/physreva.73.062330.
[21]Dominic W. Berry, Andrew M. Childs, and Robin Kothari. Hamiltonian simulation with nearly optimal dependence on all parameters. In 2015 IEEE 56th Annual Symposium on Foundations of Computer Science. IEEE, Oct 2015. doi:10.1109/focs.2015.54.
[22]Alán Aspuru-Guzik, Anthony D. Dutoi, Peter J. Love, and Martin Head-Gordon. Simulated quantum computation of molecular energies. Science, 309(5741):1704–1707, 2005. doi:10.1126/science.1113479.
[23]James D. Whitfield, Jacob Biamonte, and Alán Aspuru-Guzik. Simulation of electronic structure Hamiltonians using quantum computers. Molecular Physics, 109(5):735–750, 2011. doi:10.1080/00268976.2011.552441.
[24]Andrew M. Childs and Nathan Wiebe. Hamiltonian simulation using linear combinations of unitary operations. Quantum Information and Computation, 12(11-12):901–924, 2012. arXiv:1202.5822.
[25]Dominic W. Berry, Graeme Ahokas, Richard Cleve, and Barry C. Sanders. Efficient quantum algorithms for simulating sparse Hamiltonians. Communications in Mathematical Physics, 270(2):359–371, 2006. doi:10.1007/s00220-006-0150-x.
[26]T. Kalajdzievski, C. Weedbrook, and P. Rebentrost. Continuous-variable gate decomposition for the Bose-Hubbard model. 2018. arXiv:1801.06565.
[27]Tomasz Sowiński, Omjyoti Dutta, Philipp Hauke, Luca Tagliacozzo, and Maciej Lewenstein. Dipolar molecules in optical lattices. Physical Review Letters, 108:115301, 2012. doi:10.1103/PhysRevLett.108.115301.
[28]J. M. Arrazola, P. Rebentrost, and C. Weedbrook. Quantum supremacy and high-dimensional integration. 2017. arXiv:1712.07288.
[29]Dan Shepherd and Michael J. Bremner. Temporally unstructured quantum computation. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 465(2105):1413–1439, 2009. doi:10.1098/rspa.2008.0443.
[30]Michael J. Bremner, Ashley Montanaro, and Dan J. Shepherd. Average-case complexity versus approximate simulation of commuting quantum computations. Physical Review Letters, 2016. doi:10.1103/PhysRevLett.117.080501.
[31]Michael J. Bremner, Ashley Montanaro, and Dan J. Shepherd. Achieving quantum supremacy with sparse and noisy commuting quantum computations. Quantum, 1:8, 2017. doi:10.22331/q-2017-04-25-8.
[32]A. P. Lund, Michael J. Bremner, and T. C. Ralph. Quantum sampling problems, BosonSampling and quantum supremacy. npj Quantum Information, 2017. arXiv:1702.03061, doi:10.1038/s41534-017-0018-2.
[33]Michael J. Bremner, Richard Jozsa, and Dan J. Shepherd. Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 2010. arXiv:1005.1407, doi:10.1098/rspa.2010.0301.
[34]T. Douce, D. Markham, E. Kashefi, E. Diamanti, T. Coudreau, P. Milman, P. van Loock, and G. Ferrini. Continuous-variable instantaneous quantum computing is hard to sample. Physical Review Letters, 2017. arXiv:1607.07605, doi:10.1103/PhysRevLett.118.070503.
[35]Nathan Killoran, Thomas R Bromley, Juan Miguel Arrazola, Maria Schuld, Nicolás Quesada, and Seth Lloyd. Continuous-variable quantum neural networks. arXiv preprint arXiv:1806.06871, 2018.
[36]Maria Schuld, Ville Bergholm, Christian Gogolin, Josh Izaac, and Nathan Killoran. Evaluating analytic gradients on quantum hardware. Physical Review A, 99(3):032331, 2019.
[37]Dagmar Bruß. Characterizing entanglement. Journal of Mathematical Physics, 43(9):4237–4251, Sep 2002. URL: https://doi.org/10.1063/1.1494474, doi:10.1063/1.1494474.
[38]Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, and William K. Wootters. Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels. Physical Review Letters, 70:1895–1899, Mar 1993. doi:10.1103/PhysRevLett.70.1895.
[39]W.H. Steeb and Y. Hardy. Problems and Solutions in Quantum Computing and Quantum Information. World Scientific, 2006. ISBN 9789812567406. URL: https://books.google.ca/books?id=HGMy\_dSmfbkC.
[40]Nathan Killoran, Josh Izaac, Nicolás Quesada, Ville Bergholm, Matthew Amy, and Christian Weedbrook. Strawberry Fields: a software platform for photonic quantum computing. Quantum, 3:129, 2019. arXiv:1804.03159, doi:10.22331/q-2019-03-11-129.
[41]Gianfranco Cariolaro and Gianfranco Pierobon. Bloch-Messiah reduction of gaussian unitaries by Takagi factorization. Physical Review A, 94:062109, Dec 2016. doi:10.1103/PhysRevA.94.062109.
[42]Wayne Pullan and Holger H Hoos. Dynamic local search for the maximum clique problem. Journal of Artificial Intelligence Research, 25:159–185, 2006.
[43]Wayne Pullan. Phased local search for the maximum clique problem. Journal of Combinatorial Optimization, 12(3):303–323, 2006.
[44]Juan Miguel Arrazola and Thomas R Bromley. Using gaussian boson sampling to find dense subgraphs. Physical Review Letters, 121(3):030503, 2018.
[45]Kamil Brádler, Pierre-Luc Dallaire-Demers, Patrick Rebentrost, Daiqin Su, and Christian Weedbrook. Gaussian boson sampling for perfect matchings of arbitrary graphs. Physical Review A, 98(3):032310, 2018.
[46]Juan Miguel Arrazola, Thomas R Bromley, and Patrick Rebentrost. Quantum approximate optimization with gaussian boson sampling. Physical Review A, 98(1):012322, 2018.
[47]Jerome Kelleher and Barry O’Sullivan. Generating all partitions: a comparison of two encodings. arXiv preprint arXiv:0909.2331, 2009.
[48]Damian S. Steiger, Thomas Häner, and Matthias Troyer. ProjectQ: an open source software framework for quantum computing. Dec 2016. arXiv:1612.08091.
[49]Francesco Mezzadri. How to generate random matrices from the classical compact groups. ArXiv Mathematical Physics e-prints, Sep 2006. arXiv:math-ph/0609050.
[50]K. E. Cahill and R. J. Glauber. Ordered expansions in boson amplitude operators. Physical Review, 177:1857–1881, Jan 1969. doi:10.1103/PhysRev.177.1857.
[51]F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, and B. V. Saunders (eds.). NIST digital library of mathematical functions. Release 1.0.16 of 2017-09-18. [Online; accessed 2017-10-25]. URL: http://dlmf.nist.gov/.
[52]P Král. Displaced and squeezed Fock states. Journal of Modern Optics, 37(5):889–917, 1990. doi:10.1080/09500349014550941.
[53]Gianfranco Cariolaro and Gianfranco Pierobon. Reexamination of Bloch-Messiah reduction. Physical Review A, 93:062115, Jun 2016. doi:10.1103/PhysRevA.93.062115.
[54]M. S. Kim, W. Son, V. Bužek, and P. L. Knight. Entanglement by a beam splitter: nonclassicality as a prerequisite for entanglement. Physical Review A, 65:032323, Feb 2002. arXiv:quant-ph/0106136, doi:10.1103/PhysRevA.65.032323.
[55]Claude Bloch and Albert Messiah. The canonical form of an antisymmetric tensor and its application to the theory of superconductivity. Nuclear Physics, 39:95–106, 1962.
[56]Samuel L Braunstein. Squeezing as an irreducible resource. Physical Review A, 71(5):055801, 2005.
[57]R Simon, N Mukunda, and Biswadeb Dutta. Quantum-noise matrix for multimode systems: $U(n)$ invariance, squeezing, and normal forms. Physical Review A, 49(3):1567, 1994.
[58]Alex Graves, Greg Wayne, and Ivo Danihelka. Neural turing machines. 2014. arXiv:1410.5401.
[59]Alex Graves, Greg Wayne, Malcolm Reynolds, Tim Harley, Ivo Danihelka, Agnieszka Grabska-Barwińska, Sergio Gómez Colmenarejo, Edward Grefenstette, Tiago Ramalho, John Agapiou, and others. Hybrid computing using a neural network with dynamic external memory. Nature, 538(7626):471–476, 2016. doi:10.1038/nature20101.
[60]Seth Lloyd and Jean-Jacques E Slotine. Analog quantum error correction. Physical Review Letters, 80(18):4088, 1998. doi:10.1103/physrevlett.80.4088.
[61]Samuel L Braunstein. Error correction for continuous quantum variables. Physical Review Letters, 80(18):4084, 1998. doi:10.1103/physrevlett.80.4084.
[62]Daniel Gottesman, Alexei Kitaev, and John Preskill. Encoding a qubit in an oscillator. Physical Review A, 64(1):012310, 2001. doi:10.1103/physreva.64.012310.
[63]Seth Lloyd and Samuel L. Braunstein. Quantum computation over continuous variables. Physical Review Letters, 82:1784–1787, Feb 1999. arXiv:quant-ph/9810082, doi:10.1103/PhysRevLett.82.1784.
[64]Christian Weedbrook, Stefano Pirandola, Raúl García-Patrón, Nicolas J. Cerf, Timothy C. Ralph, Jeffrey H. Shapiro, and Seth Lloyd. Gaussian quantum information. Review of Modern Physics, 84:621–669, May 2012. arXiv:1110.3234, doi:10.1103/RevModPhys.84.621.
[65]Andrew S. Tanenbaum and David J. Wetherall. Computer networks, 5th Ed. Prentice Hall, 2011.
[66]S.M. Barnett and P.M. Radmore. Methods in Theoretical Quantum Optics. Oxford Series in Optical and Imaging Sciences. Clarendon Press, 2002. ISBN 9780198563617. URL: https://books.google.ca/books?id=Gw4sxyr6UhMC.
[67]Pieter Kok and Brendon W. Lovett. Introduction to Optical Quantum Information Processing. Cambridge University Press, 2010. ISBN 9781139486439. URL: https://books.google.ca/books?id=G2zKNooOeKcC.
[68]Victor V. Albert, Kyungjoo Noh, Kasper Duivenvoorden, R. T. Brierley, Philip Reinhold, Christophe Vuillot, Linshu Li, Chao Shen, S. M. Girvin, Barbara M. Terhal, and Liang Jiang. Performance and structure of bosonic codes. Aug 2017. arXiv:1708.05010.
[69]J J Sakurai. Modern Quantum Mechanics. Addison-Wesley Publishing Company, 1994.