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Increased Complexity

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Complexity and Control in Quantum Photonics

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

A survey of the literature reveals a rich history of experiments in which p photons are sent through an optical circuit with m modes. The experimentalist looks to see where the photons went, examining spatio-temporal correlations using an array of single-photon detectors, in an effort to determine whether the experiment is (i) working properly and/or (ii) doing anything interesting.

Actually, if we wanted to, although it’s expensive, we could put detectors all over [. . . ] and build up the whole curve simultaneously. . .

Feynman

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Notes

  1. 1.

    The third, completed very recently, is described in a pre-print [1] due to Matthews et al.

  2. 2.

    In a circuit model architecture, replacing qubits with d-level systems has been shown to give a modest multiplicative \(\log _2d\) advantage in the number of gate operations [2] and facilitate controlled-\(\hat{U}\) operations [3].

  3. 3.

    In fact, a classical random walk was used as part of a machine learning algorithm to optimize the performance of the CNOT-MZ chip [9].

  4. 4.

    Note that the momentum of the ball in the Galton board gives the system some memory of past states, and the system is therefore only approximately Markovian.

  5. 5.

    The ECT is not sufficiently well-posed to ever be formally disproved, only weakened.

  6. 6.

    or 143, depending on how you define “quantum computer” [54].

  7. 7.

    A CPU containing in excess of a billion nanoscale transistors can be bought for less than £10.

  8. 8.

    Allowing postselection on exponentially unlikely outcomes for both quantum and classical machines.

  9. 9.

    Benchmarks and optimized Cython code for the permanent are given in Appendix A.

  10. 10.

    By introducing a strong, controlled, uniform source of noise, we “override” any effects from the uncontrolled, non-uniform thermal/acoustic phase fluctuation. In this sense, the method described here shares some similarity with the techniques for precise characterization under environmental noise described in Sect. 4.5.

  11. 11.

    Higher-dimensional quadrants of hypercubes are referred to as octants or hyper-octants.

  12. 12.

    Careful control of the phase of input photons, following the classical approach of beam steering using a phased array, might conceivably reproduce this effect.

  13. 13.

    16 detectors are used in Ref. [60], but only a subset of possible detection events are recorded.

  14. 14.

    Doubts might be raised by the fact that the number of hypercube orthants which intersect with the main diagonal of the correlation matrix falls off exponentially with p.

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  1. Imperial College London, London, UK

    Peter Shadbolt

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Shadbolt, P. (2016). Increased Complexity. In: Complexity and Control in Quantum Photonics. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-21518-1_6

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