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Two Photon Quantum Walks

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Multi-Photon Quantum Information Science and Technology in Integrated Optics

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Abstract

Classical random walks are a stochastic model of a particle or walker, moving according to classical physics about a discrete space represented by a combinatoric graph—a set of vertices interconnected by edges. The application of random walks from modelling Brownian motion to constructing randomised algorithms in classical computer science [2] has inspired development of a quantum mechanical analogue in quantum computer science.

Some of the results reported in this chapter and an abbreviated discussion thereof were published as Ref. [1]

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Notes

  1. 1.

    We note that more recently, a related experiment was performed with \(n=2\) photons in a three-dimensional directly written waveguide array of \(N=6\) evanescently coupled waveguides in a ring structure [18].

  2. 2.

    The \(\frac{1}{2}\) factor for the diagonal elements arises from the normalisation of the Fock state \({a^\dagger _j}^2\left| 0 \right\rangle = \sqrt{2!}\left| 2 \right\rangle \).

  3. 3.

    We note that the simulation of higher dimensional discrete time quantum walks using two photons is treated in [28].

  4. 4.

    In for these two references, the quantum walk is modelled as a spin chain for transferring quantum information [34].

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  1. Centre for Quantum Photonics, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, UK

    Jonathan C. F. Matthews

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Matthews, J.C.F. (2013). Two Photon Quantum Walks. In: Multi-Photon Quantum Information Science and Technology in Integrated Optics. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32870-1_7

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