Abstract
Electric Dirac quantum walks, which are a discretisation of the Dirac equation for a spinor coupled to an electric field, are revisited in order to perform spatial searches. The Coulomb electric field of a point charge is used as a non local oracle to perform a spatial search on a 2D grid of N points. As other quantum walks proposed for spatial search, these walks localise partially on the charge after a finite period of time. However, contrary to other walks, this localisation time scales as for small values of N and tends asymptotically to a constant for larger Ns, thus offering a speed-up over conventional methods.
Highlights
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Given a basis (|bL i, |bR i) of an Hilbert space H2 named the ‘spin’space, the wave-function ψ ∈ H2 of the DTQW is represented by its two components ψ L
One should first stress that the DTQWs considered in this article, as previous Quantum Walks (QWs) used in spatial search algorithms, never fully localise on the desired points
Summary
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