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Preprints, Working Papers, ... Year : 2024

Adjustable-depth quantum circuit for position-dependent coin operators of discrete-time quantum walks

Abstract

Discrete-time quantum walks with position-dependent coin operators have numerous applications. For a position dependence that is sufficiently smooth, it has been provided in Ref. [1] an approximate quantum-circuit implementation of the coin operator that is efficient. If we want the quantum-circuit implementation to be exact (e.g., either, in the case of a smooth position dependence, to have a perfect precision, or in order to treat a non-smooth position dependence), but the depth of the circuit not to scale exponentially, then we can use the linear-depth circuit of Ref. [1], which achieves a depth that is linear at the cost of introducing an exponential number of ancillas. In this paper, we provide an adjustable-depth quantum circuit for the exact implementation of the position-dependent coin operator. This adjustable-depth circuit consists in (i) applying in parallel, with a linear-depth circuit, only certain packs of coin operators (rather than all of them as in the original linear-depth circuit [1]), each pack contributing linearly to the depth, and in (ii) applying sequentially these packs, which contributes exponentially to the depth.
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Dates and versions

hal-04396459 , version 1 (16-01-2024)

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Ugo Nzongani, Pablo Arnault. Adjustable-depth quantum circuit for position-dependent coin operators of discrete-time quantum walks. 2024. ⟨hal-04396459⟩
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