Adjustable-depth quantum circuit for position-dependent coin operators of discrete-time quantum walks
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929732843470848 |
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| author | Nzongani, Ugo Arnault, Pablo |
| author_facet | Nzongani, Ugo Arnault, Pablo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_10460 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Adjustable-depth quantum circuit for position-dependent coin operators of discrete-time quantum walks Nzongani, Ugo Arnault, Pablo Quantum Physics Emerging Technologies 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. |
| title | Adjustable-depth quantum circuit for position-dependent coin operators of discrete-time quantum walks |
| topic | Quantum Physics Emerging Technologies |
| url | https://arxiv.org/abs/2304.10460 |