A Quantum Algorithm for the Diffusion Step of Grid-based Filter
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
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| _version_ | 1866915825620877312 |
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| author | Choe, Yeongkwon Park, Chan Gook Duník, Jindřich Krejčí, Jan Matoušek, Jakub Brandner, Marek |
| author_facet | Choe, Yeongkwon Park, Chan Gook Duník, Jindřich Krejčí, Jan Matoušek, Jakub Brandner, Marek |
| contents | We propose a simple quantum algorithm for implementing the diffusion step of grid-based Bayesian filters. The method encodes the advected state density and the process noise density into quantum registers and realizes diffusion using a quantum Fourier transform--based adder. This avoids the explicit convolution required in classical implementations and the repeated coin-flip operations used in quantum random walk approaches. Numerical simulations using a gate-based quantum computing simulator confirm that the proposed approach reproduces the desired probability densities while requiring significantly fewer quantum gates and much shallower circuit depth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00741 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Quantum Algorithm for the Diffusion Step of Grid-based Filter Choe, Yeongkwon Park, Chan Gook Duník, Jindřich Krejčí, Jan Matoušek, Jakub Brandner, Marek Signal Processing We propose a simple quantum algorithm for implementing the diffusion step of grid-based Bayesian filters. The method encodes the advected state density and the process noise density into quantum registers and realizes diffusion using a quantum Fourier transform--based adder. This avoids the explicit convolution required in classical implementations and the repeated coin-flip operations used in quantum random walk approaches. Numerical simulations using a gate-based quantum computing simulator confirm that the proposed approach reproduces the desired probability densities while requiring significantly fewer quantum gates and much shallower circuit depth. |
| title | A Quantum Algorithm for the Diffusion Step of Grid-based Filter |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2603.00741 |