Arts & crafts: Strong random unitaries and geometric locality
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914528555433984 |
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| author | Folkertsma, Marten Grevink, Lorenzo Helsen, Jonas Dutkiewicz, Alicja |
| author_facet | Folkertsma, Marten Grevink, Lorenzo Helsen, Jonas Dutkiewicz, Alicja |
| contents | We study the problem of constructing strong approximate unitary $k$-designs on $D$-dimensional grids (and more generally on Cartesian products of graphs), building on the work of Schuster et al. arXiv:2509.26310 which establishes strong unitary designs in 1D and in all-to-all connectivity. We provide two constructions. The first construction leverages the existing all-to-all connectivity result with general routing theory to provide flexible (but slightly suboptimal) strong $k$-designs in arbitrary connectivities. The second construction is more direct, requires no auxiliaries and has provably optimal depth (in the number of qubits $n$) for $D$-dimensional grids with constant dimension. Combining these techniques also allows us to construct strong pseudorandom unitaries on $D$-dimensional grids with provably optimal depth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03023 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Arts & crafts: Strong random unitaries and geometric locality Folkertsma, Marten Grevink, Lorenzo Helsen, Jonas Dutkiewicz, Alicja Quantum Physics We study the problem of constructing strong approximate unitary $k$-designs on $D$-dimensional grids (and more generally on Cartesian products of graphs), building on the work of Schuster et al. arXiv:2509.26310 which establishes strong unitary designs in 1D and in all-to-all connectivity. We provide two constructions. The first construction leverages the existing all-to-all connectivity result with general routing theory to provide flexible (but slightly suboptimal) strong $k$-designs in arbitrary connectivities. The second construction is more direct, requires no auxiliaries and has provably optimal depth (in the number of qubits $n$) for $D$-dimensional grids with constant dimension. Combining these techniques also allows us to construct strong pseudorandom unitaries on $D$-dimensional grids with provably optimal depth. |
| title | Arts & crafts: Strong random unitaries and geometric locality |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.03023 |