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arXiv · 2605.03023

Arts & crafts: Strong random unitaries and geometric locality

Marten Folkertsma·Lorenzo Grevink·Jonas Helsen·Alicja Dutkiewicz
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Abstract

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.

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Marten Folkertsma, Lorenzo Grevink, Jonas Helsen, Alicja Dutkiewicz. 2026-05-04. Arts & crafts: Strong random unitaries and geometric locality. https://arxiv.org/abs/2605.03023

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