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Explicit orthogonal and unitary designs

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arxiv 2310.13597 v1 pith:LBEUSFAT submitted 2023-10-20 cs.CC

Ryan O'Donnell , Rocco A. Servedio , Pedro Paredes This is my paper · ORCID
classification cs.CC
keywords designsmathrmvarepsilonconstructionexplicitgrouporthogonalunitary
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abstract

We give a strongly explicit construction of $\varepsilon$-approximate $k$-designs for the orthogonal group $\mathrm{O}(N)$ and the unitary group $\mathrm{U}(N)$, for $N=2^n$. Our designs are of cardinality $\mathrm{poly}(N^k/\varepsilon)$ (equivalently, they have seed length $O(nk + \log(1/\varepsilon)))$; up to the polynomial, this matches the number of design elements used by the construction consisting of completely random matrices.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quantum Simulation of Random Unitaries from Clebsch-Gordan Transforms

    quant-ph 2025-09 accept novelty 7.0 of 10

    Clebsch-Gordan transforms give exact compressed oracles for Haar-random unitary group actions, with efficient circuits for U(d).

  2. Quantum One-Way Functions and Related Cryptographic Primitives

    quant-ph 2026-08 conditional novelty 3.0 of 10

    A topical review that clarifies the relationships and differences among quantum one-way functions, OWSGs, PRSGs, and EFI pairs, emphasizing physical realizability.

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