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arXiv · 2511.16736

Unitary synthesis with optimal brick wall circuits

David Wierichs·Korbinian Kottmann·Nathan Killoran
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Abstract

We present quantum circuits with a brick wall structure using the optimal number of parameters and two-qubit gates to parametrize $SU(2^n)$, and provide evidence that these circuits are universal for $n\leq 5$. For this, we successfully compile random matrices to the presented circuits and show that their Jacobian has full rank almost everywhere in the domain. Our method provides a new state of the art for synthesizing typical unitary matrices from $SU(2^n)$ for $n=3, 4, 5$, and we extend it to the subgroups $SO(2^n)$ and $Sp^\ast(2^n)$. We complement this numerical method by a partial proof, which hinges on an open conjecture that relates universality of an ansatz to it having full Jacobian rank almost everywhere.

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David Wierichs, Korbinian Kottmann, Nathan Killoran. 2025-11-20. Unitary synthesis with optimal brick wall circuits. https://arxiv.org/abs/2511.16736

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