Unitary synthesis with optimal brick wall circuits

• URL: http://arxiv.org/abs/2511.16736v1
• Date: Thu, 20 Nov 2025 19:00:03 GMT
• Title: Unitary synthesis with optimal brick wall circuits
• Authors: David Wierichs, Korbinian Kottmann, Nathan Killoran,
• Abstract summary: We present quantum circuits with a brick wall structure using the optimal number of parameters and two-qubit gates.<n>We show that their Jacobian has full rank almost everywhere in the domain.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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