Unitary synthesis with optimal brick wall circuits
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911277984514048 |
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| author | Wierichs, David Kottmann, Korbinian Killoran, Nathan |
| author_facet | Wierichs, David Kottmann, Korbinian Killoran, Nathan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_16736 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unitary synthesis with optimal brick wall circuits Wierichs, David Kottmann, Korbinian Killoran, Nathan Quantum Physics 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. |
| title | Unitary synthesis with optimal brick wall circuits |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2511.16736 |