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Every architecture of six two-qubit gates is locally universal on three qubits — arXiv:2609.22176

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.22176
License (as archived): CC0-1.0
Archived: 2026-10-09T22:46:26.567Z
SHA-256 of the archived text: aec658d9060a43a3d41f47394b0ff34cc7b3950e7e2c92fbe6508fbd2bf8a82f
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Every architecture of six two-qubit gates is locally universal on three qubits — arXiv:2609.22176 — arXiv (en), https://arxiv.org/abs/2609.22176 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_cfafff2cbdda (Metraipolis archive dc_cfafff2cbdda, sha256 aec658d9060a43a3d41f47394b0ff34cc7b3950e7e2c92fbe6508fbd2bf8a82f)

BibTeX

@misc{dccfafff2cbdda,
  title = {Every architecture of six two-qubit gates is locally universal on three qubits — arXiv:2609.22176},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.22176},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_cfafff2cbdda; sha256 aec658d9060a43a3d41f47394b0ff34cc7b3950e7e2c92fbe6508fbd2bf8a82f},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.22176. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We present the \emph{first} analytical determination of the exact accessible dimension for every fixed architecture of arbitrary two-qubit gates on three qubits. A support word represents which pair of qubits each two-qubit gate acts on, and its reduced length is obtained by merging consecutive gates on the same pair. If the reduced length is $r$, then the set of implementable three-qubit unitaries has accessible dimension $d(w)=\min\{63,9r+9\}$. Consequently, six arbitrary two-qubit gates are \emph{necessary and sufficient for local universality}: every fixed architecture reaches a nonempty open subset of $\mathrm{SU}(8)$ when its reduced length is at least six. The result is stronger than existence of one favorable architecture. Every reduced six-slot support word is locally universal, including the alternating nearest-neighbor line $AB,BC,AB,BC,AB,BC$. The upper bound follows from a standard parameter-counting argument. The matching lower bounds are proved by Jacobian certificates in the Pauli basis. Up to qubit relabeling and reversal, there are $22$ reduced architectures of lengths two through six. For each one, a product of rational Pauli rotations yields a nonzero maximal minor modulo the prime $1{,}000{,}003$. Thus, any obstruction to global universality with six two-qubit gates must go beyond parameter counting, connectivity, and differential rank.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-09-22 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2609.22176 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-09T22:25:52.288Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-09-22?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).