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Conditional dependence and Scrooge ensembles in shallow random quantum circuits — arXiv:2608.12255

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.12255
License (as archived): CC0-1.0
Archived: 2026-10-19T05:54:30.802Z
SHA-256 of the archived text: 563ec29218aed47282a883459745bc1016eda1486fc32a01e82f895f7cf5493d
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Conditional dependence and Scrooge ensembles in shallow random quantum circuits — arXiv:2608.12255 — arXiv (en), https://arxiv.org/abs/2608.12255 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_c92bc3bbdec0 (Metraipolis archive dc_c92bc3bbdec0, sha256 563ec29218aed47282a883459745bc1016eda1486fc32a01e82f895f7cf5493d)

BibTeX

@misc{dcc92bc3bbdec0,
  title = {Conditional dependence and Scrooge ensembles in shallow random quantum circuits — arXiv:2608.12255},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.12255},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_c92bc3bbdec0; sha256 563ec29218aed47282a883459745bc1016eda1486fc32a01e82f895f7cf5493d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.12255. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The output state of a 2D geometrically local shallow random quantum circuit does not have long range correlations due to its lightcone structure. But this changes if one measures a subset of the qubits: long-range entanglement can be induced by the measurement process, leading to conditional correlations between distant qubits. In this paper we investigate the structure of conditional dependence in these circuits and its consequences for quantum advantage. For a tripartition $ABC$ of the qubits, we consider the ensemble of post-measurement states on $A$ that is conditioned on a specific measurement outcome on $B$ and ranges over all possible measurement outcomes on $C$. For circuit depths exceeding a constant critical value $d^*$, we conjecture that this ensemble is well approximated by a certain generalization of the Haar ensemble, called the Scrooge ensemble~[Jozsa \textit{et al.}, \href{ this https URL }{Phys. Rev. A \textbf{49}, 668 (1994)}]; we also provide supporting numerical and analytical evidence. Our conjecture describes a precise sense in which the state retains its lightcone structure on the remaining unmeasured qubits, but also develops some globally random features arising from the measurement. A consequence is that $n$-qubit shallow random quantum circuits in two dimensions are classically efficiently simulable in the presence of a tiny depolarizing noise rate $\Omega(\log(n)/n)$.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-08-13 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph) ; Statistical Mechanics (cond-mat.stat-mech).
Pagina del lavoro: https://arxiv.org/abs/2608.12255 — 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 2026-10-19T05:50:27.102Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-08-13?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).