Metraipolis › archive › dc_62eaac01dcba

Optimal Scaling of Unitary Design Formation in $U(1)$-Symmetric Random Circuits: A Bottleneck Slower than Charge Transport — arXiv:2609.39458

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.39458
License (as archived): CC0-1.0
Archived: 2026-10-07T15:21:24.652Z
SHA-256 of the archived text: e5fac36587d898103a9f914f3f7eaf617eaec96c7b59b64f1ffe1651f3ca105c
Stable URL of this page: https://metraipolis.com/documento/dc_62eaac01dcba

How to cite

Optimal Scaling of Unitary Design Formation in $U(1)$-Symmetric Random Circuits: A Bottleneck Slower than Charge Transport — arXiv:2609.39458 — arXiv (en), https://arxiv.org/abs/2609.39458 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_62eaac01dcba (Metraipolis archive dc_62eaac01dcba, sha256 e5fac36587d898103a9f914f3f7eaf617eaec96c7b59b64f1ffe1651f3ca105c)

BibTeX

@misc{dc62eaac01dcba,
  title = {Optimal Scaling of Unitary Design Formation in $U(1)$-Symmetric Random Circuits: A Bottleneck Slower than Charge Transport — arXiv:2609.39458},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.39458},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_62eaac01dcba; sha256 e5fac36587d898103a9f914f3f7eaf617eaec96c7b59b64f1ffe1651f3ca105c},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.39458. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Understanding randomness formation under conservation laws is important both for characterizing chaotic phenomena in isolated quantum systems and for symmetry-constrained quantum information processing. $U(1)$-symmetric random circuits on an $N$-qubit system provide a minimal tractable setting for this problem, in which the formation rate of unitary designs was conjectured to be governed by charge transport in the underlying circuit geometry. However, whether charge transport indeed sets the slowest relaxation mode has remained an open problem, due to the difficulty in deriving a tight lower bound on the symmetric design formation rate. In this work, we resolve this problem by determining the optimal scaling of the unitary $k$-design formation rate for $k\leq O(\sqrt{\log N})$ across a wide range of circuit geometries, including lattices, expander graphs, and all-to-all interactions. In particular, for $k\geq 2$, we find that the formation rate is governed by a two-particle encounter rate---the rate at which two random walkers encounter each other in a given circuit geometry. This encounter rate is parametrically smaller than the single-particle transport rate in many geometries, thereby disproving the previous conjecture. We further establish that this encounter mechanism indeed sets the design formation rate by deriving its matching lower bound with a novel proof technique based on an auxiliary subgroup ensemble. Although this encounter mode imposes a robust bottleneck on design formation in $U(1)$-symmetric random circuits, we also show that this bottleneck can be circumvented by using symmetry-breaking local gates and provide an explicit protocol that achieves faster design formation. These results establish a new picture of randomness formation under conservation laws and provide guiding principles for characterizing and efficiently generating symmetry-constrained randomness.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-10-01 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph) ; Statistical Mechanics (cond-mat.stat-mech).
Pagina del lavoro: https://arxiv.org/abs/2609.39458 — 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 2026-10-07T14:53:56.689Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-10-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).