Finite-bath projected ensembles in dual-unitary circuits
Abstract
We study the emergent randomness in projected ensembles generated by dual-unitary circuits. Specifically, we consider evolution by solvable dual-unitary brickwork circuits followed by measurements on part of the system, which induce an ensemble of states on the unmeasured subsystem. Previous work has established that this projected ensemble of states forms a quantum state design in the limit where the bath size is large, but the rate of convergence at finite bath size has not been rigorously established. Under three inverse-polynomial assumptions, local permutation mixing, a bound on recurrent backward motion, and contraction at the measured boundary, we fill this gap and prove that a bath of polynomial size suffices to form approximate k-designs. In establishing our results, we develop a microscopic transport interpretation of emergent randomness in the projected ensemble, in which deviations from local permutation operators appear as defects, and make connections with the theory of quantum walks.
Related
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BibTeX
@misc{arvind2026finitebath,
title = {{Finite-bath projected ensembles in dual-unitary circuits}},
author = {Rahul Arvind and Nicholas Hunter-Jones},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06754},
eprint = {2610.06754},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06754},
}
RIS
TY - UNPB
TI - Finite-bath projected ensembles in dual-unitary circuits
AU - Rahul Arvind
AU - Nicholas Hunter-Jones
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06754
UR - https://arxiv.org/abs/2610.06754
AB - We study the emergent randomness in projected ensembles generated by dual-unitary circuits. Specifically, we consider evolution by solvable dual-unitary brickwork circuits followed by measurements on part of the system, which induce an ensemble of states on the unmeasured subsystem. Previous work has established that this projected ensemble of states forms a quantum state design in the limit where the bath size is large, but the rate of convergence at finite bath size has not been rigorously established. Under three inverse-polynomial assumptions, local permutation mixing, a bound on recurrent backward motion, and contraction at the measured boundary, we fill this gap and prove that a bath of polynomial size suffices to form approximate k-designs. In establishing our results, we develop a microscopic transport interpretation of emergent randomness in the projected ensemble, in which deviations from local permutation operators appear as defects, and make connections with the theory of quantum walks.
ER -