Operator spreading in random unitary circuits with orthogonal/symplectic-invariant gate distributions
Abstract
We investigate operator spreading in random quantum circuits with gates drawn from orthogonal-invariant or symplectic-invariant ensembles, revealing several key distinctions from the well-studied unitary-invariant case. We find that the ensemble-averaged Pauli-string weights relax to a ternary-valued structure, instead of the binary structure of unitary-invariant circuits. For orthogonal- or symplectic-invariant circuits, the domain wall separating trivial and scrambled regions has a finite width even for Haar-random gates, whereas domain walls are sharp for Haar-distributed random unitary circuits. We further find a fundamental dichotomy between random circuits with two-qubit gates from the two disconnected components of the orthogonal group: While the butterfly velocity for the special orthogonal ensemble lies between zero and the Haar value, the negative-determinant sector exhibits a non-zero lower bound for any gate distribution. Moreover, for qudit size q=2, the butterfly velocity can exceed that of the Haar-random ensemble.
Versions
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BibTeX
@misc{tan2026operator,
title = {{Operator spreading in random unitary circuits with orthogonal/symplectic-invariant gate distributions}},
author = {Zhiyang Tan and Piet W. Brouwer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.03956},
eprint = {2606.03956},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.03956},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Operator spreading in random unitary circuits with orthogonal/symplectic-invariant gate distributions
AU - Zhiyang Tan
AU - Piet W. Brouwer
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2606.03956
UR - https://arxiv.org/abs/2606.03956
AB - We investigate operator spreading in random quantum circuits with gates drawn from orthogonal-invariant or symplectic-invariant ensembles, revealing several key distinctions from the well-studied unitary-invariant case. We find that the ensemble-averaged Pauli-string weights relax to a ternary-valued structure, instead of the binary structure of unitary-invariant circuits. For orthogonal- or symplectic-invariant circuits, the domain wall separating trivial and scrambled regions has a finite width even for Haar-random gates, whereas domain walls are sharp for Haar-distributed random unitary circuits. We further find a fundamental dichotomy between random circuits with two-qubit gates from the two disconnected components of the orthogonal group: While the butterfly velocity for the special orthogonal ensemble lies between zero and the Haar value, the negative-determinant sector exhibits a non-zero lower bound for any gate distribution. Moreover, for qudit size q=2, the butterfly velocity can exceed that of the Haar-random ensemble.
ER -