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arXiv · 2606.03956

Operator spreading in random unitary circuits with orthogonal/symplectic-invariant gate distributions

Zhiyang Tan·Piet W. Brouwer
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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.

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Zhiyang Tan, Piet W. Brouwer. 2026-06-02. Operator spreading in random unitary circuits with orthogonal/symplectic-invariant gate distributions. https://doi.org/10.1103/p5d4-dmj6

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