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This research advances the theoretical understanding of quantum chaos by demonstrating how non-unitary invariant gate ensembles alter operator spreading dynamics, specifically introducing ternary relaxation structures and finite-width domain walls. The findings reveal a fundamental dichotomy in butterfly velocities between orthogonal group components, offering new insights into scrambling limits that could inform future error correction strategies and hardware design for complex quantum processors.
Operator spreading in random unitary circuits with orthogonal/symplectic-invariant gate distributions
arXiv:2606.03956v2 Announce Type: replace 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.
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.
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)
arXiv:2606.03956 [quant-ph]
(or arXiv:2606.03956v2 [quant-ph] for this version)
Tan, Z., & Brouwer, P. W. (2026). Operator spreading in random unitary circuits with orthogonal/symplectic-invariant gate distributions. Physical Review B, 114(7), 074308
https://doi.org/10.1103/p5d4-dmj6 DOI(s) linking to related resources
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