Random states from symplectic and orthogonal unitaries show exponentially large strong state complexity and near-orthogonality, with average-case hardness for learning circuits from these groups.
On some measures analogous to haar measure.Mathematica Scandinavica, 26(1):103–106, 1970
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On the Complexity of Quantum States and Circuits from the Orthogonal and Symplectic Groups
Random states from symplectic and orthogonal unitaries show exponentially large strong state complexity and near-orthogonality, with average-case hardness for learning circuits from these groups.