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.
Quantum simulation of time-dependent hamiltonians and the convenient illusion of hilbert space.Physical Review Letters, 106(17), April 2011
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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.