In quantum computing, the so-called Clifford gates are the hard workers, transforming
gates into other gates.
These are : the Hadamard, the phase S, and the CNOT. Only the Hadamard is hermitian.
The Hadamard as an outer product:
The Hadamard snadwiching a Pauli gate. Here it transforms an X-gate into a z-gate;
and a z-gate into an X-gate.
https://www.perplexity.ai/search/Quantum-computing-how-RNsm9Kd9QDuPZc2P5nRNsw
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