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Dynamical Lie algebra of an orthogonally-generated circuit

Theorem statement

For the $n$-qubit circuit generated by the skew-symmetric Pauli strings ($P^{\top}=-P$), the dynamical Lie algebra is the special orthogonal algebra $$\mathfrak g \;=\; \mathfrak{so}(2^n),\qquad \dim\mathfrak g=\frac{4^n-2^n}{2}.$$

Sources

  1. A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits

    Michael Ragone, Bojko N. Bakalov, Frederic Sauvage, Alexander F. Kemper, Carlos Ortiz Marrero, Martin Larocca, M. Cerezo, 2023

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