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A quantum gate is always reversible

Last updated Jun 23, 2022

A Reversible Matrix is defined as $MM^{−1} = M^{−1}M = I$. As we know that All quantum gates are unitary matrices, meaning that a quantum gate satisfies $$UU^\dagger = U^\dagger U = I.$$ Then the inverse of $U$ is simply $U^\dagger$. So a quantum gate is always reversible, and its inverse is its conjugate transpose.