An explicit family of linear reversible circuits is shown to require at least 4n−o(n) CNOT gates, asymptotically surpassing the cyclic permutations and yielding an n=17167 instance with complexity >3(n−1).
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Lower bounds for the CNOT-complexity of linear reversible operators
An explicit family of linear reversible circuits is shown to require at least 4n−o(n) CNOT gates, asymptotically surpassing the cyclic permutations and yielding an n=17167 instance with complexity >3(n−1).