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I am currently trying to implement a multi-controlled Toffoli/multi-controlled X gate in Braket, but I am confused as to the general concept of cascaded X gates and other implementations. I've read Barenco, Shors, et al's work "Elementary Gates for Quantum Computation", which touches on this, but it's not really illuminating the concept for me. I am partial to the V-gate method used in Barenco, as no ancillary qubits are required, but I'm open to the cascaded-X method as well. Any additional sources or ideas would be greatly appreciated.

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Section 4.3 "Controlled Operations" from Quantum Computation and Quantum Information (linked to pdf version of the text) by Mike and Ike may provide some good additional details.

In particular, page 183 and 184 goes into details on how to implement a general implementation of $C^nX$ or $C^nU$ gate.

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