While I'm reading some literature about synthesizing quantum circuit, I couldn't understand what cascades of Toffoli gates means. How Toffoli cascade runs in quantum circuit?
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Have you researched the meaning of a NAND-gate cascade, or in general a logic-gate cascade? When you combine/cascade a number of NAND gates together, you can realize any boolean function. The same is true of Toffoli gates. For example Wikipedia states: "logic gates can be cascaded in the same way that Boolean functions can be composed, allowing the construction of a physical model of all of Boolean logic, and therefore, all of the algorithms and mathematics that can be described with Boolean logic. " – Mark Spinelli Feb 15 '20 at 14:00
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I think a "cascade" of gates is just a fancy word for a sequence of gates that follow a certain pattern. A good example is offered in this answer that details implementing a multi-controlled-NOT gate using Toffoli gates. The pictures in that answer show Toffoli gates form two ladder-like patterns. I don't think the term "cascade" means anything more specific than that.
Mariia Mykhailova
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