nLab CNOT gate



Quantum systems

quantum logic

quantum physics

quantum probability theoryobservables and states

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The controlled NOT or reversible XOR-gate is the logic gate acting between pairs of bits which identically keeps the first bit in the pair and negates the second IFF the first was set.

This may be understood equivalently as

In quantum computing/quantum information theory, by the controlled NOT gate or CNOT gate one means the quantum logic gate which acts on a pair of qbits by the linear map which is given in this way on the canonical linear basis-elements of a pair of qbits:

Similarly, by the CCNOT-gate (or Toffoli gate) one means the operation on triples of bits/qbit which (always retains the first two and) reverses the third iff the first two are both set.


Original discussion:

Textbook accounts:

See also:

Last revised on August 16, 2023 at 10:00:45. See the history of this page for a list of all contributions to it.