quantum algorithms:
constructive mathematics, realizability, computability
propositions as types, proofs as programs, computational trinitarianism
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
the controlled quantum gate-version of the quantum NOT-gate
the reversible version of the XOR-gate.
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:
David E. Deutsch, Figure 2 in: Quantum computational networks, Proceedings of the Royal Society A, 425 1868 (1989) 73-90 [doi:10.1098/rspa.1989.0099, jstor:2398494]
Adriano Barenco, Charles H. Bennett, Richard Cleve, David P. DiVincenzo, Norman Margolus, Peter Shor, Tycho Sleator, John A. Smolin, Harald Weinfurter, pp. 8 of: Elementary gates for quantum computation, Phys. Rev. A52 (1995) 3457 [arXiv:quant-ph/9503016, doi:10.1103/PhysRevA.52.3457]
Textbook accounts:
See also:
Wikipedia, Controlled NOT gate
Wikipedia, Toffoli gate
Last revised on August 16, 2023 at 10:00:45. See the history of this page for a list of all contributions to it.