Controlled NOT gate

The Controlled NOT (also C-NOT or CNOT) gate is a Universal gate, an essential component in the construction of a quantum computer. Specifically, any quantum circuit can be simulated to an arbitrary degree of accuracy using a combination of CNOT gates and single qubit rotations.

The C-NOT gate flips the second qubit if and only if the first qubit is 1.

Input 1	Input 2	Output 1	Output 2
0	0	0	0
0	1	0	1
1	0	1	1
1	1	1	0

Comparing this quantum gate with a classical gate, the resulting value of the second qubit corresponds to the result of an XOR gate.

The first experimental realization of a cNOT gate was accomplished in 1995. Here, a single Beryllium ion in a trap was used. The two qubits were encoded into an optical state and into the vibrational state of the ion within the trap. At the time of the experiment, the reliability of the cNOT-operation was measured to be on the order of 90%.

In addition to a regular Controlled NOT gate, one could construct a Function-Controlled NOT gate, which accepts an arbitrary number n+1 of qubits as input, where n+1 is greater than or equal to 2 (a quantum register). This gate flips the last qubit of the register if and only if a built-in function, with the first n qubits as input, returns a 1. The Function-Controlled NOT gate is an essential element of the Deutsch-Jozsa algorithm.

References

• Nielsen, Michael A. & Chuang, Isaac L. (2000). Quantum Computing and Quantum Information. Cambridge University Press. ISBN 0-521-63235-8.{{cite book}}: CS1 maint: multiple names: authors list (link)

• Monroe, C. & Meekhof, D. & King, B. & Itano, W. & Wineland, D. (1995). "Demonstration of a Fundamental Quantum Logic Gate". Physical Review Letters (75): 4714–4717.{{cite journal}}: CS1 maint: multiple names: authors list (link)