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It is an example of a CC-U (controlled-controlled Unitary) gate. Since it is the quantum analog of a classical gate, it is completely specified by its truth table. The Toffoli gate is universal when combined with the single qubit Hadamard gate. [17]
That is, the target qubit (third qubit) will be inverted if the first and second qubits are both 1. It is a universal reversible logic gate, which means that any classical reversible circuit can be constructed from Toffoli gates. The truth table and permutation matrix are as follows (the permutation can be written (7,8) in cycle notation):
A NOR gate is a universal gate, meaning that any other gate can be represented as a combination of NOR gates. ... Truth Table Input A Input B Output Q 0: 0: 0 0: 1: 1 ...
The Fredkin gate (also CSWAP or CS gate), named after Edward Fredkin, is a 3-bit gate that performs a controlled swap. It is universal for classical computation. It has the useful property that the numbers of 0s and 1s are conserved throughout, which in the billiard ball model means the same number of balls are output as input.
If the truth table for a NAND gate is examined or by applying De Morgan's laws, it can be seen that if any of the inputs are 0, then the output will be 1. To be an OR gate, however, the output must be 1 if any input is 1. Therefore, if the inputs are inverted, any high input will trigger a high output.
The XNOR gate (sometimes ENOR, EXNOR, NXOR, XAND and pronounced as Exclusive NOR) is a digital logic gate whose function is the logical complement of the Exclusive OR gate. [1] It is equivalent to the logical connective ( ↔ {\displaystyle \leftrightarrow } ) from mathematical logic , also known as the material biconditional.
Ludwig Wittgenstein introduced a version of the 16-row truth table as proposition 5.101 of Tractatus Logico-Philosophicus (1921). Walther Bothe , inventor of the coincidence circuit , [ 11 ] got part of the 1954 Nobel Prize in physics, for the first modern electronic AND gate in 1924.
The 3-input Fredkin gate is functionally complete reversible gate by itself – a sole sufficient operator. There are many other three-input universal logic gates, such as the Toffoli gate. In quantum computing, the Hadamard gate and the T gate are universal, albeit with a slightly more restrictive definition than that of functional completeness.