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The √ SWAP gate performs half-way of a two-qubit swap (see Clifford gates). It is universal such that any many-qubit gate can be constructed from only √ SWAP and single qubit gates. More than one application of the √ SWAP is required to produce a Bell state from product states.
Checking if a set of quantum gates is universal can be done using group theory methods [18] and/or relation to (approximate) unitary t-designs [19] Some universal quantum gate sets include: The rotation operators R x (θ), R y (θ), R z (θ), the phase shift gate P(φ) [c] and CNOT are commonly used to form a universal quantum gate set. [20] [d]
The Fredkin gate The Toffoli gate can be constructed from single qubit T- and Hadamard-gates, and a minimum of six CNOTs. The Fredkin gate is a universal reversible 3-bit gate that swaps the last two bits if the first bit is 1; a controlled-swap operation. The n-bit Toffoli gate is a generalization of the Toffoli gate.
Logic gates can be made from quantum mechanical effects, see quantum logic gate. Photonic logic gates use nonlinear optical effects. In principle any method that leads to a gate that is functionally complete (for example, either a NOR or a NAND gate) can be used to make any kind of digital logic circuit. Note that the use of 3-state logic for ...
For example, a set of reversible gates is called functionally complete, if it can express every reversible operator. 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.
Like NAND gates, NOR gates are so-called "universal gates" that can be combined to form any other kind of logic gate. For example, the first embedded system, the Apollo Guidance Computer, was built exclusively from NOR gates, about 5,600 in total for the later versions. Today, integrated circuits are not constructed exclusively from a single ...