Quantum Computation

A set of quantum gates G (also called a basis) is said to be universal for quantum computation if any unitary operator can be approximated with arbitrary precision by a circuit involving only those gates (called a G-circuit). Since complex numbers do not help in quantum computation, we also call a set of real gates universal if it approximates arbitrary real orthogonal operators. Which set of gates are universal for quantum computation? This basic question is important both in understanding the power of quantum computing and in the physical implementations of quantum computers, and has been studied extensively. Examples of universal bases are: (1) Toffoli, Hadamard, and π 4 -gate, due to Kitaev [5] (2) CNOT, Hadamard, and π 8 -gate, due to Boykin, Mor, Pulver, Roychowdhury, and Vatan [2], and (3) CNOT plus the set of all single-qubit gate, due to Barenco, Bennett, Cleve, DiVincenzo, Margolus, Shor, Sleator, Smolin, and Weinfurter.

Here is an explanation video about Universal Quantum Computation :

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