Solovay–Kitaev Theorem
In quantum information and computation, the Solovay–Kitaev theorem says, roughly, that if a set of single-qubit quantum gates generates a dense subset of SU(2), then that set can be used to approximate any desired quantum gate with a relatively short sequence of gates. This theorem is considered one of the most significant results in the field of quantum computation and was first announced by Robert M. Solovay in 1995 and independently proven by Alexei Kitaev in 1997. Michael Nielsen and Christopher M. Dawson have noted its importance in the field. A consequence of this theorem is that a quantum circuit of m constant-qubit gates can be approximated to \varepsilon error (in operator norm) by a quantum circuit of O(m\log^c(m/\varepsilon)) gates from a desired finite universal gate set. By comparison, just knowing that a gate set is universal only implies that constant-qubit gates can be approximated by a finite circuit from the gate set, with no bound on its length. So, the Solov ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  

Qubit
In quantum computing, a qubit () or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two states can be taken to be the vertical polarization and the horizontal polarization. In a classical system, a bit would have to be in one state or the other. However, quantum mechanics allows the qubit to be in a coherent superposition of both states simultaneously, a property that is fundamental to quantum mechanics and quantum computing. Etymology The coining of the term ''qubit'' is attributed to Benjamin Schumacher. In the acknowledgments of his 1995 paper, Schumacher states that the term ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]