Magic state distillation

The Clifford group consists of a set of n-qubit operations generated by the gates {{math|{H, S, CNOT} }} (where H is Hadamard and S is \begin{bmatrix} 1 & 0 \\ 0 & i \end{bmatrix} ) called Clifford gates. The Clifford group generates stabilizer states which can be efficiently simulated classically, as shown by the Gottesman–Knill theorem. This set of gates with a non-Clifford operation is universal for quantum computation. ==Magic states ==

Magic states are purified from n copies of a mixed state \rho. These states are typically provided via an ancilla to the circuit. A magic state for the \pi/6 rotation operator is |M\rangle = \cos(\beta/2)|0\rangle + e^{i\frac{\pi}{4}}\sin(\beta/2)|1\rangle where \beta = \arccos\left(\frac{1}{\sqrt 3}\right). A non-Clifford gate can be generated by combining (copies of) magic states with Clifford gates. Since a set of Clifford gates combined with a non-Clifford gate is universal for quantum computation, magic states combined with Clifford gates are also universal. ==Purification algorithm for distilling |M〉==

The first magic state distillation algorithm, invented by Sergey Bravyi and Alexei Kitaev, is as follows. : Input: Prepare 5 imperfect states. : Output: An almost pure state having a small error probability. : repeat :: Apply the decoding operation of the five-qubit error correcting code and measure the syndrome. :: If the measured syndrome is |0000\rangle, the distillation attempt is successful. :: else Get rid of the resulting state and restart the algorithm. : until The states have been distilled to the desired purity. == See also ==