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Universal quantum computation with ideal Clifford gates and noisy ancillas

Bravyi, Sergey and Kitaev, Alexei (2005) Universal quantum computation with ideal Clifford gates and noisy ancillas. Physical Review A, 71 (Art no). pp. 1-14. ISSN 1050-2947. doi:10.1103/PhysRevA.71.022316.

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We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state |0>, and qubit measurement in the computational basis. In addition, we allow the creation of a one-qubit ancilla in a mixed state rho, which should be regarded as a parameter of the model. Our goal is to determine for which rho universal quantum computation (UQC) can be efficiently simulated. To answer this question, we construct purification protocols that consume several copies of rho and produce a single output qubit with higher polarization. The protocols allow one to increase the polarization only along certain "magic" directions. If the polarization of rho along a magic direction exceeds a threshold value (about 65%), the purification asymptotically yields a pure state, which we call a magic state. We show that the Clifford group operations combined with magic states preparation are sufficient for UQC. The connection of our results with the Gottesman-Knill theorem is discussed.

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Additional Information:©2005 The American Physical Society (Received 6 May 2004; published 22 February 2005) We thank Mikhail Vyalyi for bringing to our attention many useful facts about the Clifford group. This work has been supported in part by the National Science Foundation under Grant No. EIA-0086038.
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
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Deposited On:14 Dec 2005
Last Modified:08 Nov 2021 19:07

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