Universal quantum computation with ideal Clifford gates and noisy ancillas
- Institute for Quantum Information, California Institute of Technology, Pasadena, 91125 California (United States)
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.
- OSTI ID:
- 20650061
- Journal Information:
- Physical Review. A, Journal Name: Physical Review. A Journal Issue: 2 Vol. 71; ISSN 1050-2947; ISSN PLRAAN
- Country of Publication:
- United States
- Language:
- English
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