arXiv:quant-ph/0403025quant-ph
Universal Quantum Computation with ideal Clifford gates and noisy ancillas
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Abstract
We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state $|0\rangle$ computational basis. In addition, we allow the creation of a one-qubit ancilla in a mixed state $ρ$, which should be regarded as a parameter of the model. Our goal is to determine for which $ρ$ universal quantum computation (UQC) can be efficiently simulated. To answer this question, we construct purification protocols that consume several copies of $ρ$ 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 $ρ$ 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.
The ability to rotate 45 degrees is equivalent to the construction of a magic state, as you have correctly identified, as it is not a clifford operator, and adding it to your generators gives universal quantum computation on its own. You have pushed the problem sideways. This is…
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