We reinvestigate a plausible proposal for universal quantum gates in Kane's model, in which the authors assumed that electron spin is always downward under a background magnetic field and the value of the controlling parameters is varied instantaneously. We demonstrate that a considerable error appears, for example, in the $X$ rotation. As a result, the controlled operations do not work. This failure is caused by improper choice of the computational bases; actually, the electron spin is not always downward over time during quantum operations.We reinvestigate a plausible proposal for universal quantum gates in Kane's model, in which the authors assumed that electron spin is always downward under a background magnetic field and the value of the controlling parameters is varied instantaneously. We demonstrate that a considerable error appears, for example, in the $X$ rotation. As a result, the controlled operations do not work. This failure is caused by improper choice of the computational bases; actually, the electron spin is not always downward over time during quantum operations.

arXiv:quant-ph/0509096Physical Review AMar 17, 20060 citations

Gates for the Kane quantum computer in the presence of dephasing

Charles D. Hill, Hsi‐Sheng Goan

In this paper we investigate the effect of dephasing on proposed quantum gates for the solid-state Kane quantum computing architecture. Using a simple model of the decoherence, we find that the typical error in a controlled-NOT gate is $8.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$. We also compute the fidelities of $Z$ , $X$ , swap, and controlled $Z$ operations under a variety of dephasing rates. We show that these numerical results are comparable with the error threshold required for fault tolerant quantum computation.In this paper we investigate the effect of dephasing on proposed quantum gates for the solid-state Kane quantum computing architecture. Using a simple model of the decoherence, we find that the typical error in a controlled-NOT gate is $8.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$. We also compute the fidelities of $Z$, $X$, swap, and controlled $Z$ operations under a variety of dephasing rates. We show that these numerical results are comparable with the error threshold required for fault tolerant quantum computation.

arXiv:quant-ph/0405042Physical Review AAug 1, 200414 citations

X

rotation. As a result, the controlled operations do not work. This failure is caused by improper choice of the computational bases; actually, the electron spin is not always downward over time during quantum operations.

Z

X

, swap, and controlled

Z

operations under a variety of dephasing rates. We show that these numerical results are comparable with the error threshold required for fault tolerant quantum computation.