Optimal strategy for a single-qubit gate and the trade-off between opposite types of decoherence

We study reliable quantum-information processing (QIP) under two different types of environment. The first type is Markovian exponential decay, and the appropriate elementary strategy of protection of qubit is to apply fast gates. The second one is strongly non-Markovian and occurs solely during operations on the qubit. The best strategy is then to work with slow gates. If the two types are both present, one has to optimize the speed of gate. We show that such a trade-off is present for a single-qubit operation in a semiconductor quantum dot implementation of QIP, where recombination of exciton (qubit) is Markovian, while phonon dressing gives rise to the non-Markovian contribution.

Figure 1

The total error for an $\alpha =\pi ∕2$ rotation on a QD qubit, for $T=0$ (solid lines) and $T=10\mathrm{K}$ (dashed lines), for two dot sizes ($l_h=0.8l_e$ and $l_z=0.2l_e$). The Markovian decoherence times are inferred from the experimental data [14]. Inset: Spectral density of the phonon reservoir $R\left(\omega \right)$ at these two temperatures and the gate profile $S\left(\omega \right)$ for $\alpha =\pi ∕2$.