Environmental noise reduction for holonomic quantum gates

We study the performance of holonomic quantum gates, driven by lasers, under the effect of a dissipative environment modeled as a thermal bath of oscillators. We show how to enhance the performance of the gates by a suitable choice of the loop in the manifold of the controllable parameters of the laser. For a simplified, albeit realistic model, we find the surprising result that for a long time evolution the performance of the gate (properly estimated in terms of average fidelity) increases. On the basis of this result, we compare holonomic gates with the so-called stimulated raman adiabatic passage (STIRAP) gates.

Figure 1

The error ${\delta }_{\mathit{tr}}$ versus ${\theta }_M$ for two different $a$ values: $a=\pi ∕2$ (dashed line) and $a=\pi ∕4$ (full line) correspond to NOT and Hadamard gate, respectively.

Figure 2

The error ${\delta }_{\mathit{tr}}$ versus $v_{\max }{t}_{\mathit{ad}}$ for two different $a$ values: $a=\pi ∕2$ (dashed line) and $a=\pi ∕4$ (full line) correspond to NOT and Hadamard gate, respectively. The dotted-dashed line shows the value of the error at $\theta =\pi ∕2$. The circles show the critical value of $v_{\max }{t}_{\mathit{ad}}$ above which the best loop is the one with the minimal ${\theta }_M$.