Composite nonadiabatic holonomic quantum computation

Nonadiabatic holonomic quantum computation has a robust feature in suppressing control errors because of its holonomic feature. However, this kind of robust feature is challenged since the usual way of realizing nonadiabatic holonomic gates introduces errors due to systematic errors in the control parameters. To resolve this problem, we here propose a composite scheme to realize nonadiabatic holonomic gates. Our scheme can suppress systematic errors while preserving holonomic robustness. It is particularly useful when the evolution period is shorter than the coherence time. We further show that our composite scheme can be protected by decoherence-free subspaces. In this case, the strengthened robust feature of our composite gates and the coherence stabilization virtue of decoherence-free subspaces are combined.

Figure 1

Three possible level configurations of the three-level system with the two driving laser fields. (a) Cascaded structure, (b) V structure, and (c) $\mathrm{\Lambda }$ structure. $|0\rangle$ and $|1\rangle$ are computational states, and $|e\rangle$ is an ancillary state. ${\mathrm{\Omega }}_j\left(t\right)$ is the Rabi frequency of laser field driving the transition $|j\rangle \leftrightarrow |e\rangle$.