Designing robust unitary gates: Application to concatenated composite pulses

We propose a simple formalism to design unitary gates robust against given systematic errors. This formalism generalizes our previous observation [Y. Kondo and M. Bando, J. Phys. Soc. Jpn. 80, 054002 (2011)] that vanishing dynamical phase in some composite gates is essential to suppress pulse-length errors. By employing our formalism, we derive a composite unitary gate which can be seen as a concatenation of two known composite unitary operations. The obtained unitary gate has high fidelity over a wider range of error strengths compared to existing composite gates.

Figure 1

Fidelity $\mathcal{F}$ of (a) a plain pulse (b) CORPSE ($n_1=n_3=1,n_2=2$), (c) SCROFULOUS, and (d) the concatenated pulse sequence as a function of the error strength constants $\epsilon$ for the pulse-length error and ${\epsilon }^{\prime }$ for the off-resonance error. The target unitary operator $U$ is $\exp (-i\pi {\sigma }_2/2)$. In whiter area the fidelity $\mathcal{F}$ yields higher value.