Keeping a Quantum Bit Alive by Optimized $\pi$-Pulse Sequences

A general strategy to maintain the coherence of a quantum bit is proposed. The analytical result is derived rigorously including all memory and backaction effects. It is based on an optimized $\pi$-pulse sequence for dynamic decoupling extending the Carr-Purcell-Meiboom-Gill cycle. The optimized sequence is very efficient, in particular, for strong couplings to the environment.

Figure 1

Signal (4) vs time. Solid lines for $T=0$; dashed ones for $T=0.1{\omega }_D$. Panels (a) (linear) and (b) (double logarithmic) from bottom to top for $\alpha =0.25$, 0.1, 0.01, 0.001. Panel (c) (double logarithmic) displays $1-s(t)$ for the same values from top to bottom.

Figure 2

Signal (8) vs time for various numbers of pulses at $T=0$. Solid lines for the optimized sequence, dashed-dotted lines for the equidistant sequence (see main text). From top to bottom the curves refer to $\alpha =0.25$, 0.1, 0.01, 0.001.