Concatenated Control Sequences Based on Optimized Dynamic Decoupling

Two recent developments in quantum control, concatenation and optimization of pulse intervals, are combined to yield a strategy to suppress unwanted couplings in quantum systems to high order. Longitudinal relaxation and transverse dephasing can be suppressed so that systems with a small splitting between their energy levels can be kept isolated from their environment. The required number of pulses grows exponentially with the desired order but is only the square root of the number needed if only concatenation is used. An approximate scheme even brings the number down to polynomial growth. The approach is expected to be useful for quantum information and for high-precision nuclear magnetic resonance.

Figure 1

Right-hand side $d(x)={sin}^2(\pi x/2)$ of Eq. (1) compared to $d_{\mathrm{approx}}=-2x^3+3x^2$.