Efficient Coherent Control by Optimized Sequences of Pulses of Finite Duration

Abstract

Reliable long-time storage of arbitrary quantum states is a key element for quantum information processing. In order to dynamically decouple a spin or quantum bit from a dephasing environment, we introduce an optimized sequence of $N$ control pulses of finite durations $\tau \text{pp}$ and finite amplitudes. The properties of this sequence of length $T$ stem from a mathematically rigorous derivation. Corrections occur only in order $T^{N+1}$ and $\tau {\text{pp}}^3$ without mixed terms such as $T^N\tau \text{pp}$ or $T^N\tau {\text{pp}}^2$. Based on existing experiments, a concrete setup for the verification of the properties of the advocated realistic sequence is proposed.