Optimal pulse spacing for dynamical decoupling in the presence of a purely dephasing spin bath

Abstract

Maintaining quantum coherence is a crucial requirement for quantum computation; hence protecting quantum systems against their irreversible corruption due to environmental noise is an important open problem. Dynamical decoupling (DD) is an effective method for reducing decoherence with a low control overhead. It also plays an important role in quantum metrology, where for instance it is employed in multiparameter estimation. While a sequence of equidistant control pulses (CPMG) has been ubiquitously used for decoupling, Uhrig recently proposed that a non-equidistant pulse sequence (UDD) may enhance DD performance, especially for systems where the spectral density of the environment has a sharp frequency cutoff. On the other hand, equidistant sequences outperform UDD for soft cutoffs. The relative advantage provided by UDD for intermediate regimes is not clear. In this paper, we analyze the relative DD performance in this regime experimentally, using solid-state nuclear magnetic resonance. Our system-qubits are 13 C nuclear spins and the environment consists of a 1 H nuclear spin-bath whose spectral density is close to a normal (Gaussian) distribution. We find that in the presence of such a bath, the CPMG sequence outperforms the UDD sequence. An analogy between dynamical decoupling and interference effects in optics provides an intuitive explanation as to why the CPMG sequence performs superior to any non-equidistant DD sequence in the presence of this kind of environmental noise.

Robust dynamical decoupling

“…The overlap of this filter function with the spectral distribution of the environmental noise determines the decoherence rate [90]. Analogously, the filter shapes can be connected to diffraction patterns induced by interferences in the time domain [65]. The UDD sequence was shown theoretically to be the optimal sequence for reducing low frequency noise [47,90,91].…”

“…However, it appears that non-equidistant sequences perform better only for particular noise spectral densities that increase for higher frequencies and have a strong cutoff. In the more frequent case, where the spectral density decreases smoothly with the frequency, equidistant sequences were predicted [90][91][92] and demonstrated [49,55,56,62,63,65] to be the best option [65].…”

“…A heteronuclear spin-spin interaction involves a pure dephasing interaction. This type of interaction occurs in a wide range of solid-state spin systems, including nuclear spins in NMR [32,33,55,65], electron spins in diamonds [56], electron spins in quantum dots [86], donors in silicon [87], etc. In other cases, when the system and environment have similar energy level splittings, the SE interaction can include terms along the x-, y-and z-axis.…”

“…The delay t = 10 ms between the pulses is constant and identical for both sequences. The qubits used for this experiment were 13 C nuclear spins in a polycrystalline adamantane sample [54,55,65,67]. (Online version in colour.)…”

Uhrig dynamical control of a three-level system via non-Markovian quantum state diffusion

“…Studies on higher-order effects have also been done for non-ideal pulses [26,27], as well as optimized pulses under different environment noises [28][29][30]. In experiments, the remarkable performance of UDD in prolonging the life time of a single-qubit state in various models has been studied [31][32][33][34].…”