Robust dynamical decoupling

Abstract

Quantum computers, which process information encoded in quantum mechanical systems, hold the potential to solve some of the hardest computational problems. A substantial obstacle for the further development of quantum computers is the fact that the lifetime of quantum information is usually too short to allow practical computation. A promising method for increasing the lifetime, known as dynamical decoupling (DD), consists of applying a periodic series of inversion pulses to the quantum bits. In the present review, we give an overview of this technique and compare different pulse sequences proposed earlier. We show that pulse imperfections, which are always present in experimental implementations, limit the performance of DD. The loss of coherence due to the accumulation of pulse errors can even exceed the perturbation from the environment. This effect can be largely eliminated by a judicious design of pulses and sequences. The corresponding sequences are largely immune to pulse imperfections and provide an increase of the coherence time of the system by several orders of magnitude.

Controlling open quantum systems: tools, achievements, and limitations

“…The main limitation of the dynamical decoupling approach is the finite duration of any control field which cannot always be made suffi-ciently short. By now dynamical decoupling has grown into a field of its own which has been covered by several reviews [129][130][131], and the reader is referred to these for a more in-depth analysis.…”

“…One of the most popular control strategy in the area of quantum technologies currently is dynamical decoupling [130,131]. While already powerful in itself, dynamical decoupling can be made more robust by numerical optimization that targets specific noise features that were previously unaccounted for, using, for example, the gradient-ascent technique [167] or genetic algorithms [168].…”

“…But this may not always be possible, and slow decoherence also allows for eliminating the effects of decoherence based on average Hamiltonian theory [127] or, in more intuitive terms, spin echo techniques from nuclear magnetic resonance and generalizations thereof. This set of strategies is often referred to as dynamical decoupling [128][129][130][131]. It relies on many quasi-instantaneous actions of control fields that do not allow the system to interact with its environment, creating an effective dynamics of the system alone.…”

Arbitrarily Accurate Pulse Sequences for Robust Dynamical Decoupling

“…A common feature of most robust DD sequences so far is pulse error compensation in one or two parameters only (flip angle error, detuning). High fidelity error compensation has been proposed, e.g., by nesting of sequences, but only at the price of a very fast growth in the number of pulses [6].In this Letter, we describe a general theoretical procedure to derive universally robust (UR) DD sequences that compensate pulse imperfections in any experimental parameter (e.g., variations of pulse shapes or intensities), and the effect of a slowly changing environment to an arbitrary order in the permitted error. We note that the term universal is applied for pulse errors.…”

“…Nevertheless, protection of quantum systems from unwanted interactions with the environment remains a major challenge. Dynamical decoupling (DD) is a widely used approach that aims to do this by nullifying the average effect of the unwanted qubit-environment coupling through the application of appropriate sequences of pulses [1][2][3][4].Most DD schemes focus on dephasing processes because they have maximum contribution to information loss in many systems, e.g., in nuclear magnetic resonance and quantum information [5,6]. Then, the major limitation to DD are pulse imperfections whose impact often exceeds the effect of the perturbations from the environment [6][7][8].…”