Arbitrarily Accurate Pulse Sequences for Robust Dynamical Decoupling

Abstract

We introduce universally robust sequences for dynamical decoupling, which simultaneously compensate pulse imperfections and the detrimental effect of a dephasing environment to an arbitrary order, work with any pulse shape, and improve performance for any initial condition. Moreover, the number of pulses in a sequence grows only linearly with the order of error compensation. Our sequences outperform the state-of-the-art robust sequences for dynamical decoupling. Beyond the theoretical proposal, we also present convincing experimental data for dynamical decoupling of atomic coherences in a solid-state optical memory.Introduction.-Quantum technologies are increasingly important nowadays for a multitude of applications in sensing, processing, and communication of information. 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]. Some sequences, e.g., the widely used Carr-Purcell-Meiboom-Gill (CPMG) sequence, work efficiently for specific quantum states only [6,9]. Robust sequences for any state with limited error compensation have been demonstrated experimentally, e.g., XY4 (PDD), Knill DD (KDD) [6]. Composite pulses, designed for static errors, were also recently shown to be robust to time-dependent non-Markovian noise up to a noise frequency threshold [10]. 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. The UR sequences work at high efficiency for any initial condition. The number of pulses for higher order error compensation grows only linearly with the order of the residual error. The concept works for arbitrary pulse shapes. Our only assumptions are identical pulses in a sequence and

Distinguishing between statistical and systematic errors in quantum process tomography

“…The evolution time takes 5.8 ms matching the J-coupling between 2 ions. The qubit dephasing is protected by dynamical decoupling (DD) pulses [40] applied to both qubits using the Universally Robust (UR) DD sequence [41]. These DD-pulses are applied during the evolution time (for more experimental details see appendix C).…”

Rephasing efficiency of sequences of phased pulses in spin-echo and light-storage experiments

“…As noted in the theory section, the overall light storage efficiency is expected lower than the maximal rephasing efficiency in Eq. (20), due to reabsorption of the retrieved signal, which is not taken into account in our model. After the "projection", the rephasing efficiency of CPMG at the specific storage time does not depend on the number of pulses.…”

“…This is usually termed the "read" process, which in the perfect TABLE II. EIT light storage rephasing efficiency η ls for rephasing sequences with equal pulse separation [13,19,20].…”

Experimental demonstration of composite stimulated Raman adiabatic passage

“…It is also possible to design universal composite pulses, which compensate against any arbitrary variation of experimental parameters in the excitation process. We theoretically proposed and experimentally demonstrated such universal pulse sequences in previous work, which aimed in particular at dynamical decoupling [13,14]. It is a promising idea to combine the concepts of composite pulse sequences with adiabatic passage, in order to improve arbitrary properties of the adiabatic excitation processes, e.g., efficiency, bandwidth, or robustness.…”