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arXiv:1009.1810 · Physical Review A

Limits on preserving quantum coherence using multipulse control

Kaveh Khodjasteh, Tamás Erdélyi, Lorenza Viola

Published Feb 28, 2011• 46 citations
arXivHTMLPDF

Abstract

We explore the physical limits of pulsed dynamical decoupling methods for decoherence control as determined by finite timing resources. By focusing on a decohering qubit controlled by arbitrary sequences of $\ensuremath{\pi}$ pulses, we establish a nonperturbative quantitative upper bound to the achievable coherence for specified maximum pulsing rate and noise spectral bandwidth. We introduce numerically optimized control ``bandwidth-adapted'' sequences that saturate the performance bound and show how they outperform existing sequences in a realistic excitonic-qubit system where timing constraints are significant. As a by-product, our analysis reinforces the impossibility of fault-tolerance accuracy thresholds for generic open quantum systems under purely reversible error control.

DOI
10.1103/physreva.83.020305

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We explore the physical limits of pulsed dynamical decoupling methods for decoherence control as determined by finite timing resources. By focusing on a decohering qubit controlled by arbitrary sequences of \ensuremathπ\ensuremath{\pi}\ensuremathπ pulses, we establish a nonperturbative quantitative upper bound to the achievable coherence for specified maximum pulsing rate and noise spectral bandwidth. We introduce numerically optimized control ``bandwidth-adapted'' sequences that saturate the performance bound and show how they outperform existing sequences in a realistic excitonic-qubit system where timing constraints are significant. As a by-product, our analysis reinforces the impossibility of fault-tolerance accuracy thresholds for generic open quantum systems under purely reversible error control.
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We describe experimental and theoretical studies of open-loop quantum control techniques known as dynamical decoupling (DD) for the suppression of decoherence-induced errors in quantum systems. Our experiments on trapped atomic ion qubits demonstrate that it is possible to optimize the construction of DD sequences for a given noise power spectral density. Studies of novel sequences derived analytically or through numerical optimization – while maintaining fixed control resources – demonstrate large gains in our ability to preserve quantum coherence in arbitrary noise environments.
Dynamical decoupling pulse sequences have been used to extend coherence times in quantum systems ever since the discovery of the spin-echo effect. Here we introduce a method of recursively concatenated dynamical decoupling pulses, designed to overcome both decoherence and operational errors. This is important for coherent control of quantum systems such as quantum computers. For bounded-strength, non-Markovian environments, such as for the spin-bath that arises in electron- and nuclear-spin based solid-state quantum computer proposals, we show that it is strictly advantageous to use concatenated pulses, as opposed to standard periodic dynamical decoupling pulse sequences. Namely, the concatenated scheme is both fault tolerant and superpolynomially more efficient, at equal cost. We derive a condition on the pulse noise level below which concatenation is guaranteed to reduce decoherence.
Reliable long-time storage of arbitrary quantum states is a key element of quantum information processing. In order to dynamically decouple a spin or quantum bit from a dephasing environment by non-instantaneous pulses, we introduce an optimized sequence of N control π pulses that are realistic in the sense that they have a finite duration and a finite amplitude. We show that optimized dynamical decoupling is still applicable and that higher-order decoupling can be reached if shaped pulses are implemented. The sequence suppresses decoherence up to the order , with T being the total duration of the sequence and τ mx the maximum length of the pulses. The exponent depends on the shape of the pulse. Based on existing experiments, a concrete setup for the verification of the properties of the advocated sequence is proposed.
The external coherent control over the dynamics of quantum systems has been the aim of many studies in recent years, and several theoretical frameworks have been devised for that purpose. However, several of the proposed methods have been developed to control isolated quantum systems, disregarding the decoherence effects that impinge on the ubiquitous open quantum systems that exhibit a more complex dynamics than their isolated counterparts. In this paper, we investigate the effects of dissipation and decoherence for a quantum-control procedure based on sequences of reverse optimized electromagnetic pulses. Although the method performs well for pure quantum systems, moderate decoherence and dissipation hinders its accomplishment for ordinary conditions, irrespective of the pulse sequence rate. The method can be appropriate, nonetheless, for dynamical decoupling of the quantum subsystem from the environment.
We utilize genetic algorithms aided by simulated annealing to find optimal dynamical decoupling (DD) sequences for a single-qubit system subjected to a general decoherence model under a variety of control pulse conditions. We focus on the case of sequences with equal pulse intervals and perform the optimization with respect to pulse type and order. In this manner, we obtain robust DD sequences, first in the limit of ideal pulses, then when including pulse imperfections such as finite-pulse duration and qubit rotation (flip-angle) errors. Although our optimization is numerical, we identify a deterministic structure that underlies the top-performing sequences. We use this structure to devise DD sequences which outperform previously designed concatenated DD (CDD) and quadratic DD (QDD) sequences in the presence of pulse errors. We explain our findings using time-dependent perturbation theory and provide a detailed scaling analysis of the optimal sequences.