An optimal dynamic decoupling of a quantum system coupled to a noisy environment must take into account also the imperfections of the control pulses. We present a formalism which describes, in a closed-form expression, the evolution of the system, including the spectral function of both the environment and control noise. We show that by measuring these spectral functions, our expression can be used to optimize the decoupling pulse sequence. We demonstrate this approach with an ensemble of optically trapped ultracold rubidium atoms, and use quantum process tomography to identify the effect of the environment and control noise. Our approach is applicable and important for any realistic implementation of quantum information processing.An optimal dynamic decoupling of a quantum system coupled to a noisy environment must take into account also the imperfections of the control pulses. We present a formalism which describes, in a closed-form expression, the evolution of the system, including the spectral function of both the environment and control noise. We show that by measuring these spectral functions, our expression can be used to optimize the decoupling pulse sequence. We demonstrate this approach with an ensemble of optically trapped ultracold rubidium atoms, and use quantum process tomography to identify the effect of the environment and control noise. Our approach is applicable and important for any realistic implementation of quantum information processing.

arXiv:1303.2045Physical Review AOct 12, 20169 citations

Quantum Phase Transition Effect on Dynamical Decoupling: a Case Study

H. T. Cui, Gui Yang, Junlong Tian

International Journal of Theoretical PhysicsDec 13, 20160 citations

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

Ashok Ajoy, Gonzalo A. Álvarez, Dieter Suter

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 [the Carr-Purcell-Meiboom-Gill (CPMG) sequence] has been ubiquitously used for decoupling, Uhrig recently proposed that a nonequidistant pulse sequence [the Uhrig dynamic decoupling (UDD) sequence] 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 $^{13}\mathrm{C}$ nuclear spins and the environment consists of a $^{1}\mathrm{H}$ 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 better than any nonequidistant DD sequence in the presence of this kind of environmental noise.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 [the Carr-Purcell-Meiboom-Gill (CPMG) sequence] has been ubiquitously used for decoupling, Uhrig recently proposed that a nonequidistant pulse sequence [the Uhrig dynamic decoupling (UDD) sequence] 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 $^{13}\mathrm{C}$ nuclear spins and the environment consists of a $^{1}\mathrm{H}$ 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 better than any nonequidistant DD sequence in the presence of this kind of environmental noise.

arXiv:1011.6243Physical Review AMar 8, 2011116 citations

Universal dynamical decoupling of multiqubit states from environment

Liang Jiang, Adilet Imambekov

We study the dynamical decoupling of multiqubit states from environment. For a system of $m$ qubits, the nested Uhrig dynamical decoupling (NUDD) sequence can efficiently suppress generic decoherence induced by the system-environment interaction to order $N$ using ${(N+1)}^{2m}$ pulses. We prove that the NUDD sequence is universal, i.e., it can restore the coherence of an $m$ -qubit quantum system independent of the details of the system-environment interaction. We also construct a general mapping between dynamical decoupling problems and discrete quantum walks in certain functional spaces.We study the dynamical decoupling of multiqubit states from environment. For a system of $m$ qubits, the nested Uhrig dynamical decoupling (NUDD) sequence can efficiently suppress generic decoherence induced by the system-environment interaction to order $N$ using ${(N+1)}^{2m}$ pulses. We prove that the NUDD sequence is universal, i.e., it can restore the coherence of an $m$-qubit quantum system independent of the details of the system-environment interaction. We also construct a general mapping between dynamical decoupling problems and discrete quantum walks in certain functional spaces.

arXiv:1104.5021Physical Review ADec 28, 201134 citations

Available control in dynamical decoupled quantum systems

Yu Pan, Zairong Xi, Wei Cui

Chinese Science BulletinApr 11, 20128 citations

^{13}\mathrm{C}

nuclear spins and the environment consists of a

^{1}\mathrm{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 better than any nonequidistant DD sequence in the presence of this kind of environmental noise.

We study the dynamical decoupling of multiqubit states from environment. For a system of

m

qubits, the nested Uhrig dynamical decoupling (NUDD) sequence can efficiently suppress generic decoherence induced by the system-environment interaction to order

N

using

{(N+1)}^{2m}

pulses. We prove that the NUDD sequence is universal, i.e., it can restore the coherence of an

m

-qubit quantum system independent of the details of the system-environment interaction. We also construct a general mapping between dynamical decoupling problems and discrete quantum walks in certain functional spaces.