arXiv:0708.4267 · Physical Review A

Soft-pulse dynamical decoupling in a cavity

Leonid P. Pryadko, Gregory Quiroz

Published Jan 24, 2008• 22 citations

Abstract

Dynamical decoupling is a coherent control technique where the intrinsic and extrinsic couplings of a quantum system are effectively averaged out by application of specially designed driving fields (refocusing pulse sequences). This entails pumping energy into the system, which can be especially dangerous when it has sharp spectral features like a cavity mode close to resonance. In this work we show that such an effect can be avoided with properly constructed refocusing sequences. To this end we construct the average Hamiltonian expansion for the system evolution operator associated with a single ``soft'' $\ensuremath{\pi}$ pulse. To second order in the pulse duration, we characterize a symmetric pulse shape by three parameters, two of which can be made zero by shaping. We express the effective Hamiltonians for several pulse sequences in terms of these parameters and use the results to analyze the structure of error operators for a controlled Jaynes-Cummings Hamiltonian. When errors are cancelled to second order, numerical simulations show excellent qubit fidelity with strongly suppressed oscillator heating.

DOI: 10.1103/physreva.77.012330

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arXiv:0708.4267 · Physical Review A

Soft-pulse dynamical decoupling in a cavity

Leonid P. Pryadko, Gregory Quiroz

Published Jan 24, 2008• 22 citations

arXiv HTML PDF

Abstract

\ensuremath{\pi}

pulse. To second order in the pulse duration, we characterize a symmetric pulse shape by three parameters, two of which can be made zero by shaping. We express the effective Hamiltonians for several pulse sequences in terms of these parameters and use the results to analyze the structure of error operators for a controlled Jaynes-Cummings Hamiltonian. When errors are cancelled to second order, numerical simulations show excellent qubit fidelity with strongly suppressed oscillator heating.

DOI: 10.1103/physreva.77.012330

Related papers

Refocusing of a qubit system coupled to an oscillator

Leonid P. Pryadko, Gregory Quiroz

Refocusing, or dynamical decoupling, is a coherent control technique where the internal dynamics of a quantum system is effectively averaged out by an application of specially designed driving fields. The method has originated in nuclear magnetic resonance, but it was independently discovered in atomic physics as a ``coherent destruction of tunneling''. Present work deals with the analysis of the performance of ``soft'' refocusing pulses and pulse sequences in protecting the coherence of a qubit system coupled to a quantum oscillator.Refocusing, or dynamical decoupling, is a coherent control technique where the internal dynamics of a quantum system is effectively averaged out by an application of specially designed driving fields. The method has originated in nuclear magnetic resonance, but it was independently discovered in atomic physics as a ``coherent destruction of tunneling''. Present work deals with the analysis of the performance of ``soft'' refocusing pulses and pulse sequences in protecting the coherence of a qubit system coupled to a quantum oscillator.

arXiv:0706.0501Jun 4, 20070 citations

Soft-pulse dynamical decoupling with Markovian decoherence

Leonid P. Pryadko, Gregory Quiroz

We consider the effect of broadband decoherence on the performance of refocusing sequences, having in mind applications of dynamical decoupling in concatenation with quantum error correcting codes as the first stage of coherence protection. Specifically, we construct cumulant expansions of effective decoherence operators for a qubit driven by a pulse of a generic symmetric shape and for several sequences of $\ensuremath{\pi}$ and $\ensuremath{\pi}/2$ pulses. While, in general, the performance of soft pulses in decoupling sequences in the presence of Markovian decoherence is worse than that of the ideal $\ensuremath{\delta}$ pulses, it can be substantially improved by shaping.We consider the effect of broadband decoherence on the performance of refocusing sequences, having in mind applications of dynamical decoupling in concatenation with quantum error correcting codes as the first stage of coherence protection. Specifically, we construct cumulant expansions of effective decoherence operators for a qubit driven by a pulse of a generic symmetric shape and for several sequences of $\ensuremath{\pi}$ and $\ensuremath{\pi}/2$ pulses. While, in general, the performance of soft pulses in decoupling sequences in the presence of Markovian decoherence is worse than that of the ideal $\ensuremath{\delta}$ pulses, it can be substantially improved by shaping.

arXiv:0907.1315Physical Review AOct 20, 200923 citations

High-order dynamical decoupling in the weak-coupling regime

Leeseok Kim, Milad Marvian

We introduce a high-order dynamical decoupling (DD) scheme for arbitrary bounded system-bath interactions in the weak-coupling regime. Given any decoupling group $\mathcal G$ that averages the interaction to zero, our construction {guarantees the existence of pulse sequences with at most $(|\mathcal G|-1)K$ pulses}, while canceling all error terms linear in the system-bath coupling strength up to order $K$ in the total evolution time. As a corollary, for an $n$ -qubit system with $k$ -local system-bath interactions, we obtain an $\mathcal{O}(n^{k-1}K)$ -pulse sequence, a significant improvement over existing schemes with $\mathcal{O}(\exp(n))$ pulses (for $k=\mathcal{O}(1)$ ). The construction is obtained via a mapping to the continuous necklace-splitting problem, which asks how to cut a multi-colored interval into pieces that give each party the same share of every color. We provide explicit pulse sequences for suppressing general single-qubit decoherence, prove that the pulse count is asymptotically optimal, and verify the predicted error scaling in numerical simulations. For the same number of pulses, we observe that our sequences outperform the state-of-the-art Quadratic DD in the weak-coupling regime. We also construct explicit high-order sequences for suppressing representative 2-local noise models. Finally, the same construction extends to suppress slow, time-dependent classical noise and to filter-function design.We introduce a high-order dynamical decoupling (DD) scheme for arbitrary bounded system-bath interactions in the weak-coupling regime. Given any decoupling group $\mathcal G$ that averages the interaction to zero, our construction {guarantees the existence of pulse sequences with at most $(|\mathcal G|-1)K$ pulses}, while canceling all error terms linear in the system-bath coupling strength up to order $K$ in the total evolution time. As a corollary, for an $n$-qubit system with $k$-local system-bath interactions, we obtain an $\mathcal{O}(n^{k-1}K)$-pulse sequence, a significant improvement over existing schemes with $\mathcal{O}(\exp(n))$ pulses (for $k=\mathcal{O}(1)$). The construction is obtained via a mapping to the continuous necklace-splitting problem, which asks how to cut a multi-colored interval into pieces that give each party the same share of every color. We provide explicit pulse sequences for suppressing general single-qubit decoherence, prove that the pulse count is asymptotically optimal, and verify the predicted error scaling in numerical simulations. For the same number of pulses, we observe that our sequences outperform the state-of-the-art Quadratic DD in the weak-coupling regime. We also construct explicit high-order sequences for suppressing representative 2-local noise models. Finally, the same construction extends to suppress slow, time-dependent classical noise and to filter-function design.

quant-pharXiv:2602.05343Physical Review LettersFeb 6, 20260 citations

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We study a generic cavity QED setup under conditions where the coupling between the two-level systems and a single bosonic mode is significantly degraded by low-frequency noise. To overcome this problem, we identify pulsed dynamical decoupling strategies that suppress the effects of noise while still allowing for a coherent exchange of excitations between the individual subsystems. The corresponding pulse sequences can be further designed to realize either Jaynes-Cummings, anti-Jaynes-Cummings, or Rabi couplings, as well as different types of cavity-mediated interactions between the two-level systems. A detailed analysis of the residual imperfections demonstrates that this decoupling strategy can boost the effective cooperativity of the cavity QED system by several orders of magnitude and improve the fidelity of quantum-technologically relevant operations accordingly.We study a generic cavity QED setup under conditions where the coupling between the two-level systems and a single bosonic mode is significantly degraded by low-frequency noise. To overcome this problem, we identify pulsed dynamical decoupling strategies that suppress the effects of noise while still allowing for a coherent exchange of excitations between the individual subsystems. The corresponding pulse sequences can be further designed to realize either Jaynes-Cummings, anti-Jaynes-Cummings, or Rabi couplings, as well as different types of cavity-mediated interactions between the two-level systems. A detailed analysis of the residual imperfections demonstrates that this decoupling strategy can boost the effective cooperativity of the cavity QED system by several orders of magnitude and improve the fidelity of quantum-technologically relevant operations accordingly.

arXiv:2505.02929May 5, 20250 citations

Engineering protected cavity-QED interactions through pulsed dynamical decoupling

Íñigo Arrazola, Patrice Bertet, Yiwen Chu +1 more

npj Quantum InformationNov 21, 20251 citation

Engineering protected cavity-QED interactions through pulsed dynamical decoupling

Íñigo Arrazola, Patrice Bertet, Yiwen Chu +1 more

Nov 21, 20250 citations

\ensuremath{\pi}

We introduce a high-order dynamical decoupling (DD) scheme for arbitrary bounded system-bath interactions in the weak-coupling regime. Given any decoupling group

\mathcal G

that averages the interaction to zero, our construction {guarantees the existence of pulse sequences with at most

(|\mathcal G|-1)K

pulses}, while canceling all error terms linear in the system-bath coupling strength up to order

K

in the total evolution time. As a corollary, for an

n

-qubit system with

k

-local system-bath interactions, we obtain an

\mathcal{O}(n^{k-1}K)

-pulse sequence, a significant improvement over existing schemes with

\mathcal{O}(\exp(n))

pulses (for

k=\mathcal{O}(1)

). The construction is obtained via a mapping to the continuous necklace-splitting problem, which asks how to cut a multi-colored interval into pieces that give each party the same share of every color. We provide explicit pulse sequences for suppressing general single-qubit decoherence, prove that the pulse count is asymptotically optimal, and verify the predicted error scaling in numerical simulations. For the same number of pulses, we observe that our sequences outperform the state-of-the-art Quadratic DD in the weak-coupling regime. We also construct explicit high-order sequences for suppressing representative 2-local noise models. Finally, the same construction extends to suppress slow, time-dependent classical noise and to filter-function design.