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arXiv:quant-ph/0609222 · Physical Review A

Dynamical decoupling-induced renormalization of non-Markovian dynamics

Pochung Chen

Published Jun 4, 2007• 9 citations
arXivHTMLPDF

Abstract

In this work we develop a numerical framework to investigate the renormalization of the non-Markovian dynamics of an open quantum system to which dynamical decoupling is applied. We utilize a non-Markovian master equation of the spin-boson model. The effects of the decoupling pulses are then incorporated. A wide class of decoupling pulses can be described equally within this approach. We have performed a comprehensive investigation on the renormalized dynamics within various noise models, including the Ornstein-Uhlenbeck noise and the spin-boson model. The renormalized dynamics under bang-bang control and continuous dynamical decoupling are simulated. The condition for efficient decoupling is assessed for each scenario. Our results indicate that the renormalization of the non-Markovian dynamics critically depends on the spectral density of the environment and the envelope of the decoupling pulses. Consequently, it is difficult to have a simple universal condition that ensures the efficiency. The framework developed in this work provides a unified approach to investigate the efficiency of realistic decoupling pulses. It also opens an avenue to further optimize the decoupling via pulse shaping.

DOI
10.1103/physreva.75.062301

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In this work we develop a numerical framework to investigate the renormalization of the non-Markovian dynamics of an open quantum system to which dynamical decoupling is applied. We utilize a non-Markovian master equation of the spin-boson model. The effects of the decoupling pulses are then incorporated. A wide class of decoupling pulses can be described equally within this approach. We have performed a comprehensive investigation on the renormalized dynamics within various noise models, including the Ornstein-Uhlenbeck noise and the spin-boson model. The renormalized dynamics under bang-bang control and continuous dynamical decoupling are simulated. The condition for efficient decoupling is assessed for each scenario. Our results indicate that the renormalization of the non-Markovian dynamics critically depends on the spectral density of the environment and the envelope of the decoupling pulses. Consequently, it is difficult to have a simple universal condition that ensures the efficiency. The framework developed in this work provides a unified approach to investigate the efficiency of realistic decoupling pulses. It also opens an avenue to further optimize the decoupling via pulse shaping.
Protecting quantum coherence against realistic environmental noise remains one of the fundamental obstacles to scalable quantum technologies. We develop a noise-adaptive dynamical decoupling framework that combines analytical open-quantum-system modeling with machine-learning-based forecasting for a qubit interacting with random telegraph noise. Unlike conventional dynamical decoupling protocols based on fixed pulse schedules, the proposed approach continuously forecasts short-time coherence evolution and adaptively applies control pulses according to the instantaneous noise dynamics. We investigate stationary and non-stationary environments spanning both Markovian and non-Markovian regimes. Numerical simulations demonstrate that the machine-learning-assisted adaptive control strategy substantially outperforms conventional periodic dynamical decoupling while using a comparable number of control pulses. The improvement becomes particularly pronounced in non-Markovian and non-stationary regimes, where memory effects, coherence revivals, and temporally evolving noise strongly limit the effectiveness of static pulse protocols. These results establish predictive machine-learning-assisted dynamical decoupling as a promising and scalable framework for adaptive quantum control in realistic noisy quantum devices.
One longstanding difficult problem in quantum dissipative dynamics is to solve the spin-boson model in a non-Markovian regime where a tractable systematic master equation does not exist. The spin-boson model is particularly important due to its crucial applications in quantum noise control and manipulation as well as its central role in developing quantum theories of open systems. Here we solve this important model by developing a non-Markovian quantum Langevin approach. By projecting the quantum Langevin equation onto the coherent states of the bath, we can derive a set of non-Markovian quantum Bloch equations containing no explicit noise variables. This special feature offers a tremendous advantage over the existing stochastic Schr\"odinger equations in numerical simulations. The physical significance and generality of our approach are briefly discussed.
We investigate the relationship between non-Markovianity and the effectiveness of a dynamical decoupling (DD) protocol for qubits undergoing pure dephasing. We consider an exact model in which dephasing arises due to a bosonic environment with a spectral density of the Ohmic class. This is parametrized by an Ohmicity parameter by changing which we can model both Markovian and non-Markovian environments. Interestingly, we find that engineering a non-Markovian environment is detrimental to the efficiency of the DD scheme, leading to a worse coherence preservation. We show that each DD pulse reverses the flow of quantum information and, on this basis, we investigate the connection between DD efficiency and the reservoir spectral density. Finally, in the spirit of reservoir engineering, we investigate the optimum system-reservoir parameters for achieving maximum stationary coherences.
The research on open quantum systems is important for both quantum computing and quantum sensing. So far, we can only use the main equation to make an approximate description. The dynamics of a single Fluxonium qubit under Markovian environment satisfied Lindblad Master Equation. In experiments, pulse sequence dynamic decoupling (DD) can enhance the coherence of qubits and effectively suppress noise. Two Fluxonium qubits sensitive to two-level systems (TLS) noise. TLS formed by material defects results in noise with significant non-Markovian characteristics. The dynamics of non-Markovian noise satisfied the post Markov Master Equation (PMME). The TLS noise spectrum is mainly concentrated in low frequencies, so traditional DD cannot effectively suppress TLS noise. The relaxation and dephasing behavior with a complex dynamic characteristics. Based on Ornstein-Uhlenbeck process, we put forward a novel DD sequence and design a TLS-tailored dynamical decoupling protocol by optimizing pulse locations to minimize noise power spectral overlap with the Lorentzian shape. Using PMME-consistent framework, we can obtain a stronger low frequency suppression and significantly prolong both Bell-based fidelity and entanglement. We explore specific DD design and precise modeling of entanglement dynamics under non-Markovian TLS noise. Our dynamical decoupling protocol can effectively improve entanglement gates fidelity in NISQ quantum devices.
We outline a non-perturbative approach for simulating the behavior of open quantum systems interacting with a bosonic environment defined by a generalized spectral density function. The method is based on replacing the environment by a set of damped harmonic oscillators - the pseudomodes - thereby forming an enlarged open system whose dynamics is governed by a Markovian master equation. Each pseudomode is connected to one of the poles of the spectral density when analytically continued to the lower-half complex frequency plane. Here, we extend previous results to a completely generic class of open system models, and discuss how our framework can be used as a powerful and versatile tool for analyzing non-Markovian open system dynamics. The effectiveness of the method is demonstrated on the spin-boson model by accurately benchmarking its predictions against numerically exact results.