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arXiv:2601.00884

Entanglement dynamics of multi-fluxonium-qubits under Non-Markovian TLS noise

Chenghong Ji, Chaoying Zhao

quant-phSubmitted Dec 31, 2025• Announced Jan 1, 2026• 0 citations
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Abstract

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.

Comments
9pages,4figures,33references

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Entanglement dynamics of multi-fluxonium-qubits under non-Markovian TLS noise

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Journal of High School Science•Apr 27, 2026•0 citations
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 examine the entanglement dynamics of two capacitively connected fluxonium qubits influenced by correlated non-Markovian two-level-system (TLS) noise. The environment is represented by an Ornstein–Uhlenbeck process with a Lorentzian spectrum, and the filter-function formalism is utilized as the main framework to assess finite-memory effects and analyze dynamical-decoupling (DD) performance. We design a TLS-oriented DD sequence by optimizing pulse placements within experimentally motivated control limitations for the low-frequency-dominated TLS spectrum pertinent to fluxonium devices. Numerical results indicate that the optimized protocol more efficiently mitigates spectral overlap with TLS noise and enhances the preservation of two-qubit entanglement throughout empirically pertinent timeframes, in comparison to traditional sequences. A succinct post-Markovian master-equation analysis is incorporated solely as a phenomenological consistency verification for the finite-memory crossover. The results establish a quantifiable standard for entanglement preservation in linked fluxonium qubits subjected to colored non-Markovian noise and underscore the need for spectrum-aware DD design for superconducting qubit systems.
Correlated longitudinal noise can be partially converted into common-mode fluctuations in an oddparity two-qubit subspace. We analyze an encoded logical qubit formed by the states in two coupled fluxonium qubits. Projecting the exchange-coupled two-qubit Hamiltonian onto this subspace yields an effective logical Hamiltonian in which the exchange interaction drives XL rotations and the qubit detuning drives ZL rotations. We model correlated two-levelsystem (TLS) noise by using longitudinal stochastic processes with finite memory time and evaluate encoded-gate performance through the average gate fidelity. Within the projected model, positive spatial noise correlation suppresses the differential fluctuation and thereby improves the fidelity of encoded logical gates. We further compare Gaussian Ornstein-Uhlenbeck, Markovian, and randomtelegraph noise models and examine the role of logical dynamical decoupling. These results identify a noise-adapted control mechanism for odd-parity encoded operations in coupled fluxonium devices and motivate future multilevel simulations including leakage and pulse-level constraints.
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.
Abstract Recent studies have shown that parasitic two-level systems (TLS) in superconducting qubits, which are a leading source of decoherence, can have relaxation times longer than the qubits themselves. However, the standard techniques used to characterize qubit relaxation is only valid for measuring T 1 under the Born-Markov approximation and could mask environmental memory effects in practice. Here, we introduce two-timescale relaxometry, a technique to probe the qubit and environment relaxation simultaneously and efficiently. We apply it to high-coherence fluxonium qubits over a frequency range of 0.1-0.4 GHz, and reveal a discrete spectrum of TLS with millisecond lifetimes. Our analysis of the spectrum is consistent with a random distribution of TLS in the aluminum oxide tunnel barrier of the Josephson junction chain of the fluxonium, with a spectral and volumetric density and average electric dipole similar to previous TLS studies at much higher frequencies. Our study suggests that investigating and mitigating TLS in the junction chain is crucial to the development of various types of noise-protected qubits in circuit QED.
Non-Markovian noise can be a significant source of errors in superconducting qubits. We develop gate sequences utilising mirrored pseudoidentities that allow us to characterise and model the effects of non-Markovian noise on both idle and driven qubits. We compare three approaches to modelling the observed noise: (i) a Markovian noise model, (ii) a model including interactions with a two-level system (TLS), (iii) a model utilising the post Markovian master equation (PMME), which we show to be equivalent to the qubit-TLS model in certain regimes. When running our noise characterisation circuits on a superconducting qubit device we find that purely Markovian noise models cannot reproduce the experimental data. Our model based on a qubit-TLS interaction, on the other hand, is able to closely capture the observed experimental behaviour for both idle and driven qubits. We investigate the stability of the noise properties of the hardware over time, and find that the parameter governing the qubit-TLS interaction strength fluctuates significantly even over short time-scales of a few minutes. Finally, we evaluate the changes in the noise parameters when increasing the qubit drive pulse amplitude. We find that although the hardware noise parameters fluctuate significantly over different days, their drive pulse induced relative variation is rather well defined within computed uncertainties: both the phase error and the qubit-TLS interaction strength change significantly with the pulse strength, with the phase error changing quadratically with the amplitude of the applied pulse. Since our noise model can closely describe the behaviour of idle and driven qubits, it is ideally suited to be used in the development of quantum error mitigation and correction methods.
Decoherence is a primary barrier to practical quantum computation, causing quantum states to degrade through phase randomization and irreversible energy relaxation. This study presents a simulation-based evaluation of echo-based dynamical decoupling (DD) pulse sequences as a software-level mitigation strategy in single-qubit systems. Using the Qiskit Aer density matrix simulator, four strategies—baseline, Hahn Echo, Carr-Purcell-Meiboom-Gill (CPMG), and Mixed Synchronization—were evaluated across low-frequency phase noise, high-frequency phase noise, and combined T₁ + T₂ noise regimes. Hahn Echo restored mean fidelity to 100.00% under low-frequency noise (baseline: 57.90%), while CPMG achieved 97.62% under high-frequency noise (baseline: 2.45%). Under combined noise, all strategies showed limited improvement, with Mixed-Sync reaching 65.34% versus 60.95%. Coefficient of variation (CV) analysis across 500 Monte Carlo trials showed that CPMG reduced purity-decay variance threefold under high-frequency noise, with bootstrap confidence intervals confirming statistical significance. Time-resolved analysis showed that CPMG suppressed variance growth throughout evolution, reducing variance growth from +267% (baseline) to +89%, while baseline and Hahn Echo exhibited progressive amplification of variance. These results show that dynamical decoupling influences the temporal structure of noise, not just mean fidelity. In T₂-dominated regimes, pulse sequences constrain variability; in mixed regimes, they partially shape it; and in T₁-dominated regimes, both mean performance and variability converge to hardware-limited behavior. DD effectively corrects reversible phase errors but cannot overcome irreversible T₁ loss, with implications for NISQ circuit design.