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Applied Physics Letters

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

Chenghong Ji, Chaoying Zhao

Published May 18, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1063/5.0322109

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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.
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.
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.
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.
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.
Microscopic two-level systems (TLS) -- ubiquitous atomic-scale defects in solid-state quantum devices -- are a dominant source of qubit decoherence, yet their role is often considered local and short-memoried. Here, we report the observation of a coherent TLS that couples simultaneously to two spatially distant superconducting qubits. The TLS is identified to reside within the tunable coupler linking the qubits, enabling controllability of the TLS-qubit coupling strength via coupler frequency -- a capability absent in earlier studies. This tunability allows us to systematically probe how TLS distorts qubit dynamics, revisiting the decoherence model in the presence of non-Markovian TLS dephasing noise. This is corroborated by the reconstructed 1/f1/f1/f noise spectrum of TLS frequency fluctuation spanning more than ten orders of magnitude (0.1\,mHz -- 1\,MHz) that reveals discrete fluctuator signatures. Quantum process tomography further unveils TLS-induced correlated qubit dynamics, highlighting the long-lived TLS as an effective source of non-Markovianity. Our findings expose a previously overlooked interaction mechanism in scalable quantum architectures: defects embedded in coupling elements can simultaneously affect multiple qubits with variable impact. Beyond immediate implications for system characterization and calibration, this situation provides a powerful testbed for studying defect-driven quantum dynamics, refining error suppression strategies, and advancing architecture design for scalable quantum technologies.
In this paper, we study how to preserve entanglement and nonlocality under dephasing produced by classical noise with large low-frequency components, such as 1/f1/f1/f noise, using dynamical decoupling techniques. We first show that quantifiers of entanglement and nonlocality satisfy a closed relation valid for two independent qubits locally coupled to a generic environment under pure dephasing and starting from a general class of initial states. This result allows us to assess the efficiency of pulse-based dynamical decoupling for protecting nonlocal quantum correlations between two qubits subject to pure-dephasing local random telegraph and 1/f1/f1/f noise. We investigate the efficiency of an ``entanglement memory'' element under two-pulse echo and under sequences of periodic, Carr-Purcell, and Uhrig dynamical decoupling. The Carr-Purcell sequence is shown to outperform the other sequences in preserving entanglement against both random telegraph and 1/f1/f1/f noise. For typical 1/f1/f1/f flux-noise figures in superconducting nanocircuits, we show that entanglement and its nonlocal features can be efficiently stored up to times one order of magnitude longer than natural entanglement disappearance times employing pulse timings of current experimental reach.