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

TL;DR

The paper addresses entanglement dynamics of a two-Fluxonium qubit register under non-Markovian TLS noise by employing a Post-Markovian Master Equation (PMME) framework, modeling the TLS bath with an Ornstein–Uhlenbeck process and a Lorentzian spectrum $S_{ ext{TLS}}( obreakoldsymbol{igl)}( obreak oldsymbol{igr)} obreak( obreak abla) rac{1}{1+ au_c^2 obreak oldsymbol{igl)}( obreakoldsymbol{igr)}}$. The two-qubit dephasing is captured through $oldsymbol{ ho}_{01,10}(t)$ with $oldsymbol{ ho}_{01,10}(t)=e^{-oldsymbol{oldsymbol{ obreak obreak obrace } obreak obreak obreak} obreak}$, and the non-Markovian memory is encoded in a kernel $k(t)$ with $k(t)=rac{1}{ au_c} e^{-t/ au_c}$. The authors propose a TLS-tailored dynamical decoupling (TLS-opt) sequence built from the Heisenberg–Weyl group to minimize the overlap integral $rac{1}{oldsymbol{ obreak rac{3}{ obreak obreak}} obreak}$. Numerically, TLS-opt yields significantly longer entanglement lifetimes and higher Bell-fidelity windows in realistic parameter regimes (e.g., $ au_C^{ ext{TLS-opt}} ightarrow 1.3~oldsymbol{ ext{μ}s}$ and $T_{0.999}^{ ext{TLS-opt}} ightarrow 0.35~oldsymbol{ ext{μ}s}$) compared to no-DD or standard DD sequences, demonstrating a practical route to enhance entangling operations in NISQ devices. The study shows that spectrum-matched DD can exploit non-Markovian memory to preserve entanglement and fidelity in Fluxonium qubits.

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.

Figures (4)

• Figure 1: (a)Two fluxonium qubits circuit schematic: two fluxonium qubits (Josephson junctions $E_1/L_1$ and $E_2/L_2$) interact via the coupling capacitor $C_g$; each qubit is capacitively coupled to its local TLS through $C_1$ and $C_2$ (labeled “Added TLS coupling” in red line). $E_1$ and $E_2$ are Josephson junctions, $L_1$ and $L_2$ are super-inductors; GND denotes the common ground. (b)Time evolution of two-qubit entanglement and Bell-state fidelity. Initial state $|10\rangle$. Blue line: concurrence. Orange dashed line: fidelity with the Bell based $(|01\rangle + |10\rangle)/\sqrt{2}$. The curves show swap oscillations damped by dephasing.
• Figure 2: No-DD-(a) Under OU non-Markovian dephasing, the fidelity of $|\hat{\Phi}^+\rangle$ decays more slowly than the Markovian exponential; (b) increasing in noise correlation $\rho$ slows down the concurrence $C(t)$ decay; (c) the effective dephasing rate $\gamma_{eff}(t)=-\,d\ln F/dt$ rises from near zero and saturates around $t\!\sim\!\tau_c$, indicating a Zeno-to-Markov crossover.
• Figure 3: (a) Comparison of filter functions $F(\omega,T)$ for several DD sequences, showing that the TLS-opt sequence provides the deepest suppression at low frequencies. (b) Overlap between the TLS noise spectrum $S(\omega)$ and the filter functions, where the TLS-opt sequence strongly reduces low-frequency contributions. (c) Time-domain modulation functions $y(t)$ for CPMG-4, XY-8, and TLS-opt.
• Figure 4: (a) Comparison between the TLS noise spectrum $S(\omega)$ and the (scaled) filter functions $F(\omega)$, showing deeper low-frequency suppression and reduced spectral overlap for the TLS-opt sequence. (b) Summary of performance under different DD protocols: entanglement lifetime $\tau_C$ defined by $C=1/e$ and high-fidelity time $T_{0.999}$ defined by $\mathcal{F}=0.999$. (c) Robustness to pulse-angle errors: $\tau_C$ versus the control-error standard deviation $\sigma_\epsilon$, where each $\pi$ pulse is implemented as $(1+\epsilon)\pi$ with $\epsilon\sim\mathcal{N}(0,\sigma_\epsilon)$ and $\tau_p=10ns$.