Non-Markovianity Benefits Quantum Dynamics Simulation

TL;DR

The paper demonstrates that non-Markovian quantum noise can unexpectedly aid quantum dynamics simulations, offering memory-enhanced protection against decoherence compared to equivalent Markovian noise. It develops and analyzes a time-nonlocal master equation framework for Gaussian pure-dephasing noise, introducing two key parameters, the noise strength $\lambda$ and memory length $b$, and links non-Markovianity to transfer-tensor memory in $\rho(t)$. Through analytical results and stochastic-trajectory simulations, the work shows that finite memory can preserve coherent features in idle-qubit decoherence, enable revival of dynamical topology in a quenched QAH system (even beyond the Markovian sweet spot), and slow thermalization in many-body localized dynamics. The combination of TNQME, Lorentzian noise spectra, FFT-based stochastic simulations, and trajectory-level observables highlights practical avenues for mitigating noise in quantum simulations and informs design strategies for quantum devices and error-mitigation techniques.

Abstract

Quantum dynamics simulation on analog quantum simulators and digital quantum computer platforms has emerged as a powerful and promising tool for understanding complex non-equilibrium physics. However, the impact of quantum noise on the dynamics simulation, particularly non- Markovian noise with memory effects, has remained elusive. In this Letter, we discover unexpected benefits of non-Markovianity of quantum noise in quantum dynamics simulation. We demonstrate that non-Markovian noise with memory effects and temporal correlations can significantly improve the accuracy of quantum dynamics simulation compared to the Markovian noise of the same strength. Through analytical analysis and extensive numerical experiments, we showcase the positive effects of non-Markovian noise in various dynamics simulation scenarios, including decoherence dynamics of idle qubits, intriguing non-equilibrium dynamics observed in symmetry protected topological phases, and many-body localization phases. Our findings shed light on the importance of considering non- Markovianity in quantum dynamics simulation, and open up new avenues for investigating quantum phenomena and designing more efficient quantum technologies.

Figures (11)

• Figure 1: (a) Topological quench dynamics influenced by quantum noise. (b) Quench-induced dynamical topology defined on BIS can be destroyed by sufficiently strong noise. $\boldsymbol{k}_c$ (red stars) denotes the singularity momentum on the dBIS, where the spin polarization dynamics lose oscillation behavior ($\overline{\langle\langle \boldsymbol{\sigma}(\mathbf{k})\rangle\rangle}_r \neq 0$), leading to ill-defined dBIS and the topological trivial phase. (c) The dynamical spin polarization of $\sigma_z$ on $\boldsymbol{k}_c$ under weak noise $\lambda=0.2 < \lambda_c$ ($\lambda_c\approx 0.39$ for studied model). (d) The dynamical spin polarization of $\sigma_z$ on $\boldsymbol{k}_c$ under strong noise $\lambda=0.8 > \lambda_c$. In (c) and (d), the purple lines depict the results of the clean system, while the grey lines represent the results under Markovian noise. The blue lines labeled NM1, NM2, NM3, NM4 correspond to the results obtained with non-Markovian noise, with non-Markovianity parameter $b=2,1,0.6,0.2$, respectively. The insets in (c) and (d) display the oscillation frequency $\omega$ derived from the corresponding spin polarization dynamics.
• Figure 2: (a) Entanglement entropy of many-body localization dynamics with pure dephasing noise of strength $\lambda=0.4$. The purple line shows the results of the clean MBL system. The grey line shows the results under Markovian noise. Blue lines labeled from NM1 to NM4 show the results under non-Markovian noise with non-Markovianity parameter $b = 4, 1, 0.5, 0.2$. (b) Parameter $\alpha$ that fits the late-time entanglement entropy dynamics in scaling relation $S(t)\sim \alpha \log(t+\gamma)+\beta$ under Markovian bath (M), non-Markovian bath (NM1-NM4) and original MBL with varying noise strength $\lambda$.
• Figure 3: (a) Charge imbalance of many-body localization dynamics with pure dephasing noise of strength $\lambda=0.7$. The purple line shows the results of the clean MBL system. The grey line shows the results under Markovian noise. Blue lines labeled from NM1 to NM4 show the results under non-Markovian noise with non-Markovianity parameter $b = 4, 1, 0.5, 0.2$. (b) Parameter $\alpha$ that fits the late-time charge imbalance dynamics in scaling relation $\mathcal{I}(t)\sim e^{-\alpha t+\beta}$ under Markovian noise (M), non-Markovian noise (NM1-NM4) and clean MBL with varying noise strength $\lambda$.
• Figure S1: Non-Markovian pure dephasing noise in Lorentzian form. (a) The real part of correlation functions changes along with time with $\lambda=1$. (b) The transfer tensor maps in 2-norm change along with time distance $t=\delta t \,n$ ($\delta t=0.2$). (c) The relaxation dynamics of the idle qubit under varying noise strength $\lambda$ with $b=1$. (d) The relaxation dynamics of the idle qubit under varying non-Markovianity $b$ with $\lambda=1$. We set $\omega_c=5$.
• Figure S2: Dynamical spin polarization and time-averaged spin polarization. Under weak noise strength $\lambda=0.2 < \lambda_c$ ( $\lambda_c\approx0.39$ for the studied model): The dynamical spin polarization (a)$\langle\langle \sigma_x \rangle\rangle_r$, (c) $\langle\langle \sigma_y \rangle\rangle_r$, (e) $\langle\langle \sigma_z \rangle\rangle_r$ on dBIS at $\boldsymbol{k}_c$. $\boldsymbol{k}_c$ (red stars) denotes the singularity momentum (defined in the main text or the right plane of this figure), the spin polarization dynamics first lose oscillation on the dBIS at $\boldsymbol{k}_c$ with the increase of noise leading to ill-defined dBIS and topological trivial phases. The time averaged spin polarization (b) $\overline{\langle\langle \sigma_x \rangle\rangle}_r$, (d) $\overline{\langle\langle \sigma_y \rangle\rangle_r}$, (f) $\overline{\langle\langle \sigma_z\rangle\rangle_r}$ at the momentum line $k_y=0$. The purple lines (Ideal) show the results of a clean system. The grey lines (M) show the results under Markovian noise. The blue lines from lightest to heaviest (NM1,NM2,NM3,NM4) show the results of non-Markovian noise with non-Markovianity parameterc $b = 2, 1, 0.6, 0.2$. The system parameters are chosen as $m_z=1.2,t_{so}=0.2,t_0=1$.