Anticipating Decoherence for Enhancing Coherence in Quantum Systems

TL;DR

Decoherence limits indistinguishability across distant quantum emitters in solid-state platforms. The authors develop a replica-theory framework that reveals memory and non-Markovian structure in spectral diffusion, and implement Rosen-Nadin-inspired anticipatory systems with an attention-based Bi-LSTM to forecast ZPL dynamics for preemptive control. The approach achieves substantial reductions in spectral wandering (up to 2.1×–15.8×, depending on emitter stability) and demonstrates trajectory-resolved predictions across multiple emitters, indicating a generalizable path to coherence preservation. This work provides a platform-agnostic method for real-time decoherence engineering, enabling improved multi-node coherence and synchronization for quantum communication, computation, imaging, and sensing.

Abstract

Large-scale quantum systems require optical coherence between distant quantum devices, necessitating spectral indistinguishability. Scalable solid-state platforms offer promising routes to this goal. However, environmental disorders, including dephasing, spectral diffusion, and spin-bath interactions, influence the emitters' spectra and deteriorate the coherence. Using statistical theory, we identify correlations in spectral diffusion from slowly varying environmental coupling, revealing predictable dynamics extendable to other disorders. Importantly, this could enable the development of an anticipatory framework for forecasting and decoherence engineering in remote quantum emitters. To validate this framework, we demonstrate that a machine learning model trained on limited data can accurately forecast unseen spectral behavior. Realization of such a model on distinct quantum emitters could reduce the spectral shift by factors $\approx$ 2.1 to 15.8, depending on emitter stability, compared to no prediction. This work presents, for the first time, the application of anticipatory systems and replica theory to quantum technology, along with the first experimental demonstration of internal prediction that generalizes across multiple quantum emitters. These results pave the way for real-time decoherence engineering in scalable quantum systems. Such capability could lead to enhanced optical coherence and multi-emitter synchronization, with broad implications for quantum communication, computation, imaging, and sensing.

Figures (5)

• Figure 1: $|$Rosen/Nadin inspired Anticipatory Systems framework: The natural system ($S$), consisting of a quantum emitter and environment (setup: OL: Objective Lens, LF: Laser cleaning filter, LPF: Long Pass Filter), modeled by a formal system ($M$) using an attention-based Bi-LSTM as its internal predictive core. $M$ updates the effector ($E$), which influences both $S$ and its local environment (the control line and effector feedback, marked with dashed maroon lines, will be implemented in our follow-up). The effector ($E$) also supplies contextual inputs, such as charge or phonon background (unrelated to $S$'s current state), to $M$. The internal model receives sequential spectral inputs $(x_{t-1}, x_t, x_{t+1})$, processed by a bidirectional LSTM—one branch capturing forward, the other backward temporal dependencies. Outputs $(y_{t-1}, y_t, y_{t+1})$ from both are concatenated and passed to a self-attention layer. A final dense layer integrates this for high-fidelity estimation of future states. The framework is platform-agnostic and could be applied to both optical and spin qubits.
• Figure 2: $|$Experimental characterization of decoherence dynamics in a quantum system: Non-resonant PL map (532nm excitation laser), showing two SiN quantum emitters within the dotted green circle: (a) Energy level structure: Non-resonant PL (532nm excitation laser), the excitation laser frequency $\omega/2\pi$ is detuned from the transition frequency $\omega_0$ governed by the system Hamiltonian $H_A$ with environmental-induced disorder. In contrast, during resonant excitation, $\omega_0$ matches one of the system eigenfrequencies. The radiative decay rate between states $e$ and $g$ is denoted by $\eta \gamma_{e,g}$, for the excited to electronic and vibrational ground state, where $\eta$ is the Debye-Waller Franck-Condon factor, $v$ is the vibronic excited state, (b) Non-resonant PL spectra of two distinct SiN emitters, recorded with a $600\text{grooves}/\text{mm}$ grating and 5ms exposure: the Si Raman line at 547.44nm and zero-phonon lines (ZPLs) at 550.76nm and 539.55nm. A 532 nm dichroic mirror, in combination with a 532nm long-pass filter, was used to suppress the excitation laser. Plots have been shifted along the Y axis for better visibility.(c) PL spectra ($500\mathrm{\upmu}$s exposure) time trace illustrating the spectral diffusion of the emitter ZPL, at 539.55nm, alongside the relatively stable evolution of substrate-related Si-Raman peak at 547.44nm. This Si-Raman peak acts as a local sensor for experimental artifacts. (d) Second-order autocorrelation functions $g^{(2)}(\tau)$ for two non-resonantly excited emitters that confirm their single-photon emission characteristics; all taken at $\approx 1$mW excitation power. Plots have been shifted along the y-axis for better visibility.
• Figure 3: $|$Experimental results for decoherence channel analysis via an RP-based order parameter: (a),(c) Spectral overlap represented by RP-based order parameter $|q|$ histogram for two different quantum emitters spectra. The overlap parameter, concentrated around 0, indicates low overlap for the spectral statistics. A non-zero value of the order parameter indicates a non-trivial overall overlap of the spectra. (b),(d) shows order parameter histogram evolution for two different quantum emitters under similar excitation conditions. The evolution of the overlap parameter across successive time bins, each consisting of 100 frames, with a sliding window shifted by 10 frames in the next row, reveals a dynamic temporal structure. This indicates that the overlap parameter is not a static quantity, but rather encodes time-dependent behavior. In an ideal scenario where all samples are identical, the overlap parameter would approach zero. However, in the present case, deviations from the average reference behavior yield non-zero overlap values, reflecting correlated fluctuations across different samples relative to the ensemble mean. Notably, relative stability is assessed via the stationarity of the fitted statistics for each time step. We define instability operationally as temporal reconfiguration of the statistical properties $\mu(t)$ or $\sigma(t)$ beyond their typical fluctuation bounds, resulting in diminished overlap between consecutive distributions.
• Figure 4: $|$Decoherence channel noise analysis: (a),(b) Autocorrelation function (ACF) of the ZPL time traces for two quantum emitters, where each lag represents a temporal shift relative to itself. Slow decay in the ACF indicates non-trivial temporal correlations, while fluctuations beyond lag $>40$ for emitter (b) alternate between significant and noise-like. The shaded region shows the 95% confidence interval under the null hypothesis of no correlation; values outside this region indicate meaningful correlations. Statistical bounds were calculated as $r(k) \pm 1.96 \sqrt{\frac{1}{N} \left(1 + 2 \sum_{i=1}^{k-1} r(i)^2 \right)}$, where $N$ is the sample size. (c),(d) Power spectral density (PSD) of the ZPL traces over 10,000 spectra (individual exposure time
• Figure 5: $|$Anticipatory prediction architecture and decoherence prediction: (a) The model receives a time series of ZPL measurements up to time $t_3$. The self-adaptive sequence length mechanism dynamically determines the effective input window at each step. An attention mechanism then assigns dynamic weights to different time steps. Predicted values $\lambda_p(t_k)$ are recursively fed back as inputs for subsequent time steps, forming an auto-regressive prediction loop that internalizes forward temporal dynamics. The green region represents the tolerance for a valid prediction. (b),(c) Spectral wavelength diffusion predictions comparison for two different quantum emitters, with data acquired at 500 $\mathrm{\upmu}$s intervals. The anticipatory model (Bi-Attention-LSTM) closely tracks the measured fluctuations, while linear, polynomial, and sine-function predictors fail to capture the underlying nonlinear dynamics. (d),(e) Quantitative RMSE (Root Mean Square Error) loss performance comparison of time-series prediction models under different dataset partitioning schemes for two distinct emitters.