Learning to steer quantum many-body dynamics with tree optimization

TL;DR

This work highlights AI's potential to steer complex quantum many-body dynamics, marking a paradigm shift toward data-driven sequence design with broad applicability across spin-based quantum technologies and beyond.

Abstract

High-quality control over complex quantum systems is a key to achieving practical quantum technologies. However, progress is hindered by the exponential growth of quantum state spaces and the challenges posed by realistic experimental conditions. Here, we present an AI framework that learns to design pulse sequences for optimized quantum control over many-body spin systems, providing a powerful alternative to theory-driven methods. The framework combines customized tree search, neural network filtering, and numerical simulation guidance to navigate highly nonlinear optimization landscapes, using only desktop-level computational resources and minimal experimental input. The objective function is set to preserve coherence, a key prerequisite for quantum information processing. Our framework identifies over 900 high-performing sequences that exhibit non-intuitive structures and hence challenge long-standing design principles, while established optimization methods struggle to find such solutions. Experiments in a diamond spin ensemble show that the best AI-designed sequences achieve coherence times exceeding 200 microseconds, representing a 100% improvement over state-of-the-art baselines and approaching the temperature-imposed limit. Beyond spin coherence preservation, our framework is readily extendable through modified objective functions and incorporation of appropriate training data. This work highlights AI's potential to steer complex quantum many-body dynamics, marking a paradigm shift toward data-driven sequence design with broad applicability across spin-based quantum technologies and beyond.

Figures (5)

• Figure 1: Pipeline overview of AI-driven sequence optimization.(a) Starting from randomly low-performing pulse sequences selected from an expanded search space containing $\pi$, $\pi/2$, and $\pi/3$ rotations, along with no-pulse operation (Null). Our AI framework comprises two core components: (1) a tailored tree-based optimization algorithm, and (2) node value estimation based on numerical simulations, assisted by a continuously retrained neural network for rapid filtering of implausible candidates. Multiple optimization processes run in parallel, each using a distinct simulator, thereby increasing the likelihood of discovering experimentally successful sequences. Promising sequences learned by AI undergo experimental validation in a diamond NV spin ensemble. (b) Bloch sphere trajectories illustrate the progression from handcrafted to AI-driven sequence design, spanning more than 80 years of development originating from NMR Vandersypen2005Vandersypen2001. AI enables the inclusion of unusual $\pi/3$ rotations, expanding traditional search space ($5^n$ and $9^n$) to $13^n$. Here, $n$ denotes sequence length and the base numbers represent available pulse operations per position. The fitted coherence decay curves (below) show dramatically improved decoherence suppression with AI-optimized sequences (red curve) compared to traditional methods. (c) The diamond sample is integrated with a room-temperature confocal optical system, which enables NV spin polarization and fluorescence-based readout. For spin manipulation, microwave (MW) pulse sequences are generated by an arbitrary waveform generator (AWG) and delivered through a ring-shaped MW antenna. Additional radio-frequency (RF) pulses for nuclear spin polarization are applied via a multi-loop RF coil.
• Figure 2: (Caption next page.)
• Figure 2: Experimental calibration, algorithm benchmark and optimization results.(a) The simulation model incorporates control errors, disorder, and spin-spin interactions. Parallel optimizations use multiple simulators with varying parameter sets to mitigate simulation-experiment gap. (b) Coarse-grained decoherence budget derived from measurements of Ramsey (free decay), XY8/XY16, DROID, and spin locking protocols. Leading-order contributions from Disorder and interactions together are about 490 kHz decay, while the remaining 10 kHz (“Others”) reflects decoherence mechanisms beyond the simulation model. (c) For the expert-designed baseline sequences, the calibrated simulator demonstrates strong correlation between simulated and experimental coherence scores, with Pearson and Spearman (rank-based) coefficients of 0.93 and 0.95, respectively. (d) Optimization progress for DOESS and competing algorithms using a search space containing $\pi$, $\pi/2$, and $\pi/3$ rotations. The X-axis shows the number of sequences evaluated by numerical simulation. Only DOESS surpasses SOTA performance, while other algorithms fail. Deviating from this search space (adding $\pi/4$ or removing rotations) also substantially hinders DOESS performance. (e) Simplified coherence score correlates well with the full version while reducing computational overhead about 10-fold. High-performing sequences conform well to single-exponential decay, while most random sequences decay too rapidly for such fitting. (f) Normalized score distribution (relative to SOTA) of DOESS sequences identified across different simulation settings.
• Figure 3: Experimental validation.(a) Coherence decay curves of 931 DOESS-discovered sequences (with the best achieving 5 kHz decay) compared to SOTA (10 kHz) and XY16 (40 kHz) baseline sequences. (b) (c) Exponential fitting reveals comparable signal contrast but much improved coherence time (inverse of decay rate). The longest coherence time increases from $\sim$100 µs to $> 200$ µs, representing $\sim$100% enhancement relative to SOTA. (d) Coherence score (calculated as the normalized area under decay curve) combines contrast and decay rate, demonstrating up to a more announced $\sim$150% enhancement relative to SOTA. (e) Two representative top-performing DOESS sequences maintain their performance advantage over SOTA under considerable pulse frequency detuning. (f) Correlation between experimental and simulated scores for the 931 DOESS sequences (Pearson coefficient: 0.56) is substantially lower than that of baseline sequences in Fig. \ref{['fig2']}c (Pearson coefficient: 0.93).
• Figure 4: Unconventional sequence structures and physical insights.(a) Performance indicator # 2 distribution: original sequences without repetition (broad, average 0.1036) versus repetition-defined sequences (narrow, approaching zero). Inset: average value decays rapidly with sequence repetition and then saturates. (b) Non-identity sequences exhibit spin locking-like behavior: coherence decay reduces when initial spin orientation aligns with the effective driving axis, observed in both simulations and experiments. (c) Three failed feature engineering approaches: (1) integer pulse encoding; (2) rotation matrix representation; (3) single performance indicator representation. (d) Using repetition-defined indicator series substantially improves the prediction accuracy of the neural network-based surrogate model, achieving an R-squared of 0.795 for randomly sampled sequences. (e) Using indicator series as input features, the t-SNE algorithm clearly separates AI, baseline, and random sequences.