Timothy Heightman

Timothy Heightman, Edward Jiang, Antonio Acín

Understanding and characterising quantum many-body dynamics remains a significant challenge due to both the exponential complexity required to represent quantum many-body Hamiltonians, and the need to accurately track states in time under the action of such Hamiltonians. This inherent complexity limits our ability to characterise quantum many-body systems, highlighting the need for innovative approaches to unlock their full potential. To address this challenge, we propose a novel method to solve the Hamiltonian Learning (HL) problem-inferring quantum dynamics from many-body state trajectories-using Neural Differential Equations combined with an Ansatz Hamiltonian. Our method is reliably convergent, experimentally friendly, and interpretable, making it a stable solution for HL on a set of Hamiltonians previously unlearnable in the literature. In addition to this, we propose a new quantitative benchmark based on power laws, which can objectively compare the reliability and generalisation capabilities of any two HL algorithms. Finally, we benchmark our method against state-of-the-art HL algorithms with a 1D spin-1/2 chain proof of concept.

Fabio Falcioni, Elena Orlova, Timothy Heightman et al.

In this work, we benchmark \simulacra's synthetic data generation pipeline against a state-of-the-art Microsoft pipeline on a dataset of small to large systems. By analyzing the energy quality, autocorrelation times, and effective sample size, our findings show that Simulacra's Large Wavefunction Models (LWM) pipeline, paired with state-of-the-art Variational Monte Carlo (VMC) sampling algorithms, reduces data generation costs by 15-50x, while maintaining parity in energy accuracy, and 2-3x compared to traditional CCSD methods on the scale of amino acids. This enables the creation of affordable, large-scale \textit{ab-initio} datasets, accelerating AI-driven optimization and discovery in the pharmaceutical industry and beyond. Our improvements are based on a novel and proprietary sampling scheme called Replica Exchange with Langevin Adaptive eXploration (RELAX).

Timothy Heightman, Roman Aseguinolaza Gallo, Edward Jiang et al.

Inferring the dynamical generator of a many-body quantum system from measurement data is essential for the verification, calibration, and control of quantum processors. When the system is open, this task becomes considerably harder than in the purely unitary case, because coherent and dissipative mechanisms can produce similar measurement statistics and long-time data can be insensitive to coherent couplings. Here we tackle this so-called Lindbladian learning problem of open-system characterisation with maximum-likelihood on Pauli measurements at multiple experimentally friendly \emph{transient} times, exploiting the richer information content of transient dynamics. To navigate the resulting non-convex likelihood loss-landscape, we augment the physical model neural differential-equation term, which is progressively removed during training to distil an interpretable Lindbladian solution. Our method reliably learns open-system dynamics across neutral-atom (with 2D connectivity) and superconducting Hamiltonians, as well as the Heisenberg XYZ, and PXP models on a spin-1/2 chain. For the dissipative part, we show robustness over phase noise, thermal noise, and their combination. Our algorithm can robustly infer these dissipative systems over noise-to-signal ratios spanning four orders of magnitude, and system sizes up to $N=6$ qubits with fewer than $5 \times 10^5$ shots.

Timothy Heightman, Marcin Płodzień

Scientific progress is tightly coupled to the emergence of new research tools. Today, machine learning (ML)-especially deep learning (DL)-has become a transformative instrument for quantum science and technology. Owing to the intrinsic complexity of quantum systems, DL enables efficient exploration of large parameter spaces, extraction of patterns from experimental data, and data-driven guidance for research directions. These capabilities already support tasks such as refining quantum control protocols and accelerating the discovery of materials with targeted quantum properties, making ML/DL literacy an essential skill for the next generation of quantum scientists. At the same time, DL's power brings risks: models can overfit noisy data, obscure causal structure, and yield results with limited physical interpretability. Recognizing these limitations and deploying mitigation strategies is crucial for scientific rigor. These lecture notes provide a comprehensive, graduate-level introduction to DL for quantum applications, combining conceptual exposition with hands-on examples. Organized as a progressive sequence, they aim to equip readers to decide when and how to apply DL effectively, to understand its practical constraints, and to adapt AI methods responsibly to problems across quantum physics, chemistry, and engineering.

Timothy Heightman, Edward Jiang, Ruth Mora-Soto et al.

Quantum machine learning (QML) seeks to exploit the intrinsic properties of quantum mechanical systems, including superposition, coherence, and quantum entanglement for classical data processing. However, due to the exponential growth of the Hilbert space, QML faces practical limits in classical simulations with the state-vector representation of quantum system. On the other hand, phase-space methods offer an alternative by encoding quantum states as quasi-probability functions. Building on prior work in qubit phase-space and the Stratonovich-Weyl (SW) correspondence, we construct a closed, composable dynamical formalism for one- and many-qubit systems in phase-space. This formalism replaces the operator algebra of the Pauli group with function dynamics on symplectic manifolds, and recasts the curse of dimensionality in terms of harmonic support on a domain that scales linearly with the number of qubits. It opens a new route for QML based on variational modelling over phase-space.