On two patient-specific cardiovascular benchmarks, the structured QCML propagator matches the predictive accuracy of its classical counterpart on surface pressure spectra, pressure drop, and wall shear stress, establishing QCML as a working component of scientific machine learning and a concrete contribution towards practical quantum advantage in real-world prediction.
Abstract
Machine-learning surrogates of physical systems face a paradox: explainable models facing the challenge of expressivity to capture complex nonlinear flows, whereas expressive deep surrogates match high-fidelity simulations only through massive parameterisations that turn the learned dynamics into a black box. Here, we introduce quantum-compressed machine learning (QCML), which resolves this tension by compressing the latent propagator of a flow surrogate from $524{,}288$ trainable parameters to no more than $8$. This parameter reduction brings the learned dynamical law to the parameter scale of a physical constitutive relation rather than a black-box neural network, making the surrogate directly interpretable and controllable without sacrificing expressivity. The compression is realised by a structured quantum circuit whose unitary propagator constrains the latent spectrum to the unit circle exactly and by construction, replacing exponential error growth with linear accumulation over autoregressive rollouts. Classical regularisation only approximates this constraint: even a quantum-inspired classical baseline penalised towards unitarity collapses within one Lyapunov time on turbulent channel flow, whereas QCML remains stable over the full rollout. Shared phase and coupling angles parameterising the circuit correspond directly to modal frequencies and inter-mode interactions, giving the learned dynamics a physical interpretation in spectral space. On two patient-specific cardiovascular benchmarks, the structured QCML propagator matches the predictive accuracy of its classical counterpart on surface pressure spectra, pressure drop, and wall shear stress. These results establish QCML as a working component of scientific machine learning and a concrete contribution towards practical quantum advantage in real-world prediction.
Predicting anomalous diffusion in quantum walks with non-Markovian environmental noise is computationally demanding. We introduce FracPINN, a fractional physics-informed neural network that embeds a fully differentiable, PyTorch-based Caputo PDE solver into a classical LSTM encoder. Rather than replacing classical predictors, FracPINN acts as a compact physics regularizer that constrains the inference with emergent fractional transport dynamics; every physics-informed loss component is strictly label-free, and the ground-truth exponent enters only through an explicitly supervised regression term. Evaluated on 3709 non-Markovian DTQW simulations with exponentially correlated Gaussian coin noise (filtered from 5000 raw samples to the physically admissible exponent range), FracPINN achieves a mean absolute error of 0.214 and R2=0.682 on held-out test data, outperforming classical baselines by 5.3% in terms of the MAE overall, while adding only four interpretable physical parameters. Notably, gains concentrate in the sub-diffusive regime where memory effects dominate, with a 13.5% MAE improvement over the baseline there, yet the normal and super diffusive accuracy remains intact. Once trained, the surrogate reduces inference from seconds of simulation to fractions of a millisecond per sample. These results show that our fractional PDE networks are most compelling as targeted physics refinements with minimal overhead within stable classical pipelines.
The first numerical study of continuous-time flow and diffusion models is presented, in which time-dependent potentials and states are represented as tensor networks, and a coherent amplitude encoding is prepared that can be post-processed by quantum algorithms offering a quadratic advantage over Monte Carlo sampling.
Nathan X. Kodama, L. Wray, S. Cochran et al.· 0 citations
A key challenge in practical quantum machine learning (QML), particularly for discriminative tasks such as classification, is the limited capacity of near-term quantum devices to encode high-dimensional classical data into small quantum registers. In optimized basis-encoded (bit-bit) settings, this constraint leads to cross-class collisions, where samples with different labels are mapped to the same discrete bit-string and thus become indistinguishable to any downstream model. In this work, we investigate how data representation affects QML performance under such severe information bottlenecks. We introduce discretization-aware fine-tuning (DAFT), a method that adapts a pre-trained chemical foundation model to produce representations that remain informative after quantization. DAFT reduces collision probability through a differentiable soft collision loss. We evaluate both quantum and classical models under a controlled setting in which they receive identical discretized bit-string inputs, isolating the effect of representation from model architecture. On the blood-brain barrier penetration (BBBP) molecular property prediction benchmark using ChemBERTa-77M, DAFT reduces collision counts by several orders of magnitude and improves quantum classification accuracy by more than 12 percentage points compared to a frozen backbone. Importantly, without DAFT, classical models outperform QML under the same input constraints. With DAFT, however, this comparison reverses at higher qubit counts. At 10 qubits, the quantum model surpasses a matched classical baseline trained on identical bit-strings (0.883 vs. 0.855, $p = 0.026$). These results show that, in information-constrained regimes, achieving a quantum advantage critically depends on aligning continuous representations with discrete quantum encodings.
The field of quantum machine learning (QML) evolved to value models believed to most directly rival those providing utility in classical ML, namely large-scale neural networks. Although more recently, classical ML has been learning a hard lesson with respect to deploying un-interpretable neural networks in the wild: model interpretability matters for domain-adapted co-design and human adoption. We adopt this larger ML perspective to argue that quantum ML model value can be found through the characterization of its inherent interpretability offerings -- i.e. its mathematical structure that contributes meaningfully to desired model behavior for the specific ML task. To support our perspective, we provide a motivating example of a characterization with quantum Fourier models and random Fourier features (RFF) as approaches to approximate Gaussian process (GP) kernels for uncertainty quantification tasks in ML. The top-down and bottom-up complementarity of the two mathematical constructions reveals that quantum Fourier models offer different tools than RFFs for principled GP kernel design and interpretable discovery for uncertainty quantification with real-world data. To showcase the rich variety of inductive biases enabled by quantum information tools, we review examples from the QML literature -- including symmetry, metric geometry, and topology -- that can be used to design inherently interpretable ML models for specific tasks. We hope this framing encourages the QML community to value the inherent components and mechanisms of quantum models separately from task performance, as inherent interpretability might be the reason that a quantum model, and potentially a quantum computer, gets used in practice for ML.
We introduce Quantum Port-Hamiltonian Neural Networks (Q-pHNNs), parameterised quantum circuits that learn classical dynamics in a structure-preserving manner. The framework rests on the Isomorphic Hamiltonian Mapping (IHM): the skew-symmetric interconnection matrix $\mathbf{J}$ corresponds to unitary gate evolution, and the positive-semidefinite dissipation matrix $\mathbf{R}$ to Measurement-Induced NonLinearity (MINL), realised by mid-circuit measurement with classical feedforward. Conservation and passivity are then enforced by construction rather than by penalty terms, and dissipation becomes an intrinsically quantum effect: energy leaves through the act of measurement. We instantiate the IHM in three architectures: a Quantum HNN that extracts Hamilton's equations via the Parameter-Shift Rule; a Q-pHNN that dissipates through MINL; and a topology-entangled Quantum Graph Neural Network lifting both channels to $N$-node coupled-phasor networks. In simulation, where every model here was trained, we obtain $1.35\%$ relative energy drift under a symplectic integrator, $100\%$ energy monotonicity for the single-oscillator MINL circuit, and $92$--$98\%$ phase-space energy decay across ring, star and chain networks at $N\in\{3,6,9\}$. On an IBM Heron processor the trained energy surface and its parameter-shift gradients reproduce their simulated values, with an error budget dominated by readout rather than gate infidelity; the dissipative channel executes natively, but its decay is not separable from measurement back-action at these depths.
Parametrized quantum circuits (PQCs) form the computational backbone of variational quantum algorithms, yet their practical utility is increasingly constrained by optimisation failures as circuit depth grows. Gradient signals decay rapidly under standard random initialisation, and existing structured approaches abandon inter-layer coordination the moment independent optimisation begins. In this work, we introduce a depthconditioned parameterisation that preserves this coordination throughout training by generating all circuit parameters from a low-dimensional Fourier model over normalised depth, anchored by a task-adapted shallow-circuit prior and augmented with perlayer residuals that retain full expressivity. Gradient information from all layers is aggregated into a compact set of shared weights, providing a principled mechanism for sustaining training signals at depth. Numerically, the proposed method achieves reliable convergence in regimes where all baseline strategies fail or succeed only sporadically, reducing final validation error twoto ten-fold and reaching convergence thresholds up to 2.6 times faster, with $\mathcal{O}\left(d_{\theta}\right)$ overhead independent of circuit depth.
Thi Thuy Nga Nguyen, John Le, T. Vu et al.· 2026 IEEE International Conf...· 0 citations
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