The Inference Report

Generative models have become central across science and industry, from image and text synthesis to the design of molecules and materials. Quantum generative models are considered one of the most promising applications for quantum computers, since a quantum circuit naturally produces samples from the distribution it encodes, and for suitable circuits that distribution is believed to be hard for any classical computer to reproduce. A leading strategy trains these models on a classical computer and reserves the quantum device for generating samples at deployment. This is possible when the training loss can be evaluated on a classical computer. A prime example is the maximum mean discrepancy (MMD$^2$), a moment-matching loss that compares the model and the data through their Pauli-$Z$ correlations. Research so far has asked whether such models can be trained and whether their sampling is hard; whether minimizing such an objective yields a model that generalizes, rather than one that merely reproduces the training statistics, remains poorly understood. We benchmark a broad set of quantum and classical generative models by direct sampling and show that models trained with a moment-matching loss generally show worse generalization than the likelihood-trained models. We show this on two application-inspired datasets: first a cardinality-constrained dataset at up to $30$ qubits and second a dataset of genomic single-nucleotide variants, whose valid set is the observed data. These results indicate that a converged moment-matching loss is not a reliable measure of generalization, and that train-classical, deploy-quantum workflows will need approaches that target generalization directly, leaving open whether better training objectives suffice or whether the model architectures themselves must change.

Quantum federated learning enables collaborative model training across quantum devices without sharing raw data, and it faces the data and hardware heterogeneity inherent to noisy quantum devices. Utilizing the quantum geometric tensor is a natural remedy, yet pure-state approaches and diagonal approximations discard the correlations that encode parameter incompatibility. To address this, we extend the parameter-space geometry to the mixed states that noisy clients actually prepare. The real part of the resulting mixed-state geometric tensor is the Bures metric, which measures how fast the physical state changes under parameter variation, and the imaginary part is the mean Uhlmann curvature, which quantifies the incompatibility of estimating multiple parameters simultaneously. Accordingly, we employ the Bures metric as a local preconditioner and use the mean Uhlmann curvature to develop an achievable-precision aggregation rule that dynamically down-weights unreliable clients. Furthermore, we establish theoretical guarantees by proving a convergence theorem and a variance-dominance proposition. Empirical evaluations on a trapped-ion quantum emulator demonstrate that the proposed method maintains high accuracy across diverse device-heterogeneity conditions and outperforms standard federated averaging, whose accuracy degrades under strong noise.

Nitrogen-vacancy (NV) centers in diamond can serve as highly sensitive solid-state quantum sensors for high-sensitivity magnetometry. However, in the noisy intermediate-scale quantum (NISQ) era, extracting reliable information from noisy, finite-shot, and measurement-limited sensing data remains a considerable challenge. Whereas, quantum machine learning (QML) offers a potential path to improve parameter estimation by learning nonlinear relationships between quantum-sensing data and the underlying physical signal. In this work, we investigate the role of QML in magnetic-field estimation within an NV center-inspired magnetometry setting. We formulated magnetic field sensing as a supervised regression task. We compared the performance of several classical machine learning models trained on measurement-based classical data with that of quantum kernel-based models trained on pre-measurement coherent quantum states. Our objective is to isolate the impact of measurement-induced information loss and therefore provide a theoretical upper bound on the sensing performance. The upper bound is achievable only when coherent quantum information is directly available to the learning model. Our results show that QML-based sensing performance improves significantly with coherent quantum-state information, and not much with changes in model complexity or learning paradigm. This observation underscores the importance of learning pipelines that tightly integrate quantum sensors and QML models to enhance magnetic field sensing under realistic constraints.

Quantum noise is expected to degrade quantum machine learning by driving circuits away from their noiseless implementations. Yet recent studies show moderate noise can reduce testing error, a behavior unexplained by weak-noise perturbative error accumulation or strong-noise trainability collapse. Here we develop a statistical learning theory connecting microscopic noise processes to macroscopic learning performance. At its heart is a noise-order purity parameter, derived from a surrogate model analysis, that predicts the noise-induced reduction in model complexity and the consequent reduction in the generalization gap. Noise simultaneously increases prediction bias. Their competition explains the intermediate-noise regime left open between these limits. It produces a finite-noise optimum whose location depends on the learning setup and can disappear in the large-sample limit. Numerical experiments validate these predictions. Noise programming can move a model towards this optimum. These results make the non-monotonic effect of noise predictable and provide a route to harness it.

We prove the first quantum--classical separation for a sampling problem over a continuous domain. For a class of Gibbs states $p\propto e^{-βE}$ on the torus $\mathbb{T}^d$ with smooth ($s$-Gevrey) potential and barrier amplitude $α=e^{βΔ}$, where $Δ= \max E-\min E$, every classical algorithm---querying the value, gradient, or any higher-order derivatives of the log-density---requires $Ω(α)$ queries to sample at constant accuracy in total variation distance, while a quantum algorithm based on quantum singular value thresholding and temperature annealing samples with $\tilde{O}\left(\sqrtα\right)$ queries to an oracle for the gradient. The advantage is quadratic in the barrier amplitude, which becomes exponential in the dimension, $e^{Ω(d)}$, at low temperature. The classical bound is information-theoretic, holding for every classical algorithm with query access to the Gibbs potential and its derivatives at any order.

Similarity in many decision systems is governed not by distance alone but by interactions among variables. In fraud and anomaly detection, small local perturbations can cross interaction-sensitive decision boundaries while leaving ambient distance almost unchanged. Motivated by this setting, we introduce a thin-slab interaction model and an interaction-driven quantum kernel constructed from entangled Pauli-string feature maps. The feature map explicitly encodes sparse high-order block interactions. We show that the resulting fidelity kernel is positive semidefinite, admits an exact block-factorized formulation, and induces a geometry sensitive to changes in interaction regime. Across balanced and imbalanced synthetic experiments spanning third-, fourth-, sixth-, and eighth-order interactions, the proposed kernel consistently outperforms linear, radial basis function, Laplacian, and polynomial kernels, as well as an engineered-interaction linear baseline supplied with the planted block products. On real fraud-detection benchmarks, it achieves the highest mean accuracy and F1 on Credit Card Fraud Detection and ranks second on IEEE-CIS Fraud Detection. These findings show that quantum-kernel performance depends on alignment between feature-map geometry and the underlying predictive structure, rather than on Hilbert-space dimension alone. Because the prescribed block-factorized kernel can also be evaluated exactly on a classical computer, the results establish predictive and representational value rather than computational quantum speedup.