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新论文 · v1arXiv:2611.16903

Uncertainty-aware quantum machine learning based on Dempster-Shafer theory

Marie Kempkes, Jakob Spiegelberg, Evert van Nieuwenburg, Vedran Dunjko

原文摘要

A large body of work in quantum machine learning has centered on characterizing the expressivity and performance of quantum models. In contrast, little attention has been paid to the reliability of predictions beyond average performance measures such as accuracy. In this work, we introduce an uncertainty-aware quantum classification framework based on Dempster-Shafer theory. This theory allows to express uncertainty through weights assigned not only to individual classification labels but to sets of labels. We introduce a training strategy that enables parameterized quantum circuits to learn such assignments directly from data. This provides an efficient way to prepare the corresponding quantum states and enables the application of different post-processing strategies. In particular, it offers a practical setting for quantum Dempster-Shafer fusion procedures with polynomial resource requirements, even when the corresponding mass functions are defined over exponentially many subsets. Overall, our work represents a step toward enabling quantum models to express uncertainty about their predictions, thereby extending the evaluation of quantum models beyond predictive performance alone.

quant-ph · cs.LG · stat.ML

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2602.11042

Characterizing the Trainability of Instantaneous Quantum Polynomial Circuit Born Machines

Kevin Shen, Susanne Pielawa, Vedran Dunjko, Hao Wang

原文摘要

Instantaneous Quantum Polynomial Circuit Born Machines (IQP-QCBMs) have been proposed as quantum generative models that combine a classically tractable training objective - based on the maximum mean discrepancy (MMD) - with a potential quantum advantage motivated by sampling-complexity arguments. While recent works have explored this model across various application domains, fundamental questions remain: does the model suffer from exponentially vanishing loss gradients, known as the barren plateau problem - a pervasive obstacle in quantum machine learning - and how do regimes of trainability relate to regimes of possible quantum advantage? Here, we address both questions analytically. To study trainability, we derive closed-form expressions for the variances of the partial derivatives of the MMD loss function and establish general upper and lower bounds. We explicitly characterize how trainability depends on the generator set and the spectrum of the chosen kernel, identifying regimes in which low Hamming-weight kernels avoid exponential gradient suppression under structured topologies. Regarding potential quantum advantage, we reformulate the anti-concentration property in terms of the same generator-set quantities that govern trainability, enabling a unified analysis. We show that sparse IQP architectures can produce classically intractable output distributions while simultaneously remaining trainable, at least at lower-weight frequencies. Our analytical results corroborate the numerical observations of prior work and provide principled guidelines for designing scalable IQP-QCBM architectures.

quant-ph · cs.LG

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.26833

Supervised Learning with Quantum Hamiltonian Embeddings

Riccardo Molteni, Minjun Jeon, Paolo Braccia, Abhinav Deshpande, Vedran Dunjko, Liang Jiang, Su-un Lee, Swarnadeep Majumder 等 11 位作者

原文摘要

Machine learning is widely regarded as a promising application in which quantum computing could offer a computational advantage. However, general quantum machine learning models with provable guarantees on performance, trainability, and efficient inference remain limited. In this work, we introduce quantum Hamiltonian embeddings, a supervised learning framework in which a classical training dataset is encoded into a single effective, parameterized Hamiltonian. Training optimizes the parameters of this data-dependent Hamiltonian, whose approximate ground state defines the classification rule. Once the ground state has been approximated using a quantum algorithm, inference can be performed either classically using a classical representation of the learned state, or with a quantum representation of the state. We establish efficient methods for gradient estimation and prove favorable generalization guarantees. Furthermore, under standard cryptographic assumptions, we show that Hamiltonian embeddings can realize hypothesis functions beyond the reach of efficient classical algorithms. We then demonstrate the framework at scale on IBM Heron processors using a standard benchmark dataset. Together, these results establish Hamiltonian embeddings as a new framework for quantum machine learning, combining theoretical guarantees with a path for experimental investigations at scale on quantum hardware.

quant-ph · cs.LG

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arXiv ↗PDF ↗