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Supervised Learning with Quantum Hamiltonian Embeddings

Riccardo Molteni, Minjun Jeon, Paolo Braccia, Abhinav Deshpande, Vedran Dunjko, Liang Jiang, Su-un Lee, Swarnadeep Majumder, Javier Robledo Moreno, Parthasarathy Suryanarayanan, Kunal Sharma · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.26833 · cited by 0 works (OpenAlex) · open-access PDF

Chinese

机器学习被广泛认为是一个有前途的应用程序,在那里量子计算可以提供计算优势。然而,一般的量子机器学习模型,在性能,训练能力和高效推断的可证保证仍然有限。 在这项工作中,我们引入了量子汉密尔顿嵌入,一个受监督的学习框架,在那里一个经典的训练数据集被编码成一个有效的,参数化的汉密尔顿。 培训优化了这个数据依赖的汉密尔顿的参数,其近似的地面状态定义了分类规则。 一旦地面状态已经通过量子算法接近,推断可以通过使用学到的状态的经典表示来进行,或者使用量子状态的代表。 我们建立了高效的基准估计方法,并保证了有利的生成。 此外,在

Machine translation (Meta M2M100); the English original follows.

Abstract

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.

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Topics: Hamiltonian (control theory), Quantum, Parameterized complexity, Quantum algorithm, Computer science, Quantum computer

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