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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

Indonesian

Pembelajaran mesin secara luas dianggap sebagai aplikasi framework yang menjanjikan di mana komputasi kuantum dapat menawarkan keuntungan komputasi. Namun, model pembelajaran mesin kuantum umum dengan jaminan yang dapat diandalkan pada kinerja, pelatihan, dan inferensi yang efisien tetap terbatas. Dalam pekerjaan ini, kami memperkenalkan embeddings kuantum Hamilton, kerangka pembelajaran yang diawasi di mana dataset pelatihan klasik dikodekan menjadi satu, parameterisasi Hamiltonian yang efektif. Pelatihan mengoptimalkan parameter dari Hamiltonian yang tergantung pada data ini, yang status dasarnya mendefinisikan aturan klasifikasi. Begitu kondisi tanah telah disimulasikan menggunakan algoritma kuantum, inferensi dapat dilakukan baik secara klasik menggunakan representasi klasik dari negara yang dipelajari, atau dengan representasi kuantum dari negara. Kami menetapkan metode efisien untuk estimasi gradient dan

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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