Quantum Hamiltonian embeddings enable new supervised learning approaches
Supervised Learning with Quantum Hamiltonian Embeddings
Machine Learning
Summary
Machine learning can sometimes be hard to speed up with normal computers. This paper shows a new way to use quantum computers by turning training data into a quantum system that can learn from data patterns. The learning happens by tuning a quantum system so its simplest state helps to sort new data correctly. The authors show mathematical reasons why this works well and even demonstrate it on real quantum machines. Their method can do certain tasks that normal computers cannot do efficiently.
What this means in practice
- •For quantum computing engineers: Train and implement classification models on quantum processors using quantum Hamiltonian embeddings.
- •For cybersecurity system designers: Design classification systems that use quantum-encoded models which may outperform classical algorithms under cryptographic assumptions.
Authors
Riccardo Molteni, Minjun Jeon, Paolo Braccia, Abhinav Deshpande, Vedran Dunjko, Liang Jiang, Su-un Lee, Swarnadeep Majumder, Javier Robledo Moreno, Parthasarathy Suryanarayanan, Kunal Sharma
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.