Quantum computing has long promised transformative advances in data analysis, yet practical quantum machine learning has remained elusive due to fundamental obstacles such as a steep quantum cost for the loading of classical data and poor trainability of many quantum machine learning algorithms designed for near-term quantum hardware. In this work, we show that one can overcome these obstacles by using a linear Hamiltonian-based machine learning method which provides a compact quantum representation of classical data via ground state problems for k-local Hamiltonians. We use the recent sample-based Krylov quantum diagonalization method to compute low-energy states of the data Hamiltonians, whose parameters are trained to express classical datasets through local gradients. We demonstrate the efficacy and scalability of the methods by performing experiments on benchmark datasets using up to 50 qubits of an IBM Heron quantum processor.

翻译：量子计算长期以来一直承诺在数据分析领域带来变革性进展，然而，由于存在根本性障碍，实用的量子机器学习仍然难以实现。这些障碍包括加载经典数据所需的高昂量子成本，以及为近期量子硬件设计的许多量子机器学习算法训练性差。在本工作中，我们证明，通过使用一种基于线性哈密顿量的机器学习方法，可以克服这些障碍。该方法通过k-局域哈密顿量的基态问题，为经典数据提供了一种紧凑的量子表示。我们使用最新的基于样本的Krylov量子对角化方法来计算数据哈密顿量的低能态，其参数通过局部梯度进行训练，以表达经典数据集。我们通过在IBM Heron量子处理器上使用多达50个量子比特对基准数据集进行实验，证明了这些方法的有效性和可扩展性。