An Efficient Quantum Classifier Based on Hamiltonian Representations
Keywords: quantum computing, quantum machine learning, variational quantum circuits, quantum encoding
TL;DR: An efficient quantum machine learning method named "Hamiltonian classifier" that achieves logarithmic complexity in both qubits and gates by representing inputs as measurements rather than using traditional state preparation
Abstract: Quantum computing shows great potential for expanding the range of efficiently solvable problems. This promise arises from the advantageous resource and runtime scaling of certain quantum algorithms over classical ones. Quantum machine learning (QML) seeks to extend these advantages to data-driven methods. Initial evidence suggests quantum-based models can outperform classical ones in terms of scaling, runtime and generalization capabilities. However, critics have pointed out that many works rely on extensive feature reduction or use toy datasets to draw their conclusions, raising concerns about their applicability to larger problems. Scaling up these results is challenging due to hardware limitations and the high costs generally associated with encoding dense vector representations on quantum devices. To address these challenges, we propose an efficient approach called Hamiltonian classifier inspired by ground-state energy optimization in quantum chemistry. This method circumvents the costs associated with data encoding by mapping inputs to a finite set of Pauli strings and computing predictions as their expectation values. In addition, we introduce two variants with different scaling in terms of parameters and sample complexity. We evaluate our approach on text and image classification tasks, comparing it to well-established classical and quantum models. Our results show the Hamiltonian classifier delivers performance comparable to or better than these methods. Notably, our method achieves logarithmic complexity in both qubits and quantum gates, making it well-suited for large-scale, real-world applications.
Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
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Submission Number: 8172
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