Implementable Quantum Classifier for Nonlinear Data
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In this Letter, we propose a quantum machine learning scheme for the classification of classical nonlinear data. The main ingredients of our method are variational quantum perceptron (VQP) and a quantum generalization of classical ensemble learning. Our VQP employs parameterized quantum circuits to learn a Grover search (or amplitude amplification) operation with classical optimization, and can achieve quadratic speedup in query complexity compared to its classical counterparts. We show how the trained VQP can be used to predict future data with O(1) query complexity. Ultimately, a stronger nonlinear classifier can be established, the so-called quantum ensemble learning (QEL), by combining a set of weak VQPs produced using a subsampling method. The subsampling method has two significant advantages. First, all T weak VQPs employed in QEL can be trained in parallel, therefore, the query complexity of QEL is equal to that of each weak VQP multiplied by T. Second, it dramatically reduce the runtime complexity of encoding circuits that map classical data to a quantum state because this dataset can be significantly smaller than the original dataset given to QEL. This arguably provides a most satisfactory solution to one of the most criticized issues in quantum machine learning proposals. To conclude, we perform two numerical experiments for our VQP and QEL, implemented by Python and pyQuil library. Our experiments show that excellent performance can be achieved using a very small quantum circuit size that is implementable under current quantum hardware development. Specifically, given a nonlinear synthetic dataset with 4 features for each example, the trained QEL can classify the test examples that are sampled away from the decision boundaries using 146 single and two qubits quantum gates with 92% accuracy.
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