quantum classifier with tailored quantum kernel

• DOI: 10.48550/arxiv.1909.02611
• Publication Date: 2020-05-15
• Authors: Daniel K. Park; Carsten Blank; Francesco Petrucc...; Francesco Petrucc...; June-Koo Kevin Rhee; June-Koo Kevin Rhee
• Keywords: Quantum Physics; FOS: Physical sciences; Quantum Physics (quant-ph)

AbstractKernel methods have a wide spectrum of applications in machine learning. Recently, a link between quantum computing and kernel theory has been formally established, opening up opportunities for quantum techniques to enhance various existing machine-learning methods. We present a distance-based quantum classifier whose kernel is based on the quantum state fidelity between training and test data. The quantum kernel can be tailored systematically with a quantum circuit to raise the kernel to an arbitrary power and to assign arbitrary weights to each training data. Given a specific input state, our protocol calculates the weighted power sum of fidelities of quantum data in quantum parallel via a swap-test circuit followed by two single-qubit measurements, requiring only a constant number of repetitions regardless of the number of data. We also show that our classifier is equivalent to measuring the expectation value of a Helstrom operator, from which the well-known optimal quantum state discrimination can be derived. We demonstrate the performance of our classifier via classical simulations with a realistic noise model and proof-of-principle experiments using the IBM quantum cloud platform.