Quantum-classical reinforcement parity learning from noisy classical data

Abstract

Development of quantum algorithms for data analysis and machine learning has gained much attention recently. For practical applications of such algorithms in the big data era, the quantum advantage must be retained in noisy settings. One intriguing example in which the quantum algorithm outperforms the classical counterpart in the presence of noise is the problem of learning a parity function defined by a hidden bit string, known as learning parity with noise (LPN). However, a learner is most likely to receive noisy classical data, rather than noisy quantum data as considered in the original quantum LPN algorithm. Then, whether the quantum technique is still preferred remains an interesting open problem. Here, we present a quantum-classical reinforcement learning algorithm to solve the LPN problem efficiently for classical data. The algorithm uses classical training data to prepare an input quantum state suitable for the original quantum LPN algorithm. Based on the outcome of the quantum algorithm, a reward and an action are classically determined to update the input quantum state for the next learning cycle. Our method uses an exponentially smaller number of training samples than the direct application of the original quantum LPN algorithm to classical data.