Fast and scalable classical machine-learning algorithm with similar performance to quantum circuit learning

The application of near-term quantum devices to machine learning (ML) has attracted much attention. Recently, Mitarai et al. [Phys. Rev. A 98, 032309 (2018)] proposed a framework to use a quantum circuit for ML tasks, called quantum circuit learning (QCL). Due to the use of a quantum circuit, QCL employs an exponentially high-dimensional Hilbert space as its feature space. However, its efficiency compared to classical algorithms remains unexplored. Here, we present a classical ML algorithm that uses the same Hilbert space. In numerical simulations, our algorithm demonstrates similar performance to QCL for several ML tasks, providing a perspective for the computational and memory efficiency of quantum ML algorithms