Quantum circuit-like learning: A 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. In one such attempt, Mitarai et al. (2018) proposed a framework to use a quantum circuit for supervised ML tasks, which is called quantum circuit learning (QCL). Due to the use of a quantum circuit, QCL can employ an exponentially high-dimensional Hilbert space as its feature space. However, its efficiency compared to classical algorithms remains unexplored. In this study, using a statistical technique called count sketch, we propose a classical ML algorithm that uses the same Hilbert space. In numerical simulations, our proposed algorithm demonstrates similar performance to QCL for several ML tasks. This provides a new perspective with which to consider the computational and memory efficiency of quantum ML algorithms.Comment: 16 pages, 10 figure

Quantum-inspired canonical correlation analysis for exponentially large dimensional data.

Canonical correlation analysis (CCA) serves to identify statistical dependencies between pairs of multivariate data. However, its application to high-dimensional data is limited due to considerable computational complexity. As an alternative to the conventional CCA approach that requires polynomial computational time, we propose an algorithm that approximates CCA using quantum-inspired computations with computational time proportional to the logarithm of the input dimensionality. The computational efficiency and performance of the proposed quantum-inspired CCA (qiCCA) algorithm are experimentally evaluated on synthetic and real datasets. Furthermore, the fast computation provided by qiCCA allows directly applying CCA even after nonlinearly mapping raw input data into high-dimensional spaces. The conducted experiments demonstrate that, as a result of mapping raw input data into the high-dimensional spaces with the use of second-order monomials, qiCCA extracts more correlations compared with the linear CCA and achieves comparable performance with state-of-the-art nonlinear variants of CCA on several datasets. These results confirm the appropriateness of the proposed qiCCA and the high potential of quantum-inspired computations in analyzing high-dimensional data