Quantum Algorithm for Classical Multidimensional Scaling

Classical multidimensional scaling is an important dimensionality reduction method that is characterized by preserving the Euclidean distance between samples in high dimensional space in low dimensional space. However the high time complexity limits its application in massive samples and high-dimensional data scenarios. As a promising solution, a quantum algorithm for classical multidimensional scaling is proposed in this work, achieving polynomial speedup in terms of sample size compared to classical algorithms. Our algorithm is built on two quantum subroutines, one involving inner product and matrix multiplication, and the other utilizing quantum singular value estimation.