Variational Quantum Singular Value Decomposition

Singular value decomposition is central to many problems in engineering and scientific fields. Several quantum algorithms have been proposed determine the singular values their associated vectors of a given matrix. Although these are promising, required subroutines resources too costly on near-term devices. In this work, we propose variational algorithm for (VQSVD). By exploiting principles Ky Fan Theorem, design novel loss function such that two neural networks (or parameterized circuits) could be trained learn output corresponding values. Furthermore, conduct numerical simulations VQSVD random matrices as well its applications image compression handwritten digits. Finally, discuss our recommendation systems polar decomposition. Our work explores new avenues information processing beyond conventional protocols only works Hermitian data, reveals capability matrix