# What exactly is the "quantum singular value decomposition"?

I know what is singular value decomposition, meaning given a matrix and write it as multiplication three different matrices, and middle matrix being diagonal and entries are singular values. So, what is exactly Quantum Singular Value Decomposition?

This is a research paper: https://arxiv.org/abs/1607.05404

So, in this paper they have performed Hamiltonian Simulation of non sparse and low rank matrix A. So, is this QSVD? Meaning for some matrix A we need to perform f(A) for some function f?

• Maybe you could provide a reference for where you encountered the term. My guess is that it refers to a quantum algorithm to compute the singular value decomposition. Nov 8 at 11:26
• @Rammus I have just updated the question. Nov 8 at 12:47
• In the conclusion of the linked work: "We have shown how compute the singular value decomposition of a non-Hermitian non-sparse matrix on a quantum computer directly...". So it looks like QSVD is just an algorithm to compute singular values and singular vectors using a quantum computer. Nov 8 at 13:02
• Performing f(A) for a given matrix A is more related to QSVT: Quantum Singular Value Transformation Nov 19 at 11:35