Speaker
Description
Quantum block encoding (QBE) is a crucial step in the development of many quantum algorithms, as it embeds a given matrix into a suitable larger unitary matrix. Historically, efficient techniques for QBE have primarily focused on sparse matrices, with less attention given to data-sparse matrices, such as rank-structured matrices. In this work, we examine a specific case of rank structure: one-pair semiseparable matrices. We present a novel block encoding approach that utilizes a suitable factorization of the given matrix into the product of triangular and diagonal factors. Our algorithm requires $O(\rm{polylog}(N))$ qubits and allows us to compute matrix-vector products in $O(\rm{polylog}(N))$ quantum operations, where $N$ is the size of the matrix.
