Speaker
Description
Quantum block encoding (QBE) is a crucial step in the development of most quantum algorithms, providing an embedding of a given matrix into a suitable larger unitary matrix. Efficient techniques for QBE have primarily focused on sparse matrices, and less effort has been devoted to data-sparse matrices, such as rank-structured matrices.
In this talk, we examine a specific case of rank structure: one-pair semiseparable matrices. We present a new block encoding approach that relies on an efficient state preparation technique for the representation of the two generators and on the reordering of entries obtained through the tensor product of the generators. This process takes polylogarithmic time if the two generators can be prepared efficiently, with a scaling factor of $2\sqrt{2}^{n}$, where $n=log_2(N)$ is the number of qubits to represent the matrix.