Southwest Quantum Information and Technology

Infinite quantum signal processing

Presenting Author: Yulong Dong, University of California Berkeley
Contributing Author(s): Lin Lin Hongkang Ni Jiasu Wang

The quantum singular value transformation (QSVT) [Gilyen, Su, Low, Wiebe, STOC 2019] provides a unified viewpoint of a large class of practically useful quantum algorithms. At the heart of QSVT is a new polynomial representation, called quantum signal processing (QSP). QSP represents a degree-d polynomial using products of matrices in SU(2), parameterized by (d+1) real numbers called the phase factors. When the polynomial of interest is obtained by truncating an infinite polynomial series, a natural question is whether the phase factors have a well defined limit as $d \to \infty$. In this talk, we will show that there exists a consistent choice of the parameterization so that the limit is well defined. This generalizes QSP to represent a large class of non-polynomial functions, and this construction is referred to as infinite QSP (iQSP). We present a very simple algorithm for finding such infinitely long phase factors with provable performance guarantees. We will also show a surprising connection between the regularity of the target function and the structural properties of the phase factors.

(Session 5 : Thursday from 5:00 pm - 7:00 pm)