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This content will become publicly available on December 10, 2025

Title: Infinite quantum signal processing
Quantum signal processing (QSP) represents a real scalar polynomial of degree d using a product of unitary matrices of size 2 × 2 , parameterized by ( d + 1 ) real numbers called the phase factors. This innovative representation of polynomials has a wide range of applications in quantum computation. 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 the degree d . While the phase factors are generally not unique, we find that there exists a consistent choice of parameterization so that the limit is well defined in the 1 space. This generalization of QSP, called the infinite quantum signal processing, can be used to represent a large class of non-polynomial functions. Our analysis reveals a surprising connection between the regularity of the target function and the decay properties of the phase factors. Our analysis also inspires a very simple and efficient algorithm to approximately compute the phase factors in the 1 space. The algorithm uses only double precision arithmetic operations, and provably converges when the 1 norm of the Chebyshev coefficients of the target function is upper bounded by a constant that is independent of d . This is also the first numerically stable algorithm for finding phase factors with provable performance guarantees in the limit d more » « less
Award ID(s):
2016245
PAR ID:
10589797
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
Quantum
Date Published:
Journal Name:
Quantum
Volume:
8
ISSN:
2521-327X
Page Range / eLocation ID:
1558
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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