Berlin 2024 – scientific programme

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QI: Fachverband Quanteninformation

QI 15: Quantum Computing Theory

QI 15.5: Talk

Wednesday, March 20, 2024, 10:45–11:00, HFT-FT 101

Polynomial pre-processing for quantum singular value transformations — •Shawn Skelton and Tobias Osbourne — Leibniz Universität Hannover

Quantum signal processing (QSP), and its extension quantum singular value transformation (QSVT), are increasingly popular frameworks for developing fault-tolerant quantum algorithms. Despite their recent prominence in the literature, QSP implementations still struggle to complete a costly classical pre-processing step. Namely, one must select a set of SU(2) rotation matrices for a given polynomial P(x) using algorithms which rely upon either optimization or polynomial root-finding subroutines. These techniques either introduce undesirable constraints on the input polynomials or struggle with high-degree polynomials. Furthermore, this pre-processing can depend on how users design their problem, and notably on whether one works in the variable domain z∈ U(1) or x∈[−1, 1]. We introduce a new method for computing rotation matrices for the complex-variable case and compare the run-time and reliability of our technique to existing methods. Our benchmark functions are selected for their ubiquity in the literature - functional approximations used to implement matrix inversion, Hamiltonian simulation, and unstructured search with QSP. Because QSP/QSVT techniques are relatively new to the literature, we also consider the ease of application of each method and suggest best practices for new users.

Keywords: quantum singular value transformations; quantum algorithms; quantum singnal processing; hamiltonian simulation