Amplitude Transformation of Quantum State Based on QSVT
Lu Hou, School of Cyber Security, University of Chinese Academy of Sciences, China; Chang Lv, Key Laboratory of Cyberspace Security Defense,\\ Institute of Information Engineering, CAS, China
Session:
Quantum Data and Computation
Track:
6: Quantum Information and Coding Theory
Location:
Ypsilon I-II-III
Presentation Time:
Thu, 11 Jul, 10:05 - 10:25
Session Chair:
Holger Boche,
Abstract
THIS PAPER IS ELIGIBLE FOR THE STUDENT PAPER AWARD. Quantum singular value transformation (QSVT) is a powerful quantum algorithm that can effectively perform a polynomial transformation of the singular values of a linear operator embedded in a unitary matrix. This article extends QSVT to perform a polynomial transformation of the amplitudes of a quantum state. This article presents an algorithm that can convert quantum state $\sum_{i=0}^{N-1}x_i\ket{i}$ to quantum state $\frac{1}{\sqrt{\sum_{i=0}^{N-1}|f(x_i)|^2}}\sum_{i=0}^{N-1}f(x_i)\ket{i}$ and demonstrates the application of the algorithm in the quantum state threshold problem.