On nonlinear transformations in quantum computation
Quantum Physics
2023-02-16 v2
Abstract
While quantum computers are naturally well-suited to implementing linear operations, it is less clear how to implement nonlinear operations on quantum computers. However, nonlinear subroutines may prove key to a range of applications of quantum computing from solving nonlinear equations to data processing and quantum machine learning. Here we develop a series of basic subroutines for implementing nonlinear transformations of input quantum states. Our algorithms are framed around the concept of a weighted state, a mathematical entity describing the output of an operational procedure involving both quantum circuits and classical post-processing.
Cite
@article{arxiv.2112.12307,
title = {On nonlinear transformations in quantum computation},
author = {Zoë Holmes and Nolan Coble and Andrew T. Sornborger and Yiğit Subaşı},
journal= {arXiv preprint arXiv:2112.12307},
year = {2023}
}
Comments
10 pages, 9 figures in the main text. 14 pages, 6 figures in the Appendices