On nonlinear transformations in quantum computation

• URL: http://arxiv.org/abs/2112.12307v2
• Date: Wed, 15 Feb 2023 10:49:24 GMT
• Title: On nonlinear transformations in quantum computation
• Authors: Zo\"e Holmes, Nolan Coble, Andrew T. Sornborger, Yi\u{g}it Suba\c{s}{\i}
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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