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arXiv · 2112.12307

On nonlinear transformations in quantum computation

Zoë Holmes·Nolan Coble·Andrew T. Sornborger·Yiğit Subaşı
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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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Zoë Holmes, Nolan Coble, Andrew T. Sornborger, Yiğit Subaşı. 2021-12-23. On nonlinear transformations in quantum computation. https://arxiv.org/abs/2112.12307

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