On nonlinear transformations in quantum computation

2021/12/23 by Zoë Holmes, Holmes, Zoë, Nolan J. Coble +5 · 5 citations
Computer Science · #FOS: Physical sciences #Neural Networks and Reservoir Computing #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2112.12307

openalex publication_date 2021/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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