On nonlinear transformations in quantum computation

ORAL

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 algorithms 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.

*This work was supported by the Beyond Moore’s Law project of the Advanced Simulation and Computing Program and the Laboratory Directed Research and Development program at Los Alamos National Laboratory (LANL). ZH acknowledges support from the Mark Kac Fellowship. Part of this work was completed while NC was a particpant in the 2021 Quantum Computing Summer School at LANL, sponsored by the LANL Information Science & Technology Institute.

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Publication: https://doi.org/10.48550/arXiv.2112.12307

Presenters

  • Yigit Subasi

    • Los Alamos National Laboratory

Authors

  • Yigit Subasi

    • Los Alamos National Laboratory

  • Zoe Holmes

    • Los Alamos National Laboratory
    • École polytechnique fédérale de Lausanne

  • Nolan Coble

    • University of Maryland, College Park

  • Andrew T Sornborger

    • Los Alamos National Laboratory