On nonlinear transformations in quantum computation


Holmes, Z. (2022). On nonlinear transformations in quantum computation. Perimeter Institute. https://pirsa.org/22050067


Holmes, Zoe. On nonlinear transformations in quantum computation. Perimeter Institute, May. 25, 2022, https://pirsa.org/22050067


          @misc{ pirsa_22050067,
            doi = {10.48660/22050067},
            url = {https://pirsa.org/22050067},
            author = {Holmes, Zoe},
            keywords = {Quantum Information},
            language = {en},
            title = {On nonlinear transformations in quantum computation},
            publisher = {Perimeter Institute},
            year = {2022},
            month = {may},
            note = {PIRSA:22050067 see, \url{https://pirsa.org}}

Zoe Holmes Los Alamos National Laboratory


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.

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