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Explore how quantum computing can solve partial differential equations by leveraging periodic function structures in this 43-minute conference talk. Learn about the relationship between smoothness degrees of real-valued periodic functions and the computational complexity of preparing high-precision amplitude encodings as quantum states. Discover a novel pseudo-spectral Fourier-analytic framework for manipulating periodic functions that enables quantum algorithms for solving both time-dependent and time-independent PDEs with varying precision targets. Examine the systematic investigation of what structural forms enable quantum computational advantages in continuous-domain problems, contrasting with the well-studied discrete computational problems involving Boolean functions. Understand how these concepts apply to meaningful real-world applications through a hierarchy of many-body quantum simulation pipelines that demonstrate increasing quantum computational advantages as quantum resource scales grow, presented by Pooya Ronagh from the University of Waterloo at IPAM's Bridging the Gap Between NISQ and FTQC Workshop.
