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Learn modern quantum algorithm design and analysis techniques through an in-depth tutorial covering quantum signal processing (QSP) and quantum singular value transformation (QSVT). Explore how these revolutionary methods have transformed quantum computing over the past decade by enabling efficient manipulation of linear operators encoded in quantum computations. Discover the construction and key properties of algorithms built from simple alternating circuit ansätze that apply functions to the spectra of linear operators encoded as sub-blocks of unitary matrices. Examine how this flexible approach unifies, simplifies, and improves most quantum algorithms across disparate problem domains. Investigate recent extensions and improvements to these techniques while understanding their limitations for spectral mapping applications. Compare QSP/QSVT approaches with alternative quantum algorithms for manipulating linear operators, including linear combination of Hamiltonian simulation methods. Gain insights into open questions at the intersection of quantum algorithms, functional analysis, and numerical linear algebra through content designed to be accessible to both quantum and classical computing audiences.
