A Grand Unification of Quantum Algorithms

Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian simulation, which appear as subroutines for large families of composite quantum algorithms. A number of these quantum algorithms were recently tied together by a novel technique known as the quantum singular value transformation (QSVT), which enables one to perform a polynomial transformation of the singular values of a linear operator embedded in a unitary matrix. In this talk, I will provide a pedagogical tutorial through these developments, first discussing the emergence of QSVT, and then employing QSVT to construct intuitive quantum algorithms for search, phase estimation, and Hamiltonian simulation. This overview illustrates how QSVT is a single framework comprising the three major quantum algorithms, thus suggesting a grand unification of quantum algorithms.