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The anticipated applications of quantum computers span across science andindustry, ranging from quantum chemistry and many-body physics to optimization,finance, and machine learning. Proposed quantum solutions in these areastypically combine multiple quantum algorithmic primitives into an overallquantum algorithm, which must then incorporate the methods of quantum errorcorrection and fault tolerance to be implemented correctly on quantum hardware.As such, it can be difficult to assess how much a particular applicationbenefits from quantum computing, as the various approaches are often sensitiveto intricate technical details about the underlying primitives and theircomplexities. Here we present a survey of several potential application areasof quantum algorithms and their underlying algorithmic primitives, carefullyconsidering technical caveats and subtleties. We outline the challenges andopportunities in each area in an "end-to-end" fashion by clearly defining theproblem being solved alongside the input-output model, instantiating all"oracles," and spelling out all hidden costs. We also compare quantum solutionsagainst state-of-the-art classical methods and complexity-theoretic limitationsto evaluate possible quantum speedups.  The survey is written in a modular, wiki-like fashion to facilitatenavigation of the content. Each primitive and application area is discussed ina standalone section, with its own bibliography of references and embeddedhyperlinks that direct to other relevant sections. This structure mirrors thatof complex quantum algorithms that involve several layers of abstraction, andit enables rapid evaluation of how end-to-end complexities are impacted whensubroutines are altered.

Quantum algorithms: A survey of applications and end-to-end complexities