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Frontiers of Engineering Reports on Leading-Edge Engineering from the 2018 Symposium (2019) / Chapter Skim
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Quantum Algorithms: Promise and Perspective - Shelby Kimmel
Pages 9-12

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From page 9...
... . There is a quantum factoring algorithm whose run time scales roughly like the number of digits in the integer, whereas the best classical algorithm requires nearly exponential time.
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From page 10...
... While quantum algorithms have impressive performance for problems like factoring and quantum simulation, there are many problems where quantum computers provably do not have a large advantage over regular computers. The best-known example is the parity problem, which involves determining whether a string of 0s and 1s has an even or odd number of 1s.
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From page 11...
... Quantum programming languages have just begun to be developed, and for many existing algorithms there is not an easy way to go from the theoretical description to a programming language description. Furthermore, even when an algorithm is described by a quantum programming language, there remain many challenges in converting instructions to quantum machine code, as different physical quantum computers tend to have different sets of basic operations.
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From page 12...
... While these applications are exciting, current understanding of quantum algorithms is truly quite limited. As physical quantum computers are developed and quantum algorithms are tested on them, an unprecedented new tool will be available for the development and exploration of quantum algorithms.
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