Recent Progress in Quantum Algorithms

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Dave Bacon, who wrote the elegant overview of the research discussed in my New Year’s Day post, just published his review, joint with Wim van Dam, of Recent Progress in Quantum Algorithms. Bacon writes beautifully, and this piece is no exception.

Most people have heard of no more than two quantum algorithms: Shor’s factoring algorithm and Grover’s search algorithm. For five years after Grover’s algorithm, no one discovered a significantly novel quantum algorithm, only variations on Shor’s and Grover’s algorithms were found. The first truly new quantum algorithms were discovered starting in 2001. Now there are many quantum algorithms found using a variety of approaches, though the applications remain restricted.  My recent overview of quantum computing mentions many of these algorithms. Bacon and van Dam provide a more detailed, but still high level, view of these algorithms. They group the algorithms into four categories corresponding to different approaches: quantum random walks, wave packet scattering, finding hidden symmetries, and simulating quantum physics. I hope many of you will enjoy learning more about, in their words, “the benefits of … studying the notion of an algorithm through the perspective of the physical laws of the universe.”