Lecture Notes on Quantum Algorithms

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Lecture Notes onQuantum AlgorithmsAndrew M. ChildsDepartment of Computer Science,Institute for Advanced Computer Studies, andJoint Center for Quantum Information and Computer ScienceUniversity of Maryland29 April 2021iiContentsPrefacevii1 Quantum data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quantum circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Universal gate sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reversible computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Uniformity.

These notes were originally prepared for a course that was o ered three times at the University of Waterloo: in the winter terms of 2008 (as CO 781) and of 2011 and 2013 (as CO 781/CS 867/QIC 823). I thank the students in the course for their feedback on the lecture notes. Each o ering of the course covered a somewhat di erent set of topics.

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