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Lecture Notes on Quantum Algorithms

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 .. Quantum complexity .. Fault tolerance ..3I Quantum circuits52 Efficient universality of Quantum Subadditivity of errors .. The group commutator and a net around the identity .. Proof of the Solovay-Kitaev Theorem .. Proof of Lemma ..93 Quantum circuit synthesis over Clifford+ Converting to Matsumoto-Amano normal form .. Uniqueness of Matsumoto-Amano normal form .. Algebraic characterization of Clifford+Tunitaries.

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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