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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.

quantum algorithms for evaluating Boolean formulas. • InPart V, we describe quantum algorithms for simulating the dynamics of quantum systems. We also discuss an application of quantum simulation to an algorithm for linear systems. • InPart VI, we discuss adiabatic quantum computing, a general approach to solving optimization prob-

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