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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 .. From exact to approximate synthesis ..14II Quantum Algorithms for algebraic problems154 The abelian Quantum Fourier transform and phase Quantum Fourier transform.

This is a set of lecture notes on quantum algorithms. It is primarily intended for graduate students who have already taken an introductory course on quantum information. Such a course typically covers only the early breakthroughs in quantum algorithms, namely Shor’s factoring algorithm (1994) and Grover’s searching algorithm (1996).

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