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.

for an arbitrary superposition over the group. We assume that there is some canonical way of e ciently representing group elements using bit strings; it is usually unnecessary to make this representation explicit. If a quantum computer stores the state j iand the state j˚i, its overall state is given by the tensor product of those two states.

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