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Quantum Engineering Year 0: Mathematical Foundations Month 5Day 115

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Year 0·Month 5·Week 1

Day 115: Unitary Operators — Quantum Gates and Time Evolution

Day 115 of 2,016~11 min read

Learning Objectives

•Define unitary operators and their matrix representation
•Prove that unitary operators preserve inner products and norms
•Show that eigenvalues of unitary operators lie on the unit circle
•Understand the connection between Hermitian and unitary operators
•Apply unitary operators to quantum gates and time evolution
•Work with common quantum gates computationally

Today's Schedule (7 hours)

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On this page

1 Definition of Unitary Operators 2 Equivalent Characterizations 3 Eigenvalue Structure 4 Examples of Unitary Matrices Example 1 Rotation in Example 2 Hadamard Gate Example 3 Phase Gate Example 4 Pauli X Y Z 5 The Unitary-Hermitian Connection 6 Unitary Groups 7 Unitary Diagonalization Quantum Mechanics Connection Time Evolution Quantum Gates Why Unitary Two-Qubit Gates

Day 114Day 115 of 2,016Day 116