PHY 265: Lecture notes

Lecture notes Topics
A short introduction to Quantum Mechanics - The qubit Quantum states, the qubit, Product spaces and 2 qubits, Superposition and Entanglement, Pauli, Hadamard and controlled gates, The Bloch sphere, Quantum Measurements, Interpretations of Quantum Mechanics, Bell's inequalities, Quantum Teleportation
Introducing Quantum Computing Boolean functions on a quantum computer, the 3-bit Toffoli gate, Universality on a quantum computer, Universal gate sets.
Introducing Quantum Information Quantum information, the density matrix, mixed and pure states, Shannon and von Neumann entropy, partial traces of the density matrix, Superoperators and quantum channels, the Holevo bound.
Introducing Quantum Error Correction A 3 bit codes for correcting a bit flip error, a 3 bit code for correcting phase flip errors, a 9-bit code for correcting all errors on a single qubit, Stabilizer codes, Random Benchmarking for measuring gate errors.
Introducing Quantum Algorithms Algorithm complexity, The N-bit Walsch-Hadamard operator, The Quantum Fourier Transform, Black-box quantum algorithms, Factoring and Period finding, Search algorithms, Phase estimation and counting solutions, Solving linear equations, Solving Boolean optimization problems, Adiabatic algorithms.
Miscellaneous Topics Weak measurements, Quantum Random Walks.