Recorded 26 July 2022. Fang Song of Portland State University presents "Introduction to quantum computing III" at IPAM's Graduate Summer School Post-quantum and Quantum Cryptography. Abstract: This lecture will introduce an alternative formalism of quantum information based on density matrices. We will study mixed states, purification, quantum channels, POVM measurement, distance measures of quantum states and operators, which will be useful in modeling and analyzing security of both post-quantum and quantum cryptography. Suggested reading: Watrous qc notes 14, 15; Watrous qi note 3,4. Learn more online at: https://www.ipam.ucla.edu/programs/summer-schools/graduate-summer-school-on-post-quantum-and-quantum-cryptography/?tab=overview