This course introduces the topic of quantum computation. We will discuss computer science topics such as gate sets, circuits, algorithms, and cryptography but is meant to be accessible for interested students in other departments such as Mathematics, Physics, and Engineering.

Topics covered:

• Quantum Information. The mathematical formalism of qubits, operations, and measurements. Superposition and entanglement. Teleportation, superdense coding, no-cloning theorem. Density operators, channels, positive operator-valued measures, purifications, Schmidt de-compositions, etc.

• Quantum Algorithms. Quantum gates and circuits. Deutsch’s algorithm, the Deutsch-Jozsa algorithm, Simon’s algorithm, Phase estimation, order finding, Grover’s algorithm, Shor’s factoring algorithm.

• Cryptography. The impossibility of bit-commitment, quantum key distribution.

• Nonlocality. Bell’s theorem and the Clauser-Horne-Shimony-Holt (CHSH) nonlocal game. Time permitting: The Mermin-Peres magic square game, the Greenberger-Horne-Zeilinger (GHZ) game.

• Specialty topics. Quantum computational complexity theory, quantum communication com-plexity, entropy and compression, random access codes, the Bloch sphere.

Course Web site: https://sites.google.com/site/jamiesikora/teaching/quantum-computation

Prerequisites
MATH 2114: Introduction to linear algebra (or an equivalent course). MATH 3144: Linear alge-bra I and MATH 4144: Linear algebra II (or equivalent courses) is recommended. Basic knowledge of probability theory.