PHY631: Quantum computation and quantum information

[Cr:4, Lc:3, Tt:1, Lb:0]

Introducing quantum mechanics. Quantum kinematics, quantum dynamics, quantum measurements. (The course is self contained and does not assume a background in quantum mechanics). Single qubit, multiqubits, gates. Density operators, pure and mixed states, quantum operations, environmental effect, decoherence. Quantum no-cloning, quantum teleportation.
Cryptography, classical cryptography, introduction to quantum cryptography. BB84, B92 protocols. Introduction to security proofs for these protocols.
Introduction to quantum algorithms. Deutsch-Jozsa algorithm, Grover's quantum search algorithm, Simon's algorithm. Shor's quantum factorization algorithm.
Errors and correction for errors. Simple examples of error correcting codes in classical computation. Linear codes. Quantum error correction and simple examples. Shor code. CSS codes.
Quantum correlations, Bell's inequalities, EPR paradox. Theory of quantum entanglement. Entanglement of pure bipartite states. Entanglement of mixed states. Peres partial transpose criterion. NPT and PPT states, bound entanglement, entanglement witnesses.
Physical realization of qubit system. Different implementations of quantum computers. NMR and ensemble quantum computing, Ion trap implementations. Optical implementations.