Review of basics of quantum information and computational complexity; Simple quantum algorithms; Quantum Fourier transform and Shor factoring algorithm: Amplitude amplification, Grover search algorithm and its optimality; Completely positive trace-preserving maps and Kraus representation; Non-locality and communication complexity; Physical realizations of quantum computation: requirements and examples; Quantum error-correction, including CSS codes, and elements of fault-tolerant computation; Quantum cryptography; Security proofs of quantum key distribution protocols; Quantum proof systems. Familiarity with theoretical computer science or quantum mechanics will also be an asset, though most students will not be familiar with both.
QIC 750Quantum Information Processing Devices0.50 units
This course introduces the fundamental concepts and the most recent achievements in physical realization of quantum information devices and systems in three platforms; Nuclear Magnetic Resonance (NMR), quantum photonics, and superconducting electric circuits.
Fundamentals of quantum information theory including states, measurements, operations, and their representations as matrices; measures of distance between quantum states and operations; quantum Shannon theory including von Neumann entropy, quantum noiseless coding, strong subadditivity of von Neuman entropy, Holevo's Theorem, and capabilities of quantum channels; theory of entanglement including measures of entanglement, entanglement transformation, and classifications of mixed-state entanglement; other topics in quantum information as time permits.
An investigation of algorithms that allow quantum computers to solve problems faster than classical computers. The quantum circuit model, Quantum Fourier transform, phase estimation, computing discrete logarithms, period finding, and quantum algorithms for number fields. The hidden subgroup framework and the non-Abelian hidden subgroup problem. Quantum search, amplitude amplification, and quantum walk algorithms. Limitations on the power of quantum computers. Selected current topics in quantum algorithms.
Review of the axioms of quantum theory and derivation of generalized axioms by considering states, transformations, and measurements in an extended Hilbert space. Master equations and the Markov approximation. Standard models of system-environment interactions and the phenomenology of decoherence. Introduction to quantum control with applications in NMR, quantum optics, and quantum computing.
QIC 880Nanoelectronics for Quantum Information Processing0.50 units
Electrodynamics of superconductors, BCS theory and tunnel junctions, the Josephson effect, flux and fluxoid quantization, quantization of electric circuits, the basic types of superconducting qubits, decoherence in the solid state, circuit quantum electrodynamics, readout of nanoscale qubits, fabrication of qubit devices, measurement techniques.
QIC 885Quantum Electronics and Photonics0.50 units
The course is introductory and emphasizes the fundamental concepts and engineering applications without a previous exposure to quantum mechanics. Examples and problems are designed to address the applications of the course contents to real problems in electronic, optoelectronic, photonic and superconductive devices.