Teaching

ECE 498EC Fall 2021

Course Description – This course introduces the basic concepts and principles underlying quantum computing and quantum communication theory.  Roughly 33% of the course will be devoted to teaching the necessary mathematical tools and principles of quantum information processing, 33% to quantum computation and communication, and 33% to entanglement theory.  The specific topics covered in this course are chosen to reflect areas of high interest within the research community over the past two decades.  The student will be expected to perform detailed mathematical calculations and construct proofs.  By the end of the semester, the student should be equipped with enough background and technical skill set to begin participating in quantum information research.

Format and Schedule –  Live lectures will be given in person T/R 3:00PM – 4:20PM, and these will also be recorded for future viewing.

Prerequisites – Linear algebra required; quantum mechanics, and probability/statistics recommended.

Textbook – The primary course material will be lecture notes generated by the instructor.  A suggested supplemental textbook is Quantum Computation and Quantum Information by M.A. Nielsen and I.L. Chuang.

Grading – Grades will be based on 50% homework, 25% Midterm, and 25% Final.

Four Credit Option – This course can be taken for four credits.  The additional credit requires writing a review paper on some quantum information research article.  The paper should be at least six pages in length and provide a background discussion of the paper, a derivation of the major results, and a conclusion describing future areas of research.  All papers to be reviewed must be pre-approved by the instructor, and suggested papers can also be provided.

Syllabus 

Lecture Main Topic Subtopics
Part I:
Fundamental Principles of Quantum Information Processing
1 The State Space Axiom Bras/kets, density operator
2 Qubits and Bloch Sphere
3 Multiple System Axiom Partial Trace, Reduced Density Operator
4 Schmidt Decomposition, Two-Qubit Systems
5 The State Evolution Axiom Unitary Evolution
6 Qubit and Multi-qubit gates
7 Completely-Positive Maps
8 The Choi Matrix and Qubit Channels
9 The Quantum Measurement Axiom Projective Measurements and Superdense Coding
10 Quantum Observables and Classical Knowledge
11 Quantum Instruments and POVMs
Part II:
No-Go’s and Optimal Approximations
12 Indistinguishable States and No-Cloning The Quantum State Discrimination Problem
13 Quantifying Closeness of Quantum States Trace Distance and Fidelity
14 Helstrom’s Measurement
15 Semi-Definite Programming and Optimal State Discrimination SDP, Duality, and KKT Conditions
16 Conditions for Min-Error State Discrimination
17 No-Signaling and Nonlocality No-Signaling and State Discrimination
18 Local Hidden Variable Models and Bell Inequalities
19 The CHSH Inequality
20 Tsierlen’s Inequality and Nonlocal Boxes
21 Quantum Steering
Part III:
Quantum Communication and Entanglement Theory
22 Quantum Teleportation Teleportation Protocols, Resource Trade-offs
23 Teleportation Fidelity, Local Twirling
24 Entanglement and Separability Local Operations and Classical Communication (LOCC)
25 Separability Criterion, PPT Entanglement
26 Detecting and Measuring Entanglement Entanglement Witnesses
27 Entanglement Measures
28 Asymptotic Entanglement Transformations Pure-state Entanglement Distillation
29 Mixed-state Entanglement Distillation
30 Bound Entanglement