Teaching

ECE 498EC Fall 2020

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 – All course activities will take place through a Microsoft Teams workspace.  This includes video lectures, notes, homework, and discussions.  Live lectures will be given T/R 3:00PM – 4:20PM, and these will be recorded for future viewing.  A 90-minute virtual office hours will be held 1:30PM-3:00PM every Friday.

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 Quantum Measurement Axiom Projective Measurements
9 Quantum Instruments and POVMs
10 LOCC
Part II:
No-Go Theorems and Optimal Approximations
11 Quantifying Closeness of Quantum States Trace Distance and Fidelity
State Discrimination
12 Diamond Norm
13 Quantum State Discrimination Minimum Error Discrimination
14 Unambiguous Discrimination
15 No Quantum Cloning No-cloning theorem, optimal cloners
16 No-Signaling No-signaling, LHV models, and PR-Boxes
Part III:
Quantum Communication
17 Quantum Communication Framework Communication Tasks
18 Classical Source Compression Shannon Entropy
19 Typicality
20 Quantum Source Compression Schumacher Compression
21 Quantum Teleportation Teleportation protocols, teleportation fidelity
22 LOCC twirling
Part IV:
Entanglement Theory
23 Entanglement and Separability Separability criterion, PPT entanglement
24 Entanglement Witnesses Convex separation theorem
25 Entanglement Measures and Monotones Bipartite monotones, convex roof extensions
26 Two-qubit entanglement
27 Single-Copy Entanglement Transformations Majorization criterion
28 Asymptotic Entanglement Transformations Pure-state
29 Mixed-state Entanglement distillation
30 Bound Entanglement