ECE633

Quantum Information Processing and Quantum Error Correction
Fall
Catalog Data: 

Graduate Course Information

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ECE 633 -  Quantum Information Processing and Quantum Error Correction

Course Description

The ECE 633 course is a self-contained introduction to quantum information, quantum computation, and quantum error-correction. The course starts with basic principles of quantum mechanics including state vectors, operators, density operators, measurements, and dynamics of a quantum system. The course continues with fundamental principles of quantum computation, quantum gates, quantum algorithms, and quantum teleportation. A significant amount of time has been spent on quantum error correction codes (QECCs), in particular on stabilizer codes, Calderbank-Shor-Steane (CSS) codes, quantum low-density parity-check (LDPC) codes, subsystem codes (also known as operator-QECCs), topological codes and entanglement-assisted QECCs. The next topic in the course is devoted to the fault-tolerant QECC and fault-tolerant quantum computing. The course continues with quantum information theory. The next part of the course is spent investigating physical realizations of quantum computers, encoders and decoders; including photonic quantum realization, cavity quantum electrodynamics, and ion traps. The course concludes with quantum key distribution (QKD).

Course Objectives

This course offers in-depth exposition on the design and realization of a quantum information processing and quantum error correction. The successful student will be ready for further study in this area, and will be prepared to perform independent research. The student completed the course will be able design the information processing circuits, stabilizer codes, CSS codes, subsystem codes, topological codes and entanglement-assisted quantum error correction codes; and propose corresponding physical implementation. The student completed the course will be proficient in fault-tolerant design as well.

Course web page: http://www2.engr.arizona.edu/~ivan/ECE633/

Grading:  Regular grades will be awarded for this course: A B C D E.

Grading Policy

Homework

20%

Project

30%

Midterm Exam

15%

Final Exam

35%

Usually offered:  Fall, every second year. The course should alternate with ECE 638 (Wireless Communications).

Homeworks

Homeworks will be assigned approximately every 2 weeks.  

Prerequisite(s): 
ECE 501-B (or equivalent). Typically, basic linear algebra is sufficient.
Course Topics: 

I.              Introduction to Quantum Mechanics

A.            State Vectors

B.            Operators, Projection Operators, and Density Operators

C.            Measurements, and Uncertainty Relations

D.            Dynamics of a Quantum System

II.             Quantum Gates, Computation, Algorithms and Teleportation

A.            Superposition Principle, Quantum Parallelism, Entanglement and Decoherence

B.            Single Qubit Gates

C.            Multiple Qubit Gates, and Controlled Operations

D.            Universal Quantum Gates

E.            Deutsch’s Algorithm, and Deutsch-Jozsa Algorithm

F.            Grover Search Algorithm

G.            Quantum Fourier Transform

H.            Quantum Teleportation

III.            Quantum Error-Correction Codes (QECCs)

A.            Introduction to QECC

B.            Discretization of Errors, and Quantum Channel Models

C.            Bounds on quantum error correcting codes: quantum Hamming bound, quantum Gilbert-Varshamov bound, quantum Singleton bound, …

D.            Stabilizer Codes

E.            Calderbank-Shor-Steane (CSS) Codes

F.            Subsystem Codes

G.            Topological Codes

H.            Entanglement-Assisted QECCs

I.              Quantum LDPC Codes

IV.           Fault-Tolerant QECC and Fault-tolerant Quantum Computation

A.            Fault-tolerance basics and fault-tolerant  quantum computation concepts

B.            Fault-tolerant quantum error correction

C.            Fault-tolerant quantum computation

D.            Accuracy threshold theorem

V.            Physical Realization of Quantum Computers, Encoders and Decoders

A.            Nuclear magnetic resonance (NMR) in quantum computing

B.            Trapped Ions in quantum computing

C.            Photonic quantum implementations

D.            Photonic implementation of quantum relay

E.            Implementation of quantum encoders and decoders

F.            Cavity quantum electrodynamics (CQED)-based quantum information processing

G.            Quantum dots in quantum information processing

VI.           Quantum Information Theory

A.            Shannon Entropy

B.            Von Neumann Entropy

C.            Schumacher’s Quantum Noiseless Coding Theorem

D.            Holevo-Schumacher-Westmoreland Theorem

E.            Quantum Fano Inequality

VII.          Quantum Key Distribution (QKD)

Prepared by: 
Ivan B. Djordjevic
Prepared Date: 
April 2013

University of Arizona College of Engineering