ECE 633: Quantum Information Processing and Quantum Error Correction


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Course Syllabus


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.

Class website: http://ece.arizona.edu/~ivan/ECE633

Course Description

This 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 information processing (QIP), 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, topological codes, and entanglement-assisted QECCs. The next topic in the course is devoted to the quantum information theory, followed by the quantum key distribution (QKD). The next part of the course is spent investigating physical realizations of QIP devices and quantum computers, encoders and decoders; including photonic quantum realization, cavity quantum electrodynamics, and ion traps. The course concludes with  fault-tolerant QECC and fault-tolerant QIP.

Instructor

Ivan B. Djordjevic, Professor
Office: ECE 456B
Phone: 626-5119
Email: ivan <at> email <dot> arizona <dot> edu

Class time and location: Monday and Wednesday, 5 p.m.-6:15 p.m., Location: Elec & Comp Engr, Rm 102

Reference books [not required, available through library (both electronic and hard copies)]

  • I. B. Djordjevic, Quantum Information Processing and Quantum Error Correction: An Engineering Approach. Elsevier/Academic Press, Apr. 2012.

  • F. Gaitan, Quantum Error Correction and Fault Tolerant Quantum Computing.  CRC Press, 2008.

Office Hours

Noon - 1:00 PM, Monday and Wednesday

Prerequisites

ECE501B (or equivalent). Typically, basic linear algebra is sufficient.

Homeworks

Homeworks will be assigned approximately every 2 weeks.

Final Exam

Monday 12/10/2018 6:00 pm - 8:00 pm

Grading

Homework

  0%

Term Project

30%

Midterm Exam

30%

Final Exam

40%

Tentative Course Outline

  •  Quantum Mechanics Fundamentals

a. State Vectors

b. Operators, Projection Operators, and Density Operators

c. Measurements, and Uncertainty Relations

d. Dynamics of a Quantum System

  • Quantum Circuits, Quantum Information Processing (QIP), Quantum Algorithms

a. Single-qubit, two-qubit, and N-qubit operations

b. Qubit measurements, universal quantum gates, and quantum teleportation

c. Superposition principle, quantum parallelism, no-cloning theorem, distinguishing quantum states, entanglement, Schmidt decomposition

d. Deutsch's algorithm, Deutsch-Jozsa algorithm, Grover search algorithm, quantum Fourier transform, Shor factoring algorithm

  • Quantum Error-Correction Codes (QECCs)

 a. Introduction to QECCs: three-qubit flip code, three-qubit phase-flip code, Shor's nine-qubit code

b. Stabilizer code concepts, relationship between classical and quantum codes, quantum cyclic codes, CSS codes, quantum codes over GF(4) 

c. Redudancy and quantum error correction, stabilizer group, quantum-check matrix and syndrome equation, necessary and sufficient conditions for QECC, distance properties of QECCs, CSS codes (revisited), encoding and decoding circuits for QECC

 d. Important quantum coding bounds: Quantum Hamming bound, Quantum Gilbert-Varshamov bound, Quantum Singleton (Knill-Laflamme) bound, quantum weight enumerators, quantum MacWilliams identity 

e. Quantum operations (superoperators) and quantum channel models: operator-sum representation, generalized measurements, depolarizing channel, amplitude damping channels, etc.

 f. Stabilizer Codes and beyond: stabilizer codes, encoded operations, finite geometry interpretation, standard from of stabilizer codes, efficient encoding and decoding, nonbinary stabilizer codes

g. Subsystem codes, topological codes, entanglement-assisted quantum codes

h. Quantum LDPC Codes

  • Quantum Information Theory

a. Shannon entropy and Von Neumann entropy

b. Holevo information, accessible information, and Holevo bound 

c. Quantum data compression and Schumacher's noiseless coding theorem

d. Holevo-Schumacher-Westmoreland (HSW) theorem

  •  Quantum Key distribution (QKD)

  • Physical Realization of QIP, Encoders and Decoders

a. Nuclear magnetic resonance (NMR) in QIP

b. Trapped ions in QIP

c. Photonic quantum implementations

d.  Photonic implementation of quantum relay, implementation of quantum encoders and decoders

e. Cavity quantum electrodynamics (CQED)-based QIP

f. Quantum dots in QIP

  • Fault-Tolerant QECC and Fault-tolerant QIP

  a. Fault-tolerance basics and fault-tolerant  QIP concepts

  b. Fault-tolerant quantum error correction

  c. Fault-tolerant quantum information processing

  d. Accuracy threshold theorem

 

Study Groups

Working in study groups can be beneficial if everyone participates. Therefore, while working in study groups is allowed and even encouraged, all work submitted for a grade must be your own.