Quantum Computation

PHY 420.001 (Selected Topics in Physics) --- Fall 2011 Syllabus

Physics Department --- Mercer University

 

This course is an introduction to the exciting emerging field of quantum computation and quantum information, including basic concepts in quantum physics and requisite mathematical tools. Topics include the algorithms of Deutsch, Grover, and Shor; error correction, cryptography, teleportation, and physical realizations of quantum computers.  It should be of interest to students in physics, mathematics, computer science and engineering. Pre-requisites are MAT 192 Calculus II and PHY 162 General Physics II, or their equivalent, or instructor approval.

The field of quantum information science includes quantum computation, quantum information and quantum control: It is a dynamic new area of inter-disciplinary research involving physicists, computer scientists, mathematicians and engineers. Any computation is essentially a (quantum) physical process. As computers get smaller and faster, we approach the molecular/atomic domain where strange quantum behavior is the norm. In particular, quantum physics offers an entirely new form of computational parallelism that will make quantum computers more powerful than conventional computers by many orders of magnitude.  Recent and future lines of investigation include the control of system coherence and decoherence; quantum computer algorithms; quantum cryptography and secure quantum communications; fundamental and practical understanding of entanglement, and how this can be used in novel processes like quantum teleportation; and the continuing work on physical systems for quantum computation, including the development of the necessary logic gates and error-correction techniques to bring this theory to practice.

 

The textbook gives a self-contained introduction to the field. It begins by presenting the quantum bit (qubit) and its main properties, followed by the necessary background in quantum mechanics. The core of the subject, quantum computation, is illustrated by a detailed treatment of three quantum algorithms: Deutsch, Grover and Shor. The final chapters are devoted to the physical implementation of quantum computers, including the most recent aspects, such as superconducting qubits and quantum dots, and to a short account of quantum information. The text is written at a level suitable for undergraduates in physical sciences: no previous knowledge of quantum mechanics is assumed, and only elementary notions of physics are required.

 

The primary goal of this course is for students to develop conceptual understanding of these topics rather than detailed knowledge, which they can gain in more advanced courses. The secondary goal is for students to learn the basic conceptual and mathematical  tools of quantum physics as applied to quantum computation and quantum information. We will explore most or all of the textbook content. When necessary, we will include supplementary material in basic quantum theory, differential equations, matrix algebra and linear algebra. These will be presented as they are required by students to fully appreciate the text material and to efficiently carry out calculations in homework sets and exams.

 

TEXTBOOK: A Short Introduction to Quantum Information and Quantum Computation, by Michel le Bellac, 178 pages, Cambridge University Press (2006), ISBN-10: 9780521860567, ISBN-13: 978-0521860567.

1. Introduction.

2. What is a qubit? Polarization of light, Photon polarization, Mathematical formulation: the qubit, Principles of quantum mechanics, Quantum cryptography

3. Manipulating qubits. The Bloch sphere: spin ½, Dynamical evolution, Manipulating qubits: Rabi oscillations, Principles of NMR and MRI

4. Quantum correlations. Two-qubit states, The state operator (or density operator), The quantum no-cloning theorem, Decoherence, The Bell inequalities

5. Introduction to quantum computing. Reversible calculation, Quantum logic gates, The Deutsch algorithm, Generalization to n+m qubits, The Grover search algorithm, The quantum Fourier transform, The period of a function, Classical algorithms and quantum algorithms

6. Physical realizations. NMR as a quantum computer, Trapped ions, Superconducting qubits, Quantum dots

7. Quantum information. Teleportation, Shannon entropy, von Neumann entropy, Quantum error correction

 

Lectures: Much of the class meeting time will be devoted to conventional lectures. We will go over the text in detail, including derivations. We will also discuss the material and go over textbook questions and problems, as well as homework and test problems.

Homework: For each covered chapter of the main text the instructor will assign one or more sets of homework problems to be worked by the students and handed in for grading. Students are encouraged to collaborate on these; however, each must hand in their own separate paper. After the papers are collected, a solution sheet will be provided. Altogether, the homework will count for 60% of the total grade.

Take-home Tests: There will be two of these, containing primarily numerical problems and derivations, but also some conceptual questions. The only resources allowed each student for these are the text, class notes and the instructor. Altogether, the take-home tests will count for 20% of the total grade.

Final Exam: This will take place on Monday 12/12 at 2-5pm. It will be both quantitative and qualitative, open-book, will cover all the material from the text, and will count for 20% of the total grade.  

Grading: The percentage for each activity is shown in the left table below. To convert the total percent to a letter grade, use the scale shown in the right table below.

# total % Homework sets 12 60 Tests 2 20 Final Exam 1 20     Total: 100

GP % A 4.0 90-100 B+ 3.5 85-89 B 3.0 80-84 C+ 2.5 75-79 C 2.0 70-74 D 1.0 60-69 F 0.0 0-59

Miscellaneous policies:

If changes to this syllabus are necessary, they will be implemented after discussion and negotiation with the students. Note that the accompanying course schedule is not a part of the syllabus: it is tentative and subject to revision, including all due dates.

Assignments are always due in class on the due date: However, they will not be considered late as long as they are turned in before the next sunrise. Beyond that, any late homework sets, take-home tests or essays will suffer a 5% penalty per day (excluding weekends and holidays) until they are handed in: i.e., 5% on the first day, 10% on the second day...

There  will be no dropped grades. All work done in the course will be counted. There will be no extra-credit work.

The  College of Liberal Arts' academic misconduct policy will be followed. In addition, all students are bound by the Mercer University Honor Code.

Students are strongly encouraged to discuss with the instructors all their work during the course, regardless of their grades. Questions about point awards should be brought up as soon as possible, as all grades will be final one week after the materials are graded and returned to the students.

Students requiring accommodations for a disability should inform the instructor at the close of the first class meeting or as soon as possible.  The instructor will refer you to the Disability Support Services Coordinator to document your disability, determine eligibility for accommodations under the ADAAA/Section 504 and to request a Faculty Accommodation Form.  Disability accommodations or status will not be indicated on academic transcripts.  In order to receive accommodations in a class, students with sensory, learning, psychological, physical or medical disabilities must provide their instructor with a Faculty Accommodation Form to sign.  Students must return the signed form to the Disability Services Coordinator.  A new form must be requested each semester.  Students with a history of a disability, perceived as having a disability or with a current disability who do not wish to use academic accommodations are also strongly encouraged to register with the Disability Services Coordinator and request a Faculty Accommodation Form each semester.  For further information, please contact Carole Burrowbridge, Disability Services Coordinator, at 301-2778 or visit the Disability Support Services website at http://www.mercer.edu/studentaffairs/disabilityservices

All requests for reasonable accommodation are welcome also in regard to absence from class for school representation (i.e., athletic or other events) or personal/family problems. Let's talk about it...