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CS191x: Quantum Mechanics and Quantum ComputationBerkeleyX

About CS191x

Quantum Mechanics and Quantum Computation

Quantum computation is a remarkable subject based on one of the great computational discoveries that computers based on quantum mechanics are exponentially powerful. This course aims to make this cutting-edge material broadly accessible to undergraduate students, including computer science majors who do not have any prior exposure to quantum mechanics. The course starts with a simple introduction to the fundamental principles of quantum mechanics using the concepts of qubits (or quantum bits) and quantum gates. This treatment emphasizes the paradoxical nature of the subject, including entanglement, non-local correlations, the no-cloning theorem and quantum teleportation. The course covers the fundamentals of quantum algorithms, including the quantum fourier transform, period finding, Shor's quantum algorithm for factoring integers, as well as the prospects for quantum algorithms for NP-complete problems.

Course staff

Umesh V. Vazirani

Umesh Vazirani is the Strauch Distinguished Professor of Electrical Engineering and Computer Science at University of California, Berkeley, and is the director of the Berkeley Quantum Information and Computation Center. Professor Vazirani has done foundational work on the computational foundations of randomness, algorithms and novel models of computation. His 1993 paper with Ethan Bernstein helped launch the field of quantum complexity theory. In 2007-08, he was appointed Keenan Visiting Professor for distinguished teaching at Princeton University. He is the author of two books An Introduction to Computational Learning Theory with Michael Kearns (MIT Press) and Algorithms with Sanjoy Dasgupta and Christos Papadimitriou (McGraw Hill).

Prerequisites

This is a cross-disciplinary class, with students with backgrounds in computer science, mathematics or physics. As far as possible, the class will be self-contained. In particular, you do not need prior knowledge of quantum mechanics. However, you must have a strong background in linear algebra and the ability to think abstractly. We assume that you are fairly comfortable with basic concepts of linear algebra such as vectors, matrices, complex numbers, inner products, eigenvalues and eigenvectors, etc. We do not require a deep understanding of computer science, but we will assume that you know some basics, such as big-Oh notation, what an algorithm is and how to bound the running time of an elementary algorithm.

Course Outline

The following is a tentative outline of the course.

Lecture 1: Introduction, double-slit experiment
Lecture 2: Qubits, axioms of quantum mechanics
Lecture 3: Two-qubit systems, entanglement
Lecture 4: EPR paradox, Bell's theorem
Lecture 5: Evolution of quantum systems
Lecture 6: Two-qubit gates, no cloning theorem, quantum teleportation
Lecture 7: Observables, Schrödinger's equation, continuous quantum systems
Lecture 8: Free particle in 1D, uncertainty relations, particle in a box, simple qubits
Lecture 9: Quantum circuits
Lecture 10: Fourier sampling, Simon's algorithm
Lecture 11: Quantum Fourier Transform, period finding
Lecture 12: Shor's factoring algorithm
Lecture 13: Unstructured quantum search
Lecture 14: Quantum complexity theory
Lecture 15-16: Spin, implementing a quantum computer in the lab

Frequently Asked Questions

What is the grading policy for this course?

There will be weekly assignments and a final exam. Your final grade will be based roughly 70% on the assignments and 30% on the final. The exact logistics as well as the cutoff for receiving a certificate of accomplishment will be announced in the first week.

Do I need a textbook for this class?

No. Notes will be posted each week. If you wish to consult other references, a list of related textbooks and online resources will be provided.

What is the estimated effort for course?

About 5-12 hrs/week.

Why is the work load range so wide?

How long you spend on the course depends upon your background and on the depth to which you wish to understand the material. The topics in this course are quite open ended, and will be presented so you can understand them at a high level or can try to follow it at a sophisticated level with the help of the posted notes.

How much does it cost to take the course?

Nothing! The course is free.

Will the text of the lectures be available?

Yes. All of our lectures will have transcripts synced to the videos.

Do I need to watch the lectures live?

No. You can watch the lectures at your leisure.

Will certificates be awarded?

Yes. Online learners who achieve a passing grade in a course can earn a certificate of mastery. These certificates will indicate you have successfully completed the course, but will not include a specific grade. Certificates will be issued by edX under the name of BerkeleyX, designating the institution from which the course originated.

Can I contact the Instructor or Teaching Assistants?

Yes, but not directly. The discussion forums are the appropriate venue for questions about the course. The instructors will monitor the discussion forums and try to respond to the most important questions; in many cases response from other students and peers will be adequate and faster.