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Mathematics of Materials and Macromolecules

New Directions Short Course:

Quantum Computation

August 15-26, 2005

Principal Speakers:

Alexei Kitaev

Department of Physics & Computer Science
California Institute of Technology
http://www.iqi.caltech.edu/people/kitaev_a.html

Peter W. Shor

Department of Mathematics
Massachusetts Institute of Technology
http://www-math.mit.edu/~shor/

Schedule Participants Survey
New Directions Program
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Photo Gallery Talk Materials

Description:

From August 15-26, 2005 the IMA will host an intensive short course designed to efficiently provide mathematicians the basic knowledge prerequisite to undertake research in quantum computation. The course will be taught by Peter Shor, Professor of Mathematics at MIT and Alexei Kitaev, Professor of Physics and Computer Science, Caltech. The primary audience for the course is mathematics faculty. No prior background in quantum computation is expected. Participants will receive full travel and lodging support during the workshop.

Course content and structure. The course will begin with an introduction to quantum mechanics and quantum computation. Then it will pursue two tracks: quantum algorithms and error correction led by Peter Shor, and topological quantum computation, led by Alexei Kitaev. A typical day during the two weeks course will consist of two general lectures, one by the principal speakers in the morning, each one-and-a-half hours in duration. Afternoons will be used for topical lectures by guest speakers, and for problem solving and brain-storming sessions.

Application and selection procedure. The IMA New Directions Short Courses will be limited to 25 participants. All successful applicants will be funded for travel and local expenses. Please see the IMA reimbursement policy for details about airfare. Applicants are required to submit a curriculum vita and a statement about their interest in the course, its place in their future research plans, and its expected impact on their research and teaching. A committee consisting of the course instructors and IMA directors will select the participants from among the applicants. Application deadline has passed.

Schedule
Monday, August 15
8:30a-10:00a Lecture: Introduction, quantum states, operations, etc. Peter W. Shor (Massachusetts Institute of Technology) Lind Hall 409
10:00a-10:30a Break   Lind Hall 400
10:30a-12:00p Lecture: Overview Alexei Kitaev (California Institute of Technology) Lind Hall 409
12:00p-1:30p Lunch    
1:30p-3:30p Problem Solving and Brain Storming Session   Lind Hall 409
3:45p-4:00p Group Photo    
4:00p-5:00p Reception   Lind Hall 400
Tuesday, August 16
8:30a-10:00a Lecture: Teleportation, superdense coding, introduction to quantum error correcting codes Peter W. Shor (Massachusetts Institute of Technology) Lind Hall 409
10:00a-10:30a Break   Lind Hall 400
10:30a-12:00p Lecture: The toric code and its variations Alexei Kitaev (California Institute of Technology) Lind Hall 409
12:00p-1:30p Lunch    
1:30p-2:30p Problem Solving and Brain Storming Session   Lind Hall 409
Wednesday, August 17
8:30a-10:00a Lecture: Algorithms - periodicity Peter W. Shor (Massachusetts Institute of Technology) Lind Hall 409
10:00a-10:30a Break   Lind Hall 400
10:30a-12:00p Lecture: Spin Hamiltonians, ground states and excitations Alexei Kitaev (California Institute of Technology) Lind Hall 409
12:00p-1:30p Lunch    
1:30p-2:30p Problem Solving and Brain Storming Session   Lind Hall 409
Thursday, August 18
8:30a-10:00a Lecture: Algorithms - Grover's algorithm and quantum walk algorithms Peter W. Shor (Massachusetts Institute of Technology) Lind Hall 409
10:00a-10:30a Break   Lind Hall 400
10:30a-12:00p Lecture: Lattice models based on discrete groups Alexei Kitaev (California Institute of Technology) Lind Hall 409
12:00p-1:30p Lunch    
1:30p-2:30p Problem Solving and Brain Storming Session   Lind Hall 409
6:30p-8:30p Dinner   Loring Pasta Bar 
Friday, August 19
8:30a-10:00a Lecture: Measures of entanglement Peter W. Shor (Massachusetts Institute of Technology) Lind Hall 409
10:00a-10:30a Break   Lind Hall 400
10:30a-12:00p Lecture: Quantum computation with S_3 anyons Alexei Kitaev (California Institute of Technology) Lind Hall 409
12:00p-1:30p Lunch    
1:30p-2:30p Problem Solving and Brain Storming Session   Lind Hall 409
Saturday, August 20
All Day No lecture scheduled.    
Sunday, August 21
All Day No lecture scheduled.    
Monday, August 22
8:30a-10:00a Lecture: Quantum channels and their capacities Peter W. Shor (Massachusetts Institute of Technology) Lind Hall 409
10:00a-10:30a Break   Lind Hall 400
10:30a-12:00p Lecture:The honeycomb lattice model Alexei Kitaev (California Institute of Technology) Lind Hall 409
12:00p-1:30p Lunch    
1:30p-2:30p Problem Solving and Brain Storming Session   Lind Hall 409
Tuesday, August 23
8:30a-10:00a Lecture: Quantum cryptography Peter W. Shor (Massachusetts Institute of Technology) Lind Hall 409
10:00a-10:30a Break   Lind Hall 400
10:30a-12:00p Lecture: Algebraic theory of anyons Alexei Kitaev (California Institute of Technology) Lind Hall 409
11:30a-1:00p Lunch    
1:30p-2:30p Quantum Proofs John Watrous (University of Calgary) Lind Hall 409
2:30p-3:30p Problem Solving and Brain Storming Session   Lind Hall 409
Wednesday, August 24
8:30a-10:00a Lecture: Quantum fault-tolerant computation Peter W. Shor (Massachusetts Institute of Technology) Lind Hall 409
10:00a-10:30a Break   Lind Hall 400
10:30a-12:00p Lecture: Algebraic theory of anyons, cont. Alexei Kitaev (California Institute of Technology) Lind Hall 409
12:00p-1:30p Lunch    
1:30p-2:30p Problem Solving and Brain Storming Session   Lind Hall 409
Thursday, August 25
8:30a-10:00a Lecture: Quantum error correcting codes: the stabilizer construction Peter W. Shor (Massachusetts Institute of Technology) Lind Hall 409
10:00a-10:30a Break   Lind Hall 400
10:30a-12:00p Lecture:Computation with Fibonacci anyons Alexei Kitaev (California Institute of Technology) Lind Hall 409
1:30p-2:30p Problem Solving and Brain Storming Session   Lind Hall 409
Friday, August 26
8:30a-10:00a Lecture: Additivity questions in quantum information theory Peter W. Shor (Massachusetts Institute of Technology) Lind Hall 409
10:00a-10:30a Break   Lind Hall 400
10:30a-12:00p Lecture: More models and the physical perspective Alexei Kitaev (California Institute of Technology) Lind Hall 409
12:00p-1:30p Lunch    
1:30p-2:30p Problem Solving and Brain Storming Session   Lind Hall 409
2:30p-2:45p Wrap up   Lind Hall 409

LIST OF CONFIRMED PARTICIPANTS

Name Department Affiliation
Douglas N. Arnold Institute for Mathematics and its Applications University of Minnesota
John Baxter School of Mathematics University of Minnesota
Animikh Biswas Department of Mathematics and Statistics University of North Carolina - Charlotte
Suneal K. Chaudhary Department of Mathematics University of Utah
Jintai Ding Department of Mathematical Sciences University of Cincinnati
John Rhodes Dixon Department of Statistics Florida State University
Lara Faoro Department of Physics Rutgers University
Paul Garrett School of Mathematics University of Minnesota
Jason Gower Department of Mathematical Sciences University of Cincinnati
Palle E. T. Jorgensen Department of Mathematics University of Iowa
Alexei Kitaev Department of Physics & Computer Science California Institute of Technology
Soumendra Nath Lahiri Department of Statistics Iowa State University
Melvin Leok Department of Mathematics University of Michigan
Debra Lewis Institute for Mathematics and its Applications University of Minnesota
Chjan Chin Lim Department of Mathematical Sciences Rensselaer Polytechnic Institute
Enbing Lin Department of Mathematics University of Toledo
Elebeoba E. May Department of Computational Biology Sandia National Laboratories
David Meintrup EIT 1 University of the Federal Arms Munich
Oleg Pikhurko Department of Mathematical Sciences Carnegie Mellon University
Karel L. Prikry School of Mathematics University of Minnesota
Maurice Rahe Department of Mathematics Texas A & M University
S. S. Ravindran Department of Mathematical Sciences University of Alabama - Huntsville
Arnd Scheel Institute for Mathematics and its Applications University of Minnesota
Tanush Shaska   University of Idaho
Peter W. Shor Department of Mathematics Massachusetts Institute of Technology
Warren Sinnott Department of Mathematics Ohio State University
Kai-Sheng Song Department of Statistics Florida State University
Tzyh-Jong Tarn Department of Systems Science & Mathematics Washington University
Pham Huu Tiep Department of Mathematics University of Florida
Igor Tsukerman Department of Electrical & Computer Engineering University of Akron
Imre Tuba UMM Division of Science and Mathematics University of Minnesota - Morris
John Watrous Department of Computer Science University of Calgary

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