Group meeting (Summer quarter 2009)

Room & time: AP&M 7218, Mondays and Thursdays 2:00pm-3:30pm

Description

This is an informal seminar on applicable mathematics, especially quantum computing [Nielsen & Chuang], for the group of students, postdocs and faculty who are working on these topics. Potentially interested students, graduate or undergraduate, are welcome to attend.

Schedule (incremental)

31 aug 09 David Meyer: "More than useless quantum queries"
background: Hunziker, et al.
27 aug 09 Jamie Pommersheim: "Classical decoding of Reed-Muller codes"
24 aug 09 Jean-Christophe Gomez-Lavocat: "Quantum learning algorithms for Hamming distance oracles"
background: Hunziker, et al.
20 aug 09 Orest Bucicovschi: "Quantum algorithm for Pell's equation"
background: Hallgren
17 aug 09 Jon Grice: "Decoding Reed-Muller codes"
background: Barg & Zhou
13 aug 09 Andrew Shao: "Multiparticle simulation of a piston"
background: Hurtado & Redner
10 aug 09 Ben Wilson: "Generalized persistence"
background: Carlsson
6 aug 09 no meeting
3 aug 09 no meeting
30 jul 09 David Meyer: "Towards simulating correlated binary random variables"
27 jul 09 no meeting
23 jul 09 no meeting
20 jul 09 no meeting
15 jul 09 David Meyer: "Using wavelets to estimate long-range dependence"
background: Flandrin
13 jul 09 Matt Cha: "Solitonic solutions to 1-dimensional nonlinear PDEs"
background: Arovas notes, Eilenberger
9 jul 09 Tyler Ross: "A potential physical solution to P = NP"
background: Abrams & Lloyd, Czachor
6 jul 09 Jean-Christophe Gomez-Lavocat: "The MAJORITY problem"
background: Hunziker, et al.
2 jul 09 Nolan Wallach: "Hidden subgroups in ax+b groups revisited"
29 jun 09 Jon Grice: "Integrals on the space of density matrices" and "Algebraic characterization of X-states"
background: Blume-Kohout, Rau
24 jun 09
wednesday 		David Meyer: "Discrete nonlinear Dirac equations in 1+1 dimensions"
18 jun 09 Organization
David Meyer: "Grover's algorithm and perceptron learning"

Bibliography

[1] D. S. Abrams and S. Lloyd, "Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems", arXiv:quant-ph/9801041.
[2] D. Arovas, "Solitons", Physics 221A lecture notes, Chap. 10.
[3] A. Barg and S. Zhou, "A quantum decoding algorithm for the simplex code", in Proceedings of the 36th Annual Allerton Conference on Communication, Control and Computing (1998).
[4] R. Blume-Kohout, "Optimal, reliable estimation of quantum states", arXiv:quant-ph/0611080.
[5] G. Carlsson, "Topology and data", Bulletin of the AMS 46 (2009) 255-308.
[6] M. Czachor, "Notes on nonlinear quantum algorithms", arXiv:quant-ph/9802051.
[7] M. Czachor, "Local modification of the Abrams-Lloyd nonlinear algorithm", arXiv:quant-ph/9803019.
[8] G. Eilenberger, Solitons: Mathematical Methods for Physicists (New York: Springer-Verlag 1981).
[9] P. Flandrin, "Wavelet analysis and synthesis of fractional brownian motion", IEEE Transactions on Information Theory 38 (1992) 910-917.
[10] S. Hallgren, "Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem", Journal of the ACM 54 (2007) 1-19.
[11] M. Hunziker, D. A. Meyer, J. Park, J. Pommersheim and M. Rothstein, "The geometry of quantum learning", arXiv:quant-ph/0309059.
[12] P. I. Hurtado and S. Redner, "Simplest piston problem. I. Elastic collisions", Physical Review E 73 (2006) 016136.
[13] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge: Cambridge University Press 2000) [website].
[14] A. R. P. Rau, "Algebraic characterization of X-states in quantum information", arXiv:0906.4716.
Last modified: 30 aug 09.