Starting today: Kazhdan Sunday seminar: “Computation, quantumness, symplectic geometry, and information”

Sunday, 27 October, 2019 – 14:00 to 16:00

Repeats every week every Sunday until Sat Feb 01 2020

Location: Ross 70

See also: Seminar announcement; previous post Symplectic Geometry, Quantization, and Quantum Noise.

The Google supremacy claims are discussed (with updates from time to time) in this earlier post. Don’t miss our previous post on combinatorics.

Tentative syllabus for “Computation, quantumness, symplectic geometry, and information”

1. Mathematical models of classical and quantum mechanics.

2. Correspondence principle and quantization.

3. Classical and quantum computation: gates, circuits, algorithms (Shor, Grover). Solovay-Kitaev. Some ideas of cryptography

4. Quantum noise and measurement, and rigidity of the Poisson bracket.

5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev’s surface code.

6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.

7. Time-energy uncertainty and quantum computation (Dorit or her student?)

8. Berezin transform, Markov chains, spectral gap, noise.

9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture [? under discussion]

10. Noise stability and noise sensitivity of Boolean functions, noisy boson sampling

11. Connection to quantum field theory (Guy?).

Literature: Aharonov, D. Quantum computation, In “Annual Reviews of Computational Physics” VI, 1999 (pp. 259-346). https://arxiv.org/abs/quant-ph/9812037

Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606. https://arxiv.org/abs/1801.02602

Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.

Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018. https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig…

Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9] https://sites.google.com/site/polterov/miscellaneoustexts/function-theor…

Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019. https://www.math.ias.edu/files/mathandcomp.pdf