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Seminar for Graduate Students in Theoretical Physics

Seminar for Graduate Students in Theoretical Physics Speaker: Yong Zhang (School of Physics and Technology, University Wuhan ) Place : Teaching Building I-107, Wuhan University Time ： PM 3:45-4:45, December 5, 2014. Integrable Quantum Computing (2004-2011-2014). 1.

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Seminar for Graduate Students in Theoretical Physics

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  1. Seminar for Graduate Students in Theoretical Physics Speaker: Yong Zhang (School of Physics and Technology, University Wuhan ) Place: Teaching Building I-107, Wuhan University Time：PM 3:45-4:45, December 5, 2014 Integrable Quantum Computing (2004-2011-2014) ＩＱＣ： 1

  2. Quantum Mechanics Niels Bohr: For those who are not shocked when they first come across quantum theory can not possibly have understood it. Albert Einstein: Quantum mechanics: Real black magic calculus. Richard Feynman: I think I can safely say that nobody understands quantum mechanics. ＩＱＣ： 2

  3. Quantum Information and Computation Quantum information and computation represents a modern development of quantum mechanics, and can be regarded as a new kind of advanced quantum mechanics! ＩＱＣ： 3

  4. Special Distinguished Performance Award Paul A. Benioff was honored for his pioneering work that first proved that quantum computing was a theoretical possibility. Front, from left, Paul A. Benioff, Laboratory Director Hermann A. Grunder. Back, from left: University of Chicago Vice President for Research and Argonne National Laboratory Robert J. Zimmer and University of Chicago President Don Randel. ＩＱＣ： 4

  5. ＩＱＣ： 5

  6. “ Computers are physical objects, and computations are physical processes” ----- David Deutsch (1985) Computer Physical system Computation Motion Input Initial state Rules Law of motion Output Final state ＩＱＣ： 6

  7. Quantum Gates Quantum Circuit Model: A network consisting of a). Object: qubit （two-dimensional Hilbert space） b). Operation: quantum gate （unitary transformation） qubit qubit 7 ＩＱＣ：

  8. Type Topological and Integrable Quantum Computing Item In Topological quantum computing, quantum gates are solutions of the braid group relation. In Integrable quantum computing, quantum gates are solutions of the Yang—Baxter equation. ＩＱＣ： 8

  9. The Yang--Baxter Equation Jacques H.H. Perk, Helen Au-Yang, Yang-Baxter Equations, arXiv: math-ph/0606053 9 ＩＱＣ：

  10. Topological Quantum Computing (1997-2000) • New models: Kitaev’s models (1997): • Known models: Topological quantum field theory Freedman, Larsen, Wang (2000) Fractional quantum Hall effect New paradigm iN physics (Xiao-Gang Wen) ＩＱＣ： 10

  11. Quantum Computing via the Yang—Baxter equation (2004) Zhang, Louis H. Kauffman and Mo-Lin Ge, arXiv:quant-ph/0412095 Int. J. Quantum Information, Vol.3, No.4, pp.669-678, 2005. ＩＱＣ： 11

  12. Quantum Computing via the Yang—Baxter equation Zhang, Kauffman, Ge, arXiv:quant-ph/0412095; arXiv:quant-ph/0502015 ＩＱＣ： 12

  13. Zhang, Kauffman, Ge, arXiv:quant-ph/0412095; arXiv:quant-ph/0502015 ＩＱＣ： 13

  14. What is the physics underlying a quantum computer? (quantum computer as quantum circuit model) David Deutsch: Quantum computing supports the existence of Many Worlds( the many-universes interpretation of quantum mechanics ) Philosophy! ＩＱＣ： 14

  15. “A detailed examination and attempted justification of the physics underlying the quantum circuit model is outside the scope of the present discussion, and, indeed, outside the scope of present knowledge!” Nielsen & Chuang, “Quantum Information and Quantum Computation”, pp 203-204, 2000 Nielsen & Chuang, “Quantum Information and Quantum Computation”, pp 203-204, 2011 ＩＱＣ： 15

  16. What is the physics underlying quantum circuit model? Zhang arXiv:1106.3982 The physics underlying the quantum circuit model is associated with an exactly solvable model satisfying the integrable condition Quantum Information Processing, Vol.11, No.2, pp. 585-590, 2012. ＩＱＣ： 16

  17. 3-qubit Quantum Gates 2-qubit gate 2-qubit gate David DiVincenzo (1994): An arbitrary N-qubit quantum gate can beexpressed exactly as a sequence of products of some two-qubit gates. 2-qubit gate 2-qubit gate Locality principle （Preskill, online lecture notes, 1997-1998 ）. ＩＱＣ： 17

  18. Murray T. Batchelor （2007）：“His ansatz thus effectively factorizes interactions among many particles into two-body interactions. Such factorization is intimately entwined with the concept of integrability.” Bethe Ansatz H. A. Bethe, Z. Phys. 71, 205 (1931). ＩＱＣ： 18

  19. Feynman (May 11, 1918 – February 15, 1988) I got really fascinated by these (1 + 1) dimensional models that are solved by the Bethe ansatz and how mysteriously they jump out at you and work and you don’t know why. I am trying to understand all this better. ( Feynman, Asia-Pacific Physics News 3, 22 (June/July 1988)). Feynman (1982). Simulating Physics with Computers. International Journal of Theoretical Physics21 (6–7): 467–488 Feynman (1986).Quantum Mechanical ComputersFoundations of Physics, Vol. 16, No. 6, 1986 春秋·鲁·孔丘《论语·泰伯》： “曾子言曰：鸟之将死，其鸣也哀；人之将死，其言也善” 19

  20. Quantum Computing via the Bethe Ansatz (2011) Factorisable scattering in BA Quantum circuit model 1. qubit: spin-1/2 particles or others; 2. two-qubit quantum gate: two-body scattering matrix; 3. N-qubit quantum gate: N-body scattering matrix Zhang, arXiv:1106.3982 Quantum Information Processing, Vol.11, No.2, pp. 585-590, 2012. ＩＱＣ： 20

  21. One-dimension delta-function interaction model • C.N. Yang, Phys. Rev. Lett. 19 (1967) 1312-1314. Model: N spin-1/2 particles (qubits) in one-dimension two-body scattering operator (two-qubit gate) ＩＱＣ： 21

  22. Quantum Computing viadelta-function interaction model Two-body scattering operator = two-qubit quantum gate Ref. 1. Bose and Korepin, arXiv:1106.2329 Ref.2. Zhang, arXiv:1106.3982. ＩＱＣ： 22

  23. Quantum Computing viadelta-function interaction model Construction of an entangling two-qubit (the root of Swap gate) Universal quantum computation = the root of the Swap gate + single-qubit transformations Zhang, arXiv:1106.3982 ＩＱＣ： 23

  24. XXX spin chain: Heisenberg Interaction Universal quantum computation via Heisenberg interaction D.P. DiVincenzo et al., Nature 408, 339-342 (16 Nov. 2000) Delta-function interaction vs. Heisenberg interaction Zhang, arXiv:1106.3982 ＩＱＣ： 24

  25. Definitions of Integrable Quantum Computing 1. Quantum computing via the Yang—Baxter equation Zhang, arXiv:0801.2561 (2008/01) 2. Quantum computing via the Beth ansatz Zhang, arXiv:1106.3982 (2011/06) ＩＱＣ： 25

  26. Integrable quantum computing (2011) With the support of Professor Lu Yu, I have made a formal proposal on Integrable Quantum Computing during my visiting Institute of Physics, Chinese Academy of Sciences, in 2011. Yong Zhang, Integrable quantum computation, arXiv:1111.3940 Quantum Information Processing, Vol.12, No.1, pp. 631-639, 2013. ＩＱＣ： 26

  27. Definition of Integrable Quantum Computing 3. Quantum Computing via the integrable condition Zhang, “Integrable Quantum Computation”, arXiv:1111.3940 (2011/11) ＩＱＣ： 27

  28. Integrable quantum computing(2012-2014, Wuhan University) arXiv:1309.0955 Title: Space-Time Topology in Teleportation-Based Quantum Computation Authors:Yong Zhang, Jinglong Pang arXiv:1401.7009 Title: Bell Transform, Teleportation Operator and Teleportation-Based Quantum Computation Authors:Yong Zhang, Kun Zhang ＩＱＣ： 28

  29. Richard Feynman (1918 —1988) Whynot Integrable Quantum Computation? WhyIntegrable Quantum Computation? ＩＱＣ： 29

  30. Integrable Quantum Computing New Integrable models from Integrable Quantum Computation for New Paradigm in Physics ? ＩＱＣ： 30

  31. New paradigm in physics! Physics underlying the quantum circuit model Integrable quantum computing Thank You ! ＩＱＣ： 31

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