1. ＩＱＣ： 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 1 Integrable Quantum Computing (2004-2011-2014)

2. ＩＱＣ： 2 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.

3. ＩＱＣ： 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! 3

4. ＩＱＣ： 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.

5. ＩＱＣ： 5

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

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

8. ＩＱＣ： 8 Topological Quantum Computing Integrable Quantum Computing Quantum Gate Braiding Non-braiding; Braiding Fault -tolerance Topology Integrable condition Model Fractional Quantum Hall Effect Integrable models 8 Type Item Topological and Integrable Quantum Computing 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.

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

10. ＩＱＣ： 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) 10

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

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

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

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

15. ＩＱＣ： “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 15 Nielsen & Chuang, “Quantum Information and Quantum Computation”, pp 203-204, 2011

16. ＩＱＣ： What is the physics underlying quantum circuit model? Zhang arXiv:1106.3982arXiv:1106.3982 16 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.

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

18. ＩＱＣ： 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.” 18 Bethe Ansatz H. A. Bethe, Z. Phys. 71, 205 (1931).

19. Feynman (May 11, 1918 – February 15, 1988) 19 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 Physics 21 (6–7): 467–488 Feynman (1986). Quantum Mechanical Computers Foundations of Physics, Vol. 16, No. 6, 1986 春秋 · 鲁 · 孔丘《论语 · 泰伯》：论语 “ 曾子言曰：鸟之将死，其鸣也哀；人之将死，其言也善 ”

20. ＩＱＣ： 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 20 Quantum Computing via the Bethe Ansatz (2011) Zhang, arXiv:1106.3982arXiv:1106.3982 Quantum Information Processing, Vol.11, No.2, pp. 585-590, 2012.

21. ＩＱＣ：  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) 21 One-dimension delta-function interaction model

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

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

24. ＩＱＣ： 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:1106.3982arXiv:1106.3982 24 XXX spin chain: Heisenberg Interaction

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

26. ＩＱＣ： 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. 26 Yong Zhang, Integrable quantum computation, arXiv:1111.3940 Quantum Information Processing, Vol.12, No.1, pp. 631-639, 2013.

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

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

29. ＩＱＣ： 29 Why not Integrable Quantum Computation? Why Integrable Quantum Computation? Richard Feynman (1918 — 1988)

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

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