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Seminar for Graduate Students in Theoretical PhysicsSpeaker: 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

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Integrable Quantum Computing (2004-2011-2014)

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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.

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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!

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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.

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“ Computers are physical objects, and computations are physical processes” ----- David Deutsch (1985)

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Rules

Initial state

Output

Input

Computation

Computer

Final state

Law of motion

Motion

Physical system

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Quantum Circuit Model: A network consisting ofa). Object: qubit （two-dimensional Hilbert space）b). Operation: quantum gate （unitary transformation）

qubit qubit

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QuantumGates

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Topological Quantum Computing

Integrable Quantum Computing

Quantum Gate

Braiding Non-braiding; Braiding

Fault -tolerance

Topology Integrable condition

Model Fractional Quantum Hall Effect

Integrable models

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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.

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The Yang--Baxter Equation

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

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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)

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Zhang, Louis H. Kauffman and Mo-Lin Ge, arXiv:quant-ph/0412095

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Quantum Computing via the Yang—Baxter equation (2004)

Int. J. Quantum Information, Vol.3, No.4, pp.669-678, 2005.

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Quantum Computing via the Yang—Baxter equation

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

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

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What is the physics underlying a quantum computer? (quantum computer as quantum circuit model)

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David Deutsch: Quantum computing supports the existence of Many Worlds ( the many-universes interpretation of quantum mechanics ) Philosophy!

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“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

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Nielsen & Chuang, “Quantum Information and Quantum Computation”, pp 203-204, 2011

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What is the physics underlying quantum circuit model?

Zhang arXiv:1106.3982

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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.

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David DiVincenzo (1994): An arbitrary N-qubit quantum gate can be expressed exactly as a sequence of products of some two-qubit gates.

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3-qubit Quantum

Gates

2-qubit gate 2-

qubit gate

2-qubit gate

2-qubit gate

Locality principle （ Preskill, online lecture notes, 1997-1998 ） .

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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.”

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Bethe Ansatz H. A. Bethe, Z. Phys. 71, 205 (1931).

Feynman (May 11, 1918 – February 15, 1988)

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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》： “曾子言曰：鸟之将死，其鸣也哀；人之将死，其言也善”

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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

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Quantum Computing via the Bethe Ansatz (2011)

Zhang, arXiv:1106.3982

Quantum Information Processing, Vol.11, No.2, pp. 585-590, 2012.

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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)

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One-dimension delta-function interaction model

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Two-body scattering operator = two-qubit quantum gate

Ref. 1. Bose and Korepin, arXiv:1106.2329Ref.2. Zhang, arXiv:1106.3982.

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Quantum Computing via delta-function interaction model

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Construction of an entangling two-qubit (the root of Swap gate)

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Quantum Computing via delta-function interaction model

Universal quantum computation = the root of the Swap gate + single-qubit transformations

Zhang, arXiv:1106.3982

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Universal quantum computation via Heisenberg interactionD.P. DiVincenzo et al., Nature 408, 339-342 (16 Nov. 2000)

Delta-function interaction vs. Heisenberg interaction Zhang, arXiv:1106.3982

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XXX spin chain: Heisenberg Interaction

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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)

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Integrable quantum computing (2011)

With the support of Professor Lu Yu, I have made a formal proposal onIntegrable Quantum Computing

during my visiting Institute of Physics, Chinese Academy of Sciences, in 2011.

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Yong Zhang, Integrable quantum computation, arXiv:1111.3940

Quantum Information Processing, Vol.12, No.1, pp. 631-639, 2013.

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Definition of Integrable Quantum Computing

3. Quantum Computing via the integrable condition

Zhang, “Integrable Quantum Computation”, arXiv:1111.3940 (2011/11)

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Integrable quantum computing(2012-2014, Wuhan University)

arXiv:1401.7009 Title: Bell Transform, Teleportation Operator and Teleportation-Based Quantum Computation Authors: Yong Zhang, Kun Zhang

arXiv:1309.0955 Title: Space-Time Topology in Teleportation-Based Quantum Computation Authors: Yong Zhang, Jinglong Pang

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Why not Integrable Quantum Computation?

Why Integrable Quantum Computation?

Richard Feynman (1918 — 1988)

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Integrable Quantum Computing

New Integrable models from Integrable Quantum Computation

for New Paradigm in Physics ?

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Physics underlying the quantum circuit model

Integrable quantum

computing

Newparadigm in physics!

Thank You !