By Kazem Mahdavi, Deborah Koslover

This quantity represents the talks given on the convention on Interactions among illustration conception, Quantum box idea, classification idea, Mathematical Physics, and Quantum details thought, held in September 2007 on the college of Texas at Tyler. The papers during this quantity, written via most sensible specialists within the box, tackle actual facets, mathematical facets, and foundational problems with quantum computation. This quantity will gain researchers attracted to advances in quantum computation and conversation, in addition to graduate scholars who desire to input the sector of quantum computation

**Read Online or Download Advances in Quantum Computation: Representation Theory, Quantum Field Theory, Category Theory, Mathematical Physics, September 20-23, 2007, University of Texas at Tyler PDF**

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**Additional resources for Advances in Quantum Computation: Representation Theory, Quantum Field Theory, Category Theory, Mathematical Physics, September 20-23, 2007, University of Texas at Tyler**

**Example text**

K. L. K. Lo (Wiley-VCH, 2001), 155–173. P. DiVincenzo, Two-bit quantum gates are universal for quantum computation, Phys. Rev. A 51(1995), 1015–1022. [14] W. Hansel, J. Reichel, P. W. Hansch, Trapped-atom interferometer in magnetic microtrap, Phys. Rev. A 64(2001), 063607. [15] D. J. I. W. Gardiner, and P. Zoller, Entanglement of atoms via cold controlled collisions, Phys. Rev. Lett 82(1999), 1975 – 1978. A. L. , 2000. [17] J. Normand, A Lie Group: Rotations in Quantum Mechanics, North-Holland, New York, 1980.

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*Since these 1-qubit gates can always be compensated, we obtain an entangled 2-qubit gate by combining the above matrix MATHEMATICAL FORMULATIONS OF ATOM TRAP QUANTUM GATES with additional 1-qubit operations: ⎡ (87) ⎢ U2 = ⎢ ⎣ 1 21 ⎤ ⎥ ⎥. 3. A controlled phase shift gate can be obtained by using U2 and two additional NOT gate on the qubit 2: (88) 2 2 CP HASE = Unot · U2 · Unot , 2 is a NOT gate on qubit 2 and where Unot ⎡ 0 ⎢ 0 2 (89) Unot = ⎢ ⎣ 1 0 can be written in matrix form: ⎤ 0 1 0 0 0 1 ⎥ ⎥. *