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By Eleanor Rieffel and Wolfgang Polak

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NIELSEN, M. , AND LAFLAMME, R. 1998. Complete Quantum Teleportation using Nuclear Magnetic Resonance. lanl. gov/abs/quant-ph/9811020. SCHULMAN, L. J. AND VAZIRANI, U. 1998. Scalable NMR Quantum Computation. lanl. gov/abs/quant-ph/9804060. SHOR, P. W. 1994. Algorithms for quantum computation: Discrete log and factoring. ), 124–134. Institute of Electrical and Electronic Engineers Computer Society Press. Z. SHOR, P. W. 1997. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer.

And the error E= 3 4 X ⊗ I ⊗ I + I ⊗ X ⊗ I. 5 5 The resulting error state is − 330 E. Rieffel and W. Polak 4 3 X ⊗I⊗I+ I⊗X ⊗I 5 5 1 × √ (|000 − |111 ) 2 1 4 = X ⊗ I ⊗ I √ (|000 − |111 ) 5 2 3 1 + I ⊗ X ⊗ I √ (|000 − |111 ) 5 2 4 = √ X ⊗ I ⊗ I (|000 − |111 ) 5 2 3 + √ I ⊗ X ⊗ I (|000 − |111 ) 5 2 4 = √ (|100 − |011 ) 5 2 3 + √ (|010 − |101 ). 5 2 E|φ = Next apply the syndrome extraction to (E|φ ) ⊗ |000 as follows: SC ((E|φ ) ⊗ |000 ) 4 = SC ( √ (|100000 − |011000 ) 5 2 3 + √ (|010000 − |101000 )) 5 2 4 = √ (|100110 − |011110 ) 5 2 3 + √ (|010101 − |101101 ) 5 2 4 = √ (|100 − |011 ) ⊗ |110 5 2 3 + √ (|010 − |101 ) ⊗ |101 .

1998. Generalized grover search algorithm for arbitrary initial amplitude distribution. gov/abs/quant-ph/9801066. , MARTINI, F. , AND POPESCU, S. 1998. Experimental realization of teleporting an unknown pure quantum state via dual classical and einstein-podolski-rosen channels. Physical Review Letters 80, 1121–1125. , AND ZEILINGER, A. 1997. Experimental quantum teleportation. Nature 390, 575. , AND TAPP, A. 1996. Tight bounds on quantum search. In Proceedings of the Workshop on Physics of Computation: PhysComp ’96 (Los Alamitos, CA, 1996), 36–43.

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An Introduction to Quantum Computing for Non-Physicists by Eleanor Rieffel and Wolfgang Polak


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