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Unformatted text preview: arXiv:quantph/0111098v1 19 Nov 2001 Approximate Quantum Cloning with Nuclear Magnetic Resonance Holly K. Cummins, 1 Claire Jones, 2 Alistair Furze, 2 Nicholas F. Soffe, 3 Michele Mosca, 4 Josephine M. Peach, 2 and Jonathan A. Jones 1, 3, ∗ 1 Centre for Quantum Computation, Clarendon Laboratory, University of Oxford, Parks Road, OX1 3PU, United Kingdom 2 Dyson Perrins Laboratory, University of Oxford, South Parks Road, OX1 3QY, United Kingdom 3 Oxford Centre for Molecular Sciences, Central Chemistry Laboratory, University of Oxford, South Parks Road, OX1 3QTH, United Kingdom 4 Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada (Dated: February 1, 2008) Here we describe a Nuclear Magnetic Resonance (NMR) experiment that uses a three qubit NMR device to implement the one to two approximate quantum cloning network of Buˇ zek et al . PACS numbers: 03.67.a, 76.60.k, 82.56.Jn Quantum information processing [1] has been the sub ject of much recent interest, not only because it offers new modes of computation and communication, but also because quantum information differs from classical in formation in several fundamental ways. One important example is the fact that it is impossible to accurately clone (copy) an unknown quantum state [2], and so quan tum bits (qubits) cannot be duplicated. It is, however, possible to prepare an approximate copy [3], and several schemes for optimal approximate cloning have been de veloped. Nuclear Magnetic Resonance (NMR) [4, 5, 6] has already been used to demonstrate simple quantum information processing methods [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], and here we de scribe an NMR experiment that uses a three qubit NMR device to implement the one to two approximate cloning network [25] of Buˇ zek et al . We started by slightly modifying the approximate cloning network [25] of Buˇ zek et al. to take advantage of our specific hardware; our version of the network is shown in Fig. 1. This takes in one qubit in an arbitrary q 1 y q 2 y y FIG. 1: Our slightly modified version of the approximate quantum cloning network developed by Buˇ zek et al . The initial “preparation” stage has been replaced by an alter native network, which is simpler to implement with NMR techniques; the second “copy” stage is unchanged. Filled cir cles connected by control lines indicate controlled π phase shift gates [24], empty circles indicate single qubit Hadamard gates, while grey circles indicate other single qubit rota tions. The two rotation angles in the preparation stage are θ 1 = arcsin ( 1 / √ 3 ) ≈ 35 ◦ and θ 2 = π/ 12 = 15 ◦ . 100 5050100 Hz C C P Cl OD O OD H A H B FIG. 2: The three qubit system provided by E(2chloro ethenyl)phosphonic acid dissolved in D 2 O and its 1 H NMR spectrum. The broad peak near 50 Hz is a folded signal arising from residual HOD....
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This note was uploaded on 02/07/2011 for the course PHYS 101 taught by Professor Aster during the Spring '11 term at East Tennessee State University.
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