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Unformatted text preview: arXiv:quant-ph/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  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 , and so quan- tum bits (qubits) cannot be duplicated. It is, however, possible to prepare an approximate copy , 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  of Buˇ zek et al . We started by slightly modifying the approximate cloning network  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 The initial “preparation” stage has been replaced by an alter- native network, which is simpler to implement with NMR techniques; the second “copy” stage is unchanged.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 , 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 50-50-100 Hz C C P Cl OD O OD H A H B FIG. 2: The three qubit system provided by E-(2-chloro- 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.
- Spring '11