Implementation of quantum algorithms by NMR

The first experimental implementation of a quantum algorithm by NMR was reported by J.A. Jones and M. Mosca [3]. They demonstrated the Deutsch algorithm using as qubits the spins of two protons in a sample of partially deuterated cytosine. The observed /-coupling in this system is only 7.2 Hz, and the doublets were separated by 763 Hz. 

The first full implementation of Grover search algorithm by NMR was reported by Chuang, Gershenfeld and Kubinec, in 1998 [8], The authors used hydrogen and carbon nuclear spins in chloroform as qubits. One important aspect of this work is the reconstruction of the density matrix, and its comparison with the theoretical prediction. They constructed four optimized sequences of radiofrequency pulses, one for each element labeled by the oracle of the quantum search algorithm (see Chapter 3). The result is shown in Figure 5.3. One observes that the deviation from the theoretical prediction increases with... 

HP xenon has also been used to enhance the polarization of a two-qubit NMR quantum computer using the C-enriched chloroform.Using the SPINOE transfer mechanism, this approach led to a polarization enhancement of the chloroform that was approximately 10 times the thermal values for H and Temporal spin-labeling methods along with measurements of the deviation density matrix were used to observe the formation of a pure spin state. The authors then demonstrated their approach by implementing a 2-qubit Grover s search algorithm. 

Figure 5.10 Quantum circuit and NMR spectra corresponding to the implementation of the Deutsch-Jozsa algorithm in a quadmpole 7 = 3/2 nucleus by Das and Kumar [6). The two qubits are represented by the central and outer transitions. Transitions pointing to the same direction represent constant functions, and to opposite directions balanced ones. Adapted with permission from Ref. [6].

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