NMR implementations of Gauss sums
PHYSICS LETTERS A 372:36 (2008) 5758-5759
Arbitrary precision composite pulses for NMR quantum computing.
J Magn Reson 189:1 (2007) 114-120
Abstract:
We discuss the implementation of arbitrary precision composite pulses developed using the methods of Brown et al. [K.R. Brown, A.W. Harrow, I.L. Chuang, Arbitrarily accurate composite pulse sequences, Phys. Rev. A 70 (2004) 052318]. We give explicit results for pulse sequences designed to tackle both the simple case of pulse length errors and the more complex case of off-resonance errors. The results are developed in the context of NMR quantum computation, but could be applied more widely.Quantum information processing with delocalized qubits under global control.
Phys Rev Lett 99:3 (2007) 030501
Abstract:
Conventional quantum computing schemes are incompatible with nanometer-scale "hardware," where the closely packed spins cannot be individually controlled. We report the first experimental demonstration of a global control paradigm: logical qubits delocalize along a spin chain and are addressed via the two terminal spins. Using NMR studies on a three-spin molecule, we implement a globally clocked quantum mirror that outperforms the equivalent swap network. We then extend the protocol to support dense qubit storage and demonstrate this experimentally via Deutsch and Deutsch-Jozsa algorithms.Comment on "NMR Experiment Factors Numbers with Gauss Sums"
ArXiv 0704.2065 (2007)
Abstract:
Mehring et al. have recently described an elegant nuclear magnetic resonance (NMR) experiment implementing an algorithm to factor numbers based on the properties of Gauss sums. Similar experiments have also been described by Mahesh et al. In fact these algorithms do not factor numbers directly, but rather check whether a trial integer $\ell$ is a factor of a given integer $N$. Here I show that these NMR schemes cannot be used for factor checking without first implicitly determining whether or not $\ell$ is a factor of $N$.Contrasting photochemical and thermal reactivity of Ru(CO)2(PPh3)(dppe) towards hydrogen rationalised by parahydrogen NMR and DFT studies.
Dalton Trans (2006) 2072-2080