NMR quantum computing

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 $N$.

Abstract:

The synthesis, characterisation and thermal and photochemical reactivity of Ru(CO)2(PPh3)(dppe) 1 towards hydrogen are described. Compound proved to exist in both fac (major) and mer forms in solution. Under thermal conditions, PPh3 is lost from 1 in the major reaction pathway and the known complex Ru(CO)2(dppe)(H)2 2 is formed. Photochemically, CO loss is the dominant process, leading to the alternative dihydride Ru(CO)(PPh3)(dppe)(H)2 3. The major isomer of 3, viz. 3a, contains hydride ligands that are trans to CO and trans to one of the phosphorus atoms of the dppe ligand but a second isomer, 3b, where both hydride ligands are trans to distinct phosphines, is also formed. On the NMR timescale, no interconversion of 3a and 3b was observed, although hydride site interchange is evident with activation parameters of DeltaH(double dagger) = 95 +/- 6 kJ mol(-1) and DeltaS(double dagger) = 26 +/- 17 J K(-1) mol(-1). Density functional theory confirms that the observed species are the most stable isomeric forms, and suggests that hydride exchange occurs via a transition state featuring an eta2-coordinated H2 unit.