NMR quantum computing

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.

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.

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.