Geometric quantum computation

J.A. Jones, V. Vedral, A. Ekert, G. CastagnoU, Geometric quantum computation using nuclear magnetic resonance. Nature 403 (2000) 869. 

Many systems are being studied to manipulate quantum information. Some make use of individual atoms cold trapped ions, neutral atoms in optical lattices, atoms in crystals. Other involve particle spins or photons in cavity QED or nonlinear optical setups as well as more exotic ones where geometric combinations of elementary excitations are defined as qubits, such as in topological quantum computing [8]. However, none of these systems has yet emerged as a definitive way to build a quantum information processor. A reason for this is that there is an essential dichotomy we need... 

Fortunately very recently a thanks to the work of Kauffman and Lomonaco [12], a new direction in anyonic topological quantum computation was formulated. This line Kauffman-Lomonaco is based on geometric topology and representation theory and it is more accessible for the computer scientists. 

As we said in the introduction the anyonic topological quantum computation was formulated originally inside the domain of the TQFT s of the algebraic topology. Also we said that Kauffman and Lomonaco were able to construct the ATQC inside the domain of the geometric topology. 

In quantum computing there are various computational models such as the standard model with quantum circuits, the geometrical model with quantum gates derived from holonomy groups and the adiabatic model with its application of the adiabatic theorem of the quantum mechanics [30]. All these models are very well known in quantum computing and computer science and it is not necessary to describe them here. 

Carbo-Dorca R, Besalii E, Mercado LD (2011) Communications on quantum similarity. Part 3 a geometric-quantum similarity molecular superposition algorithm. J Comput Chem 32 582-599... 

The relative shift of the peak position of the rotational distiibution in the presence of a vector potential thus confirms the effect of the geometric phase for the D + H2 system displaying conical intersections. The most important aspect of our calculation is that we can also see this effect by using classical mechanics and, with respect to the quantum mechanical calculation, the computer time is almost negligible in our calculation. This observation is important for heavier systems, where the quantum calculations ai e even more troublesome and where the use of classical mechanics is also more justified. 

With the advent of quantum mechanics, quite early attempts were made to obtain methods to predict chemical reactivity quantitatively. This endeavor has now matured to a point where details of the geometric and energetic changes in the course of a reaction can be calculated to a high degree of accuracy, albeit still with quite some demand on computational resources. 

CODESSA can compute or import over 500 molecular descriptors. These can be categorized into constitutional, topological, geometric, electrostatic, quantum chemical, and thermodynamic descriptors. There are automated procedures that will omit missing or bad descriptors. Alternatively, the user can manually define any subset of structures or descriptors to be used. 

Although even the smaller structural units of zeolites are large enough to tax the most advanced quantum chemical computational methods to their limits, nevertheless, it is now possible to determine the fundamental electronic properties of zeolite structural units. In addition to their unique geometrical (in fact, topological) properties, the electronic structure and charge distribution of zeolites are of fundamental importance in explaining their catalytic and other chemical properties. 

Electron diffraction provides experimental diffraction spectra for comparison with computed spectra obtained from various intuitive geometrical models, but this technique alone is generally insufficient to locate the hydrogen atoms. A quantum approach, on the other hand, indicates the positions of the H atoms, which can then be introduced into the calculation of the theoretical spectra in order to complete the determination of the geometry. 

In order to examine the nature of the unusual geometric distortions observed in the X-ray structures of complexes 3 and 4, we have performed a series of density functional theory (DFT) and combined quantum mechanics and molecular mechanics (QM/MM) calculations [22-27], Although the computational resources to wholly treat both 3 and 4 at the DFT level are available, we have employed the combined QM/MM method to unravel the... 

---