Quantum circuit model

There are several other ways of approaching QIP that do not use the quantum circuit model. The global control paradigm, embodied in the seminal proposal of... 

The conjugated-circuits model is one of the simplest quantitative models that has been reasonably well studied. As already mentioned this model may be motivated from classical chemical bonding theory (extended a la Clar s classical empiricist argument) or from Simpson s existential quantum-theoretic argument [ 121 ], or from a quantum chemical derivation indicated in our hierarchy of section 3.2. But beyond derivation of the model there is the question of its solution, such as we now seek to address. 

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. 

XIV. Quantum Chemical Justification of the Conjugated 3509 Circuits Model... 

On the other hand, if a model is simple, empirical, and parametric, that does not necessarily means that it has no firm, apparently hidden link to generally accepted fundamental laws, such as those of quantum chemistry. Just as the opposite may be the case, a model that is thought to be based on basic axioms may turn out not to reflect this deep connection with quantum chemistry. It thus was found, mostly through the work of D. J. Kleln, that the conjugated circuits model has a quite firm foundation in quantum chemical principles, while as we all know, the Hiickel molecular orbital (MO) model that started as a quantum chemical model turned out to be a consequence of molecular topology, rather than an intricate interaction of r-electrons governed by the Schrodinger equation. 

We will briefly review various VB approximate methods here and show that the conjugated circuits method can be related to VB approaches and that, therefore, it has a sound quantum chemistry basis. This is needed because later we will relate Clar s /r-sextet model to the conjugated circuits model and will show that, therefore, one can justify Clar s empirical approach by quantum chemical arguments. 

The conjugated circuits model was successfully applied to a variety of conjugated systems. In Table 28 we list the types of molecules studied so far using the conjugated circuits model. This table represents a slightly modified and updated version of a table first shown in a paper on quantum mechanical and computational aspects of the conjugated circuits model by Trinajstic, Nikolic, and Klein.Incidentally, that paper was Dedicated to Professor Milan... 

In chemistiy, priority is to be given to experimental facts, not to calculations. Clar has offered experimental facts to support his model of the aromatic jr-sextet, but as we know, theoretical chemists have for the most part ignored his works. Recall the opening remark by R. G. Parr in this section. That is what has happened to Clar s aromatic jr-sextet. Now, with the synthesis of helical [/j]phenylenes by Vollhardt and co-workers, we may expect additional quantum chemical computations from theoretical circles. These are welcome. However, to fully appreciate the conjugated circuits model and the work of Clar, and to accept his model of the aromatic jr-sextet, apparently requires some imagination, or at least a... 

The harmonic oscillator is a model which has several important applications in both classical and quantum mechanics. It serves as a prototype in the mathematical treatment of such diverse phenomena as elasticity, acoustics, AC circuits, molecular and crystal vibrations, electromagnetic fields and optical properties of matter. 

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