Quantum hardware

Quantum systems of any kind can in principle be candidates for quantum hardware, including different kinds of spin qubits we briefly review some of these in the next section. Much effort has been expended on the question of which physical systems are best suited for use in QIP, but no ultimate answer has been found so far. A much quoted list of conditions to build computers was established by DiVincenzo [35], but one has to note that some of these restrictions are specific to the quantum circuit paradigm. 

Molecular orbitals were one of the first molecular features that could be visualized with simple graphical hardware. The reason for this early representation is found in the complex theory of quantum chemistry. Basically, a structure is more attractive and easier to understand when orbitals are displayed, rather than numerical orbital coefficients. The molecular orbitals, calculated by semi-empirical or ab initio quantum mechanical methods, are represented by isosurfaces, corresponding to the electron density surfeces Figure 2-125a). 

With better hardware and software, more exact methods can be used for the representation of chemical structures and reactions. More and more quantum mechanical calculations can be utilized for chemoinformatics tasks. The representation of chemical structures will have to correspond more and more to our insight into theoretical chemistry, chemical bonding, and energetics. On the other hand, chemoinformatics methods should be used in theoretical chemistry. Why do we not yet have databases storing the results of quantum mechanical calculations. We are certain that the analysis of the results of quantum mechanical calculations by chemoinformatics methods could vastly increase our chemical insight and knowledge. 

This line of research has not lost his momentum. One of the reasons is the eontinuing progress in the computer hardware and software. Methods and algorithms are, and will be, continuously updated to exploit new features made available by eomputer seienee, as for example the parallel architectures, or the neuronal networks, to mention things at present of widespread interest, or even conceptually less significant improvements, as the inerease of fast memory in commereial computers. Computer quantum chemistry is not a mere recipient of progresses in eomputer seienee. Many progresses in the software comes from... 

The spectrometer supports phase cycling, asynchronous sequence implementation, and parameter-array experiments. Thus, most standard solid-state NMR experiments are feasible, including CPMAS, multiple-pulse H decoupling such as TPPM, 2D experiments, multiple-quantum NMR, and so on. In addition, the focus of development is on its extension of, or modification to, the hardware and/or the software, in the spirit of enabling the users to put their own new ideas into practice. In this paper, several examples of such have been described. They include the compact NMR and MRI systems, active compensation of RF pulse transients, implementation of a network analyzer, dynamic receiver-gain increment,31 and so on. 

The main hardware types offered by physics are mentioned, namely trapped ions (or trapped atoms), quantum dots, quantum optical cavities, rf superconducting quantum interference devices (SQUIDs) and nitrogen-vacancy (NV) defects on diamond. Some are important simply as a benchmark to evaluate the quality of the implementations offered by chemistry, whereas others might be combined with lanthanide complexes to produce heterogeneous quantum information processors which combine the advantages of different hardware types. 

A wide variety of proof-of-principle systems have been proposed, synthesized and studied in the field of molecular spin qubits. In fact, due to the fast development of the field, several chemical quantum computation reviews using magnetic molecules as spin qubits have been published over the past decade, covering both experimental and theoretical results [67-69]. Only in a minority of experiments implementing non-trivial one- or two-qubit gates has been carried out, so in this aspect this family is clearly not yet competitive with other hardware candidates.1 Of course, the main interest of the molecular approach that makes it qualitatively different is that molecules can be chemically engineered to tailor their properties and acquire new functionalities. 

In this chapter, we focus on the use of lanthanides as spin-based hardware for QC. The remainder of this introductory section provides some essential concepts and definitions and then it succinctly describes some of the existing proposals for QC. The second section provides a brief overview of results obtained with spin-based systems other than lanthanides. The following two sections review experiments made on qubits and quantum gates, respectively, based on lanthanides, highlighting their specific properties and advantages for QC applications. 

For the first time in the history of chemical sciences, theoretical predictions have achieved the level of reliability that allows them to rival experimental measurements in accuracy on a routine basis. Only a decade ago, such a statement would be valid only with severe qualifications as high-level quantum-chemical calculations were feasible only for molecules composed of a few atoms. Improvements in both hardware performance and the level of sophistication of electronic structure methods have contributed equally to this impressive progress that has taken place only recently. 

It is apparent that only a trickle of work has been, and is currently being, done on momentum densities in comparison with the torrent of effort devoted to the position space electron density. Moreover, much of the early work on II( p) has suffered from an undue emphasis on linear molecules. Nevertheless, some useful insights into the electronic structure of molecules have been achieved by taking the electron momentum density viewpoint. The most recent phenomenal developments in computer hardware, quantum chemical methods and software for generating wavefunctions, and visualization software suggest that the time is ripe to mount a sustained effort to understand momentum densities from a chemical perspective. Readers of this chapter are urged to take part in this endeavor. 

Recent progress in computational hardware and the development of efficient algorithms have assisted the routine development of molecular quantum-mechanical calculations. New semiempirical methods calculate realistic quantum-chemical molecular quantities in a relatively short computational time frame. Quantum-chemical calculations are thus an attractive source for molecular descriptors that can express all of the electronic and geometric properties of molecules and their interactions. Quantum-chemical methods can be applied to QSARs by direct derivation of electronic descriptors from the molecular wave function. 

The decision of which quantum mechanical model to use boils down to what size molecule you want to calculate, how reliable an answer you want, and how much time are you willing to wait for the results. Fortunately, as software and hardware improve, the tipping point of the balance weighing the pros and cons of semiempirical vs. DFT vs. ab initio is shifting such that larger molecules can be handled by the better methods. In special situations, a molecule with a couple of hundred atoms can be treated by an ab initio method (46,47), but the typical molecule of interest to theorists, spectrosco-pists, and physicists is smaller than what a pharmaceutical chemist usually wants to treat. Large molecular systems are often best left to one of the FF approaches (see next section). 

The rapidly developing field of quantum mechanics (and the even more rapid improvements in computational hardware and software) are very promising for those in need of better estimation techniques, and an increasing number of chemists and engineers are turning to these techniques for routine use. Yet the empirical methodologies still hold an important place in the toolbox of the scientist simply because these methods are so easy to use and are of proven reliability. 

This situation, well known to the workers in the field, has occurred due to a factor external to quantum chemistry itself, namely the intense development of computational hardware during the past few decades. The numerical point of view, which reduces the subject of Quantum Chemistry to obtaining certain numbers, has thus become predominant. It might be acceptable, but the situation changes completely when we find ourselves in the realm of complex systems (for which, as we shall see, hybrid modeling is basically necessary) obtaining numerical results for the complex systems or their subsequent interpretation in the frame of the standard procedures becomes too costly if at all possible and the answer obtained numerically becomes unobservable (if some one does not understand just one number to be the answer... 

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