How can the D-Wave machine exhibit long-time quantum behaviour

Extensive experiments have demonstrated quantum behaviour in the long-time operation of the D-Wave quantum computer. The decoherence time of a single flux qubit is reported to be on the order of nanoseconds [1],which is much shorter than the time required to carry out a computation on the timescale of seconds [2, 3]. Previous judgements of whether the D-Wave device should be thought of as a quantum computer have been based on correlations of the input-output behaviour of the D-Wave machine with a quantum model, called simulated quantum annealing, or classical models, called simulated annealing and classical spin dynamics [4]. Explanations for a factor of 10(8) discrepancy between the single flux qubit decoherence time and the long-time coherent quantum behaviour of many integrated flux qubits of the D-Wave device have not been offered so far. In our contribution we investigate a model of four qubits with one qubit coupled to a phonon and (optionally) to environmental particles of high density of states, called gravonons. The calculations indicate that when no gravonons are present, the current in the qubit is flipped at some time and adiabatic evolution is discontinued. The time dependent wave functional becomes a non-correctable superposition of many excited states. The results demonstrate the possibility of effectively suppressing the current flip and allowing for continued adiabatic evolution when the entanglement to gravonons is included. This adiabatic evolution is, however, a coherent evolution in high dimensional spacetime and cannot be understood as a solution of Schrodinger's time dependent equation in 4 dimensional spacetime. Compared to Schrodinger's time development in 4D, the evolution is considerably slowed down, though still adiabatic. The properties of our model reflect correctly the experimentally found behaviour of the D-Wave machine and explain the factor of 10(8) discrepancy between decoherence time and quantum computation time. The observation and our explanation are in anology to the 10(8) discrepancy factor found, when comparing experimental results on adsorbate quantum diffusion rate with predictions of Schrodinger's time dependent equation, which can also be resolved in a model with the coupling to gravonons included

Emergence of four dimensional quantum mechanics from a deterministic theory in 11 dimensions

We develop a deterministic theory which accounts for the coupling of a high dimensional continuum of environmental excitations (called gravonons) to massive particle in a very localized and very weak fashion. For the model presented Schrodinger's equation can be solved practically exactly in 11 spacetime dimensions and the result demonstrates that as a function of time an incoming matter wave incident on a screen extinguishes, except at a single interaction center on the detection screen. This transition is reminiscent of the wave - particle duality arising from the "collapse" (also called "process one") postulated in the Copenhagen-von Neumann interpretation. In our theory it is replaced by a sticking process of the particle from the vacuum to the surface of the detection screen. This situation was verified in experiments by using massive molecules. In our theory this "wave-particle transition" is connected to the different dimensionalities of the space for particle motion and the gravonon dynamics, the latter propagating in the hidden dimensions of 11 dimensional spacetime. The fact that the particle is detected at apparently statistically determined points on the screen is traced back to the weakness and locality of the interaction with the gravonons which allows coupling on the energy shell alone. Although the theory exhibits a completely deterministic "chooser" mechanism for single site sticking, an apparent statistical character results, as it is found in the experiments, due to small heterogeneities in the atomic and gravonon structures

Advances in atomic force microscopy

This article reviews the progress of atomic force microscopy (AFM) in ultra-high vacuum, starting with its invention and covering most of the recent developments. Today, dynamic force microscopy allows to image surfaces of conductors \emph{and} insulators in vacuum with atomic resolution. The mostly used technique for atomic resolution AFM in vacuum is frequency modulation AFM (FM-AFM). This technique, as well as other dynamic AFM methods, are explained in detail in this article. In the last few years many groups have expanded the empirical knowledge and deepened the theoretical understanding of FM-AFM. Consequently, the spatial resolution and ease of use have been increased dramatically. Vacuum AFM opens up new classes of experiments, ranging from imaging of insulators with true atomic resolution to the measurement of forces between individual atoms.Comment: In press (Reviews of Modern Physics, scheduled for July 2003), 86 pages, 44 figure