Quantum superposition

These devices allow utilizing new computational algorithms based on quantum superposition of states, allowing simultaneous representing many different numbers (so-called quantum computation). In a quantum computer information is loaded as a string of qubits (quantum mechanical representation of bits), which are quantum objects that can occupy different quantum states. A material implementation of qubits requires finding a medium, which can keep superpositional states from the destruction by interaction with the... 

The advances in this field are related with the development of the theory of configuration interaction between different excitation channels in nuclear physics including quantum superposition of states corresponding to different spatial locations for interpretation of resonances in nuclear scattering cross-section [7] related with the Fano configuration interaction theory for autoionization processes in atomic physics [8],... 

The interband interaction is controlled by the details of the quantum superposition of states corresponding to different spatial locations i.e, between the wave functions of the pairing electrons in the different subbands of the superlattice... 

The interaction between light and matter can be viewed as the creation of a coherent quantum superposition of initial and final electron states that has an associated polarization [3], as shown in Figure 1. The coherence between states with different wave vector requires an intermediate virtual state and the presence of a coherent phonon. A transition between the initial and final states may occur when the coherence of the system is broken either due to the finite width of an optical wave packet or by scattering from the environment. The transition results in the absorption of a photon and the creation of a hot electron-hole pair. Otherwise, the photon is re-radiated with a different phase and, perhaps, polarisation. 

In this section we report the first study of the micro-SQUID response of a low-spin molecular system, V15, to electromagnetic radiation. The advantages of our micro-SQUID technique in respect to pulsed electron paramagnetic resonance (EPR) techniques consist in the possibility to perform time-resolved experiments (below 1 ns) [59] on submicrometer sizes samples (about 1000 spins) [22] at low temperature (below 100 mK). Our first results on Vi5 open the way for time-resolved observations of quantum superposition of spin-up and spin-down states in SMMs. Other results obtained in similar systems but with large spins concern for example EPR measurements [10], resonant photon-assisted tunneling in a Feg SMM [60]. 

As discussed in Ref. 108, decoherence theory implies that the quantum superposition of two macroscopically distinct states, A) and B), is forbidden by the entanglement process... 

Finally, we should mention the possibility of coherent excitation transfer when the donor-acceptor interaction is strong, but the coupling of the system to the thermal bath is weak. The resulting two-level weakly damped system lends itself to the time-dependent density-matrix approach [33], which is essentially identical to the familiar spin-1/2 treatment in magnetic resonance. Under certain circumstances, coherence effects can be important for singlet energy transfer, because the donor states are populated instantaneously by direct photoexcitation. With a sufficient band width of the excitation source (e.g., ultrashort femtosecond pulses), quantum superposition states can be prepared in a coherent fashion even in condensed media at room... 

Only after the box is opened and the cat observed will the wavefunction collapse to a recognizable state of bliss or annoyance. In an extension of this experiment, an observer known as Wigner s friend is invited into a closed room with the apparatus. And until the door is opened. Wigner s friend himself will also become part of a quantum superposition, which is starting to become ridiculous We might be able to accept the concept of an atomic system being described as a superposition of quantum states. But a cat ... 

Quantum superposition does remain alive and well on the atomic scale. Christopher Monroe and co-workers in 1996 were able to prepare a single beryllium ion as a superposition of wavepackets representing two different electronic states spatially separated by as much as 80 nm. By an appropritate sequence of laser pulses, they were able to detect interference between the two wavepackets. Inevitably, this experiment has been referred to as Schrodinger s cation. ... 

Quantum coherence is extremely sensitive to environmental interactions. This is a main stumbling block in the attempts to build quantum computers, and in spite of the fact that such devices are planned to be based on very weakly interacting systems (entanglement of photons or atoms well isolated in cavities) it is extremely difficult to preserve coherence over a sufficiently large number of basic operations steps. Coherent states in molecules are still more perturbed, as displayed for instance by the difference between the spectra of NHs and AsHs gases [Omnes 1994], Here, the H-atom in NH3 is delocalized in a quantum superposition, being on both sides of the //.rplane, while the spatial coherence of the heavier As-atom disappears during the time of observation which results in quite different optical properties. 

More recent proposals have involved MNMs which have S = 1/2 ground states, with the two microstates l- -l/2> and l-l/2> acting as the 0 and 1 that will undergo quantum superposition. Most work has been published on CryNi rings, ° with other work on V15 poly-oxometallates (POMs) ° and on a mixed valence polyoxometallate [PM012O40 this last case contains two S = 1/2 centres on... 

Consider once again a pure quantum superposition state consisting of M levels ... 

This paper reviews this classical S-matrix theory, i.e. the semiclassical theory of inelastic and reactive scattering which combines exact classical mechanics (i.e. numerically computed trajectories) with the quantum principle of superposition. It is always possible, and in some applications may even be desirable, to apply the basic semiclassical model with approximate dynamics Cross7 has discussed the simplifications that result in classical S-matrix theory if one treats the dynamics within the sudden approximation, for example, and shown how this relates to some of his earlier work8 on inelastic scattering. For the most part, however, this review will emphasize the use of exact classical dynamics and avoid discussion of various dynamical models and approximations, the reason being to focus on the nature and validity of the basic semiclassical idea itself, i.e., classical dynamics plus quantum superposition. Actually, all quantum effects—being a direct result of the superposition of probability amplitudes—are contained (at least qualitatively) within the semiclassical model, and the primary question to be answered regards the quantitative accuracy of the description. 

Whereas coherence can persist up to the nanosecond range for atomic and molecular systems exposed to dilute gaseous environments, the situation is radically different in liquids and solids. Interactions with neighbouring atoms, with phonons in crystalline materials and with conduction electrons in metals, shift the coherence times down by several orders of magnitude, and local quantum superpositions are usually not observable. Intermediate cases are the electronic states used as qubits in the form of superconducting islands introduced by Y. Nakamura et al. [4]. The latest reports [5] show coherence times up to 10 s for these objects, which would allow time for operations of a quantum computer. The decoherence mechanisms in such circuits have been discussed theoretically by Burkhard et al. [6],... 

For experiments on protons in condensed matter at normal temperatures, all decohering mechanisms are supposed to be fully active and possible local quantum superpositions states are expected to be extremely short-lived. The time diagram in Fig. 22.1 illustrates the existence ranges for the above-mentioned open quantum systems and indicates also the intervals where coherence or decoherence will be observable with the specific method to be described in the next section. 

If prepared in a general superposition state, quantum registers consisting of N qubits can store 2 bits of information simultaneously, as compared to classical registers where only N bits of information are stored. However, not all the information contained in quantum memories can be accessed by physical measurements. Nevertheless, so-called quantum parallelism makes quantum computers very fast they can process quantum superpositions of many numbers in one computational step, where each computational step is a unitary transformation of quantum registers. To achieve this, a universal quantum computer should be able to perform an arbitrary unitary transformation on any superposition of states. 

After Benioff, in the year of 1985, David Deutsch gave a decisively important step towards quantum computers presenting the first example of a quantum algorithm [6]. The Deutsch algorithm shows how quantum superposition can be used to speed up computational processes. Another influent name is Richard Feynman, who was involved about the same time in the discussions of the viability of quantum computers and their use for quantum systems simulations [7]. 

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