Developing the quantum probability ranking principle

In this work, we summarise the development of a ranking principle based on quantum probability theory, called the Quantum Probability Ranking Principle (QPRP), and we also provide an overview of the initial experiments performed employing the QPRP. The main difference between the QPRP and the classic Probability Ranking Principle, is that the QPRP implicitly captures the dependencies between documents by means of quantum interference". Subsequently, the optimal ranking of documents is not based solely on documents' probability of relevance but also on the interference with the previously ranked documents. Our research shows that the application of quantum theory to problems within information retrieval can lead to consistently better retrieval effectiveness, while still being simple, elegant and tractable.

On the use of complex numbers in quantum models for information retrieval

Quantum-inspired models have recently attracted increasing attention in Information Retrieval. An intriguing characteristic of the mathematical framework of quantum theory is the presence of complex numbers. However, it is unclear what such numbers could or would actually represent or mean in Information Retrieval. The goal of this paper is to discuss the role of complex numbers within the context of Information Retrieval. First, we introduce how complex numbers are used in quantum probability theory. Then, we examine van Rijsbergen’s proposal of evoking complex valued representations of informations objects. We empirically show that such a representation is unlikely to be effective in practice (confuting its usefulness in Information Retrieval). We then explore alternative proposals which may be more successful at realising the power of complex numbers.

Document ranking with quantum probabilities

In this thesis we investigate the use of quantum probability theory for ranking documents. Quantum probability theory is used to estimate the probability of relevance of a document given a user's query. We posit that quantum probability theory can lead to a better estimation of the probability of a document being relevant to a user's query than the common approach, i. e. the Probability Ranking Principle (PRP), which is based upon Kolmogorovian probability theory. Following our hypothesis, we formulate an analogy between the document retrieval scenario and a physical scenario, that of the double slit experiment. Through the analogy, we propose a novel ranking approach, the quantum probability ranking principle (qPRP). Key to our proposal is the presence of quantum interference. Mathematically, this is the statistical deviation between empirical observations and expected values predicted by the Kolmogorovian rule of additivity of probabilities of disjoint events in configurations such that of the double slit experiment. We propose an interpretation of quantum interference in the document ranking scenario, and examine how quantum interference can be effectively estimated for document retrieval. To validate our proposal and to gain more insights about approaches for document ranking, we (1) analyse PRP, qPRP and other ranking approaches, exposing the assumptions underlying their ranking criteria and formulating the conditions for the optimality of the two ranking principles, (2) empirically compare three ranking principles (i. e. PRP, interactive PRP, and qPRP) and two state-of-the-art ranking strategies in two retrieval scenarios, those of ad-hoc retrieval and diversity retrieval, (3) analytically contrast the ranking criteria of the examined approaches, exposing similarities and differences, (4) study the ranking behaviours of approaches alternative to PRP in terms of the kinematics they impose on relevant documents, i. e. by considering the extent and direction of the movements of relevant documents across the ranking recorded when comparing PRP against its alternatives. Our findings show that the effectiveness of the examined ranking approaches strongly depends upon the evaluation context. In the traditional evaluation context of ad-hoc retrieval, PRP is empirically shown to be better or comparable to alternative ranking approaches. However, when we turn to examine evaluation contexts that account for interdependent document relevance (i. e. when the relevance of a document is assessed also with respect to other retrieved documents, as it is the case in the diversity retrieval scenario) then the use of quantum probability theory and thus of qPRP is shown to improve retrieval and ranking effectiveness over the traditional PRP and alternative ranking strategies, such as Maximal Marginal Relevance, Portfolio theory, and Interactive PRP. This work represents a significant step forward regarding the use of quantum theory in information retrieval. It demonstrates in fact that the application of quantum theory to problems within information retrieval can lead to improvements both in modelling power and retrieval effectiveness, allowing the constructions of models that capture the complexity of information retrieval situations. Furthermore, the thesis opens up a number of lines for future research. These include: (1) investigating estimations and approximations of quantum interference in qPRP; (2) exploiting complex numbers for the representation of documents and queries, and; (3) applying the concepts underlying qPRP to tasks other than document ranking.

Response to “Comment on ‘Indications of energetic consequences of decoherence at short times for scattering from open quantum systems’” [AIP Advances 1, 049101 (2011)]

The Comment by Mayers and Reiter criticizes our work on two counts. Firstly, it is claimed that the quantum decoherence effects that we report in consequence of our experimental analysis of neutron Compton scattering from H in gaseous H2 are not, as we maintain, outside the framework of conventional neutron scatteringtheory. Secondly, it is claimed that we did not really observe such effects, owing to a faulty analysis of the experimental data, which are claimed to be in agreement with conventional theory. We focus in this response on the critical issue of the reliability of our experimental results and analysis. Using the same standard Vesuvio instrument programs used by Mayers et al., we show that, if the experimental results for H in gaseous H2 are in agreement with conventional theory, then those for D in gaseous D2 obtained in the same way cannot be, and vice-versa. We expose a flaw in the calibration methodology used by Mayers et al. that leads to the present disagreement over the behaviour of H, namely the ad hoc adjustment of the measured H peak positions in TOF during the calibration of Vesuvio so that agreement is obtained with the expectation of conventional theory. We briefly address the question of the necessity to apply the theory of open quantum systems.

Indications of energetic consequences of decoherence at short times for scattering from open quantum systems

Decoherence of quantum entangled particles is observed in most systems, and is usually caused by system-environment interactions. Disentangling two subsystems A and B of a quantum systemAB is tantamount to erasure of quantum phase relations between A and B. It is widely believed that this erasure is an innocuous process, which e.g. does not affect the energies of A and B. Surprisingly, recent theoretical investigations by different groups showed that disentangling two systems, i.e. their decoherence, can cause an increase of their energies. Applying this result to the context of neutronCompton scattering from H2 molecules, we provide for the first time experimental evidence which supports this prediction. The results reveal that the neutron-proton collision leading to the cleavage of the H-H bond in the sub-femtosecond timescale is accompanied by larger energy transfer (by about 3%) than conventional theory predicts. It is proposed to interpreted the results by considering the neutron-proton collisional system as an entangled open quantum system being subject to decoherence owing to the interactions with the “environment” (i.e., two electrons plus second proton of H2).

The sphynx's new riddle : how to relate the canonical formula of myth to quantum interaction

We introduce Claude Lévi Strauss' canonical formula (CF), an attempt to rigorously formalise the general narrative structure of myth. This formula utilises the Klein group as its basis, but a recent work draws attention to its natural quaternion form, which opens up the possibility that it may require a quantum inspired interpretation. We present the CF in a form that can be understood by a non-anthropological audience, using the formalisation of a key myth (that of Adonis) to draw attention to its mathematical structure. The future potential formalisation of mythological structure within a quantum inspired framework is proposed and discussed, with a probabilistic interpretation further generalising the formula

The Quantum Probability Ranking Principle for Information Retrieval

While the Probability Ranking Principle for Information Retrieval provides the basis for formal models, it makes a very strong assumption regarding the dependence between documents. However, it has been observed that in real situations this assumption does not always hold. In this paper we propose a reformulation of the Probability Ranking Principle based on quantum theory. Quantum probability theory naturally includes interference effects between events. We posit that this interference captures the dependency between the judgement of document relevance. The outcome is a more sophisticated principle, the Quantum Probability Ranking Principle, that provides a more sensitive ranking which caters for interference/dependence between documents’ relevance.

Quantum of damages under the Workcover Queensland Act 1996 - some questions of construction

The decision of Wilson J in Calvert v Nickless Ltd [2004] QSC 449 involves significant questions of interpretation of sections 315 and 317 of the Workcover Queensland Act 1996 (Qld) relating to claims for damages for future economic loss and for gratuitous services.

Fast, energy-efficient synthesis of luminescent carbon quantum dots

A simple, fast, energy and labour efficient, carbon dot synthesis method involving only the mixing of a saccharide and base is presented. Uniform, green luminescent carbon dots with an average size of 3.5 nm were obtained, without the need for additional energy input or external heating. Detection of formation moment for fructose-NaOH-produced carbon dots is also presented.

Energy and matter-efficient size-selective growth of thin quantum wires in a plasma

It is shown that plasmas can minimize the adverse Gibbs-Thompson effect in thin quantum wire growth. The model of Si nanowirenucleation includes the unprecedented combination of the plasma sheath, ion- and radical-induced species creation and heating effects on the surface and within an Au catalyst nanoparticle. Compared to neutral gas thermal processes, much thinner, size-selective wires can nucleate at the same temperature and pressure while much lower energy and matter budget is needed to grow same-size wires. This explains the experimental observations and may lead to energy- and matter-efficient synthesis of a broader range of one-dimensional quantum structures.

Self-organized quantum dot arrays : kinetic mapping of adatom capture

Deterministic synthesis of self-organized quantum dot arrays for renewable energy, biomedical, and optoelectronic applications requires control over adatom capture zones, which are presently mapped using unphysical geometric tessellation. In contrast, the proposed kinetic mapping is based on simulated two-dimensional adatom fluxes in the array and includes the effects of nucleation, dissolution, coalescence, and process parameters such as surface temperature and deposition rate. This approach is generic and can be used to control the nanoarray development in various practical applications. © 2009 American Institute of Physics.

Control of core-shell structure and elemental composition of binary quantum dots

The possibility of initial stage control of the elemental composition and core/shell structure of binary SiC quantum dots by optimizing temporal variation of Si and C incoming fluxes and surface temperatures is shown via hybrid numerical simulations. Higher temperatures and influxes encourage the formation of a stoichiometric outer shell over a small carbon-enriched core, whereas lower temperatures result in a larger carbon-enriched core, Si-enriched undershell, and then a stoichiometric SiC outer shell. This approach is generic and is applicable to a broad range of semiconductor materials and nanofabrication techniques. © 2007 American Institute of Physics.

Si quantum dots embedded in an amorphous SiC matrix : nanophase control by non-equilibrium plasma hydrogenation

Nanophase nc-Si/a-SiC films that contain Si quantum dots (QDs) embedded in an amorphous SiC matrix were deposited on single-crystal silicon substrates using inductively coupled plasma-assisted chemical vapor deposition from the reactive silane and methane precursor gases diluted with hydrogen at a substrate temperature of 200 °C. The effect of the hydrogen dilution ratio X (X is defined as the flow rate ratio of hydrogen-to-silane plus methane gases), ranging from 0 to 10.0, on the morphological, structural, and compositional properties of the deposited films, is extensively and systematically studied by scanning electron microscopy, high-resolution transmission electron microscopy, X-ray diffraction, Raman spectroscopy, Fourier-transform infrared absorption spectroscopy, and X-ray photoelectron spectroscopy. Effective nanophase segregation at a low hydrogen dilution ratio of 4.0 leads to the formation of highly uniform Si QDs embedded in the amorphous SiC matrix. It is also shown that with the increase of X, the crystallinity degree and the crystallite size increase while the carbon content and the growth rate decrease. The obtained experimental results are explained in terms of the effect of hydrogen dilution on the nucleation and growth processes of the Si QDs in the high-density plasmas. These results are highly relevant to the development of next-generation photovoltaic solar cells, light-emitting diodes, thin-film transistors, and other applications.

Single-step, rapid low-temperature synthesis of Si quantum dots embedded in an amorphous SiC matrix in high-density reactive plasmas

A simple, effective and innovative approach based on low-pressure, thermally nonequilibrium, high-density inductively coupled plasmas is proposed to rapidly synthesize Si quantum dots (QDs) embedded in an amorphous SiC (a-SiC) matrix at a low substrate temperature and without any commonly used hydrogen dilution. The experimental results clearly demonstrate that uniform crystalline Si QDs with a size of 3-4 nm embedded in the silicon-rich (carbon content up to 10.7at.%) a-SiC matrix can be formed from the reactive mixture of silane and methane gases, with high growth rates of ∼1.27-2.34 nm s-1 and at a low substrate temperature of 200 °C. The achievement of the high-rate growth of Si QDs embedded in the a-SiC without any commonly used hydrogen dilution is discussed based on the unique properties of the inductively coupled plasma-based process. This work is particularly important for the development of the all-Si tandem cell-based third generation photovoltaic solar cells.

Increased size selectivity of Si quantum dots on SiC at low substrate temperatures : an ion-assisted self-organization approach

A simple, effective, and innovative approach based on ion-assisted self-organization is proposed to synthesize size-selected Si quantum dots (QDs) on SiC substrates at low substrate temperatures. Using hybrid numerical simulations, the formation of Si QDs through a self-organization approach is investigated by taking into account two distinct cases of Si QD formation using the ionization energy approximation theory, which considers ionized in-fluxes containing Si3+ and Si1+ ions in the presence of a microscopic nonuniform electric field induced by a variable surface bias. The results show that the highest percentage of the surface coverage by 1 and 2 nm size-selected QDs was achieved using a bias of -20 V and ions in the lowest charge state, namely, Si1+ ions in a low substrate temperature range (227-327 °C). As low substrate temperatures (≤500 °C) are desirable from a technological point of view, because (i) low-temperature deposition techniques are compatible with current thin-film Si-based solar cell fabrication and (ii) high processing temperatures can frequently cause damage to other components in electronic devices and destroy the tandem structure of Si QD-based third-generation solar cells, our results are highly relevant to the development of the third-generation all-Si tandem photovoltaic solar cells.