Using the quantum probability ranking principle to rank interdependent documents

A known limitation of the Probability Ranking Principle (PRP) is that it does not cater for dependence between documents. Recently, the Quantum Probability Ranking Principle (QPRP) has been proposed, which implicitly captures dependencies between documents through “quantum interference”. This paper explores whether this new ranking principle leads to improved performance for subtopic retrieval, where novelty and diversity is required. In a thorough empirical investigation, models based on the PRP, as well as other recently proposed ranking strategies for subtopic retrieval (i.e. Maximal Marginal Relevance (MMR) and Portfolio Theory(PT)), are compared against the QPRP. On the given task, it is shown that the QPRP outperforms these other ranking strategies. And unlike MMR and PT, one of the main advantages of the QPRP is that no parameter estimation/tuning is required; making the QPRP both simple and effective. This research demonstrates that the application of quantum theory to problems within information retrieval can lead to significant improvements.

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.

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.

Quantum-Ohmic Resistance Fluctuation In Disordered Conductors - An Invariant Imbedding Approach

It is now well known that in extreme quantum limit, dominated by the elastic impurity scattering and the concomitant quantum interference, the zero-temperature d.c. resistance of a strictly one-dimensional disordered system is non-additive and non-self-averaging. While these statistical fluctuations may persist in the case of a physically thin wire, they are implicitly and questionably ignored in higher dimensions. In this work, we have re-examined this question. Following an invariant imbedding formulation, we first derive a stochastic differential equation for the complex amplitude reflection coefficient and hence obtain a Fokker-Planck equation for the full probability distribution of resistance for a one-dimensional continuum with a Gaussian white-noise random potential. We then employ the Migdal-Kadanoff type bond moving procedure and derive the d-dimensional generalization of the above probability distribution, or rather the associated cumulant function –‘the free energy’. For d=3, our analysis shows that the dispersion dominates the mobilitly edge phenomena in that (i) a one-parameter B-function depending on the mean conductance only does not exist, (ii) an approximate treatment gives a diffusion-correction involving the second cumulant. It is, however, not clear whether the fluctuations can render the transition at the mobility edge ‘first-order’. We also report some analytical results for the case of the one dimensional system in the presence of a finite electric fiekl. We find a cross-over from the exponential to the power-low length dependence of resistance as the field increases from zero. Also, the distribution of resistance saturates asymptotically to a poissonian form. Most of our analytical results are supported by the recent numerical simulation work reported by some authors.

Anisotropic transport in quantum waveguides due to the spin-orbit interactions

We theoretically investigate the charge transport in the quantum waveguides in the presence of the Rashba spin-orbit interaction and the Dresselhaus spin-orbit interaction. We find that the interplay between the Rashba spin-orbit interaction and Dresselhaus spin-orbit interaction can induce a symmetry breaking and consequently leads to the anisotropic charge transport in the quantum waveguides, the conductance through the quantum waveguides depends sensitively on the crystallographic orientations of the quantum waveguides. The anisotropy of the charge transport can even survive in the presence of disorder effect in realistic systems.

Research progress of electronic properties of self-assembled semiconductor quantum dots

Self-assembled semiconductor quantum dot is a new type of artificially designed and grown function material which exhibits quantum size effect, quantum interference effect, surface effect, quantum tunneling-Coulumb-blockade effect and nonlinear optical effect. Due to its advantages of less crystal defects and relatively simpler fabrication technology, this material may be of important value in the research of future nanoelectronic device. In the order of vertical transport, lateral transport and charge storage, recent advances in the electronic properties of this material are brefly introduced, and the problems and perspectives are analyzed.

QUANTUM WAVE-GUIDE THEORY FOR MESOSCOPIC STRUCTURES

A one-dimensional quantum waveguide theory for mesoscopic structures is proposed, and the boundary conditions of the wave functions at an intersection are given. The Aharonov-Bohm effect is quantitatively discussed with use of this theory, and the reflection, transmission amplitudes, etc., are given as functions of the magnetic flux, the arm lengths, and the wave vector. It is found that the oscillating current consists of a significant component of the second harmonic. This theory is also applied to investigate quantum-interference devices. The results on the Aharonov-Bohm effect and the quantum-interference devices are found to be in agreement with previous theoretical results.

THIN-FILM BIPBSRCACUO DIRECT-CURRENT SUPERCONDUCTING QUANTUM INTERFERING DEVICES OPERATING AT 78-K

Direct current SQUIDs (superconducting quantum interference devices) have been successfully fabricated by using a Pb-doped BiSrCaCuO superconducting thin film made by mixed evaporation of a single source composed of related components with a resistance heater. The dc SQUID comprises a square washer with a small hole. These SQUIDs show perfectly periodic voltage-flux characteristics without magnetic shield, that is, typically, the flux noise and energy resolution at a frequency range from dc to 1 Hz and at 78 K being 1.7 x 10(-3) PHI-0/ square-root Hz and 3.6 x 10(-26) J/Hz, respectively. Meanwhile, we have found out that one of the SQUIDs still was able to operate on flux-locked mode without bias currents and showed voltage-flux second harmonic characteristics. This phenomenon is not well understood, but it may be related to I-V (current-voltage) characteristics of the dc SQUID.

Fano effect on shot noise through a Kondo-correlated quantum dot

Transport in a semiopen Kondo- correlated quantum dot is mediated through more than one quantum state. Using the Keldysh technique and the equation of motion method, we study the shot noise S for a wide range of source- drain voltages V-sd within a model incorporating the additional states as a background continuum, demonstrating the importance of the Fano interference. In the absence of the interference, the noise is revealed to be a probe of the second moment of the local density of states, and our theory reproduces the well- known peak structure around the Kondo temperature in the S-V-sd curve. More significantly, it is found that taking account of the background transmission, the voltage dependence of the noise exhibits rich peak- dip line shapes, indicating the presence of the Fano effect. We further demonstrate that due to its two- particle nature, the noise is more sensitive to the quantum interference effect than the simple current.

Flux-dependent shot noise through an Aharonov-Bohm interferometer with an embedded quantum dot

Shot noise through a closed Aharonov-Bohm interferometer carrying a quantum dot in one of its two current paths is investigated. It is found that the shot noise can be modulated by the magnetic flux Phi, the dot level, and the direct tunneling. Due to the interference between the two transmission channels, the Kondo correlation manifests itself in the flux dependence of the shot noise, which exhibits oscillation behavior with a period of Phi(0)/2 (Phi(0) is the flux quantum) for small voltages below the Kondo temperature T-K. At voltages well above T-K or outside the Kondo regime, the shot noise is determined by high-energy Coulomb and hybridization processes, and its Aharonov-Bohm oscillations restore the fundamental period of Phi(0). As a result of its two-particle nature, the shot noise contains higher-order harmonics absent in the current, demonstrating the fact that the noise is more sensitive to the effects of quantum interference than the current.

Local order and magnetic field effects on the electronic properties of disordered binary alloys in the quantum site percolation limit

Electronic properties of disordered binary alloys are studied via the calculation of the average Density of States (DOS) in two and three dimensions. We propose a new approximate scheme that allows for the inclusion of local order effects in finite geometries and extrapolates the behavior of infinite systems following finite-size scaling ideas. We particularly investigate the limit of the Quantum Site Percolation regime described by a tight-binding Hamiltonian. This limit was chosen to probe the role of short range order (SRO) properties under extreme conditions. The method is numerically highly efficient and asymptotically exact in important limits, predicting the correct DOS structure as a function of the SRO parameters. Magnetic field effects can also be included in our model to study the interplay of local order and the shifted quantum interference driven by the field. The average DOS is highly sensitive to changes in the SRO properties and striking effects are observed when a magnetic field is applied near the segregated regime. The new effects observed are twofold: there is a reduction of the band width and the formation of a gap in the middle of the band, both as a consequence of destructive interference of electronic paths and the loss of coherence for particular values of the magnetic field. The above phenomena are periodic in the magnetic flux. For other limits that imply strong localization, the magnetic field produces minor changes in the structure of the average DOS. © World Scientific Publishing Company.

Dirac fermions in strong electric field and quantum transport in graphene

Our previous results on the nonperturbative calculations of the mean current and of the energy-momentum tensor in QED with the T-constant electric field are generalized to arbitrary dimensions. The renormalized mean values are found, and the vacuum polarization contributions and particle creation contributions to these mean values are isolated in the large T limit; we also relate the vacuum polarization contributions to the one-loop effective Euler-Heisenberg Lagrangian. Peculiarities in odd dimensions are considered in detail. We adapt general results obtained in 2 + 1 dimensions to the conditions which are realized in the Dirac model for graphene. We study the quantum electronic and energy transport in the graphene at low carrier density and low temperatures when quantum interference effects are important. Our description of the quantum transport in the graphene is based on the so-called generalized Furry picture in QED where the strong external field is taken into account nonperturbatively; this approach is not restricted to a semiclassical approximation for carriers and does not use any statistical assumptions inherent in the Boltzmann transport theory. In addition, we consider the evolution of the mean electromagnetic field in the graphene, taking into account the backreaction of the matter field to the applied external field. We find solutions of the corresponding Dirac-Maxwell set of equations and with their help we calculate the effective mean electromagnetic field and effective mean values of the current and the energy-momentum tensor. The nonlinear and linear I-V characteristics experimentally observed in both low-and high-mobility graphene samples are quite well explained in the framework of the proposed approach, their peculiarities being essentially due to the carrier creation from the vacuum by the applied electric field. DOI: 10.1103/PhysRevD.86.125022

Decoherence of quantum kinematical correlations: Elastic scattering of identical particles

We include the dynamics of the angular straggling process in the angular distributions of Mott scattering of heavy ions. We model the passage of an incoming nucleus through a target as a diffusion process. It is then possible to derive a simple and physically transparent expression for the angular dispersion due to the straggling. The angular dispersion should be folded with the theoretical Mott cross section to see its effect on the amplitude of the Mott oscillations. Our results agree very well with data of Pb-208 + Pb-208 scattering. We define the "classical" limit as the limit when the angular dispersion due to straggling becomes comparable with the Mott oscillation period and get the disappearance of quantum interference occurring at the limit 0.050 root xi Z(4)/E-3/2 >= 1, where xi stands for the target thickness, Z is the system's charge, and E is the center-of-mass energy. The experiments on lead are very close to this limit. We show that the kinematical correlations due to the identity of the particles is maintained, as it should be, and the action of the environment is to reduce the fringe visibility.

Error models for mode mismatch in linear optics quantum computing

One of the most significant challenges facing the development of linear optics quantum computing (LOQC) is mode mismatch, whereby photon distinguishability is introduced within circuits, undermining quantum interference effects. We examine the effects of mode mismatch on the parity (or fusion) gate, the fundamental building block in several recent LOQC schemes. We derive simple error models for the effects of mode mismatch on its operation, and relate these error models to current fault-tolerant-threshold estimates.

Hong-Ou-Mandel interference with a single atom

The Hong-Ou-Mandel (HOM) effect is widely regarded as the quintessential quantum interference phenomenon in optics. In this work we examine how nonlinearity can smear statistical photon bunching in the HOM interferometer. We model both the nonlinearity and a balanced beam splitter with a single two-level system and calculate a finite probability of anti-bunching arising in this geometry. We thus argue that the presence of such nonlinearity would reduce the visibility in the standard HOM setup, offering some explanation for the diminution of the HOM visibility observed in many experiments. We use the same model to show that the nonlinearity affects a resonant two-photon propagation through a two-level impurity in a waveguide due to a " weak photon blockade" caused by the impossibility of double-occupancy and argue that this effect might be stronger for multi-photon propagation.