Quantum Chaos, Delocalization, and Entanglement in Disordered Heisenberg Models

We investigate disordered one- and two-dimensional Heisenberg spin lattices across a transition from integrability to quantum chaos from both a statistical many-body and a quantum-information perspective. Special emphasis is devoted to quantitatively exploring the interplay between eigenvector statistics, delocalization, and entanglement in the presence of nontrivial symmetries. The implications of basis dependence of state delocalization indicators (such as the number of principal components) is addressed, and a measure of {\em relative delocalization} is proposed in order to robustly characterize the onset of chaos in the presence of disorder. Both standard multipartite and {\em generalized entanglement} are investigated in a wide parameter regime by using a family of spin- and fermion- purity measures, their dependence on delocalization and on energy spectrum statistics being examined. A distinctive {\em correlation between entanglement, delocalization, and integrability} is uncovered, which may be generic to systems described by the two-body random ensemble and may point to a new diagnostic tool for quantum chaos. Analytical estimates for typical entanglement of random pure states restricted to a proper subspace of the full Hilbert space are also established and compared with random matrix theory predictions.Comment: 17 pages, 10 figures, revised versio

Parameters of Pseudorandom Quantum Circuits

Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudorandom circuits, with the goal of identifying relevant tradeoffs and optimizing convergence. The parameters we explore include the choice of single- and two-qubit gates, the topology of the underlying physical qubit architecture, the probabilistic application of two-qubit gates, as well as circuit size, initialization, and the effect of control constraints. Building on the equivalence between pseudorandom circuits and approximate t-designs, a Markov matrix approach is employed to analyze asymptotic convergence properties of pseudorandom second-order moments to a 2-design. Quantitative results on the convergence rate as a function of the circuit size are presented for qubit topologies with a sufficient degree of symmetry. Our results may be useful towards optimizing the efficiency of random state and operator generation

Quantum Pseudorandomness from Cluster-State Quantum Computation

We show how to efficiently generate pseudorandom states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudorandom algorithms in the cluster-state picture, we identify a strategy for optimizing pseudorandom circuits by properly choosing single-qubit rotations. A Markov chain analysis provides the tool for analyzing convergence rates to the Haar measure and finding the optimal single-qubit gate distribution. Our results may be viewed as an alternative construction of approximate unitary 2-designs

Quantum pseudo-randomness from cluster-state quantum computation

We show how to efficiently generate pseudo-random states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudo-random algorithms in the cluster-state picture, we identify a strategy for optimizing pseudo-random circuits by properly choosing single-qubit rotations. A Markov chain analysis provides the tool for analyzing convergence rates to the Haar measure and finding the optimal single-qubit gate distribution. Our results may be viewed as an alternative construction of approximate unitary 2-designs.Comment: 4 pages, 4 figures, version appearing in Phys. Rev.

Parameters of Pseudo-Random Quantum Circuits

Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudo-random circuits, with the goal of identifying relevant trade-offs and optimizing convergence. The parameters we explore include the choice of single- and two-qubit gates, the topology of the underlying physical qubit architecture, the probabilistic application of two-qubit gates, as well as circuit size, initialization, and the effect of control constraints. Building on the equivalence between pseudo-random circuits and approximate $t$-designs, a Markov matrix approach is employed to analyze asymptotic convergence properties of pseudo-random second-order moments to a 2-design. Quantitative results on the convergence rate as a function of the circuit size are presented for qubit topologies with a sufficient degree of symmetry. Our results may be theoretically and practically useful to optimize the efficiency of random state and operator generation.Comment: 17 pages, 14 figures, 2 Appendice

Analysing user physiological responses for affective video summarisation

This is the post-print version of the final paper published in Displays. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2009 Elsevier B.V.Video summarisation techniques aim to abstract the most significant content from a video stream. This is typically achieved by processing low-level image, audio and text features which are still quite disparate from the high-level semantics that end users identify with (the ‘semantic gap’). Physiological responses are potentially rich indicators of memorable or emotionally engaging video content for a given user. Consequently, we investigate whether they may serve as a suitable basis for a video summarisation technique by analysing a range of user physiological response measures, specifically electro-dermal response (EDR), respiration amplitude (RA), respiration rate (RR), blood volume pulse (BVP) and heart rate (HR), in response to a range of video content in a variety of genres including horror, comedy, drama, sci-fi and action. We present an analysis framework for processing the user responses to specific sub-segments within a video stream based on percent rank value normalisation. The application of the analysis framework reveals that users respond significantly to the most entertaining video sub-segments in a range of content domains. Specifically, horror content seems to elicit significant EDR, RA, RR and BVP responses, and comedy content elicits comparatively lower levels of EDR, but does seem to elicit significant RA, RR, BVP and HR responses. Drama content seems to elicit less significant physiological responses in general, and both sci-fi and action content seem to elicit significant EDR responses. We discuss the implications this may have for future affective video summarisation approaches

Distribution of an Invasive Aquatic Pathogen (Viral Hemorrhagic Septicemia Virus) in the Great Lakes and Its Relationship to Shipping

Viral hemorrhagic septicemia virus (VHSV) is a rhabdovirus found in fish from oceans of the northern hemisphere and freshwaters of Europe. It has caused extensive losses of cultured and wild fish and has become established in the North American Great Lakes. Large die-offs of wild fish in the Great Lakes due to VHSV have alarmed the public and provoked government attention on the introduction and spread of aquatic animal pathogens in freshwaters. We investigated the relations between VHSV dispersion and shipping and boating activity in the Great Lakes by sampling fish and water at sites that were commercial shipping harbors, recreational boating centers, and open shorelines. Fish and water samples were individually analyzed for VHSV using quantitative reverse transcription-polymerase chain reaction (qRT-PCR) and cell culture assays. Of 1,221 fish of 17 species, 55 were VHSV positive with highly varied qRT-PCR titers (1 to 5,950,000 N gene copies). The detections of VHSV in fish and water samples were closely associated and the virus was detected in 21 of 30 sites sampled. The occurrence of VHSV was not related to type of site or shipping related invasion hotspots. Our results indicate that VHSV is widely dispersed in the Great Lakes and is both an enzootic and epizootic pathogen. We demonstrate that pathogen distribution information could be developed quickly and is clearly needed for aquatic ecosystem conservation, management of affected populations, and informed regulation of the worldwide trade of aquatic organisms

Abnormal reward prediction-error signalling in antipsychotic naive individuals with first-episode psychosis or clinical risk for psychosis.

Ongoing research suggests preliminary, though not entirely consistent, evidence of neural abnormalities in signalling prediction errors in schizophrenia. Supporting theories suggest mechanistic links between the disruption of these processes and the generation of psychotic symptoms. However, it is unknown at what stage in the pathogenesis of psychosis these impairments in prediction-error signalling develop. One major confound in prior studies is the use of medicated patients with strongly varying disease durations. Our study aims to investigate the involvement of the meso-cortico-striatal circuitry during reward prediction-error signalling in earliest stages of psychosis. We studied patients with first-episode psychosis (FEP) and help-seeking individuals at-risk for psychosis due to sub-threshold prodromal psychotic symptoms. Patients with either FEP (n = 14), or at-risk for developing psychosis (n = 30), and healthy volunteers (n = 39) performed a reinforcement learning task during fMRI scanning. ANOVA revealed significant (p < 0.05 family-wise error corrected) prediction-error signalling differences between groups in the dopaminergic midbrain and right middle frontal gyrus (dorsolateral prefrontal cortex, DLPFC). FEP patients showed disrupted reward prediction-error signalling compared to controls in both regions. At-risk patients showed intermediate activation in the midbrain that significantly differed from controls and from FEP patients, but DLPFC activation that did not differ from controls. Our study confirms that FEP patients have abnormal meso-cortical signalling of reward-prediction errors, whereas reward-prediction-error dysfunction in the at-risk patients appears to show a more nuanced pattern of activation with a degree of midbrain impairment but preserved cortical function