649 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Fault-tolerant quantum computation of molecular observables

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    Over the past three decades significant reductions have been made to the cost of estimating ground-state energies of molecular Hamiltonians with quantum computers. However, comparatively little attention has been paid to estimating the expectation values of other observables with respect to said ground states, which is important for many industrial applications. In this work we present a novel expectation value estimation (EVE) quantum algorithm which can be applied to estimate the expectation values of arbitrary observables with respect to any of the system's eigenstates. In particular, we consider two variants of EVE: std-EVE, based on standard quantum phase estimation, and QSP-EVE, which utilizes quantum signal processing (QSP) techniques. We provide rigorous error analysis for both both variants and minimize the number of individual phase factors for QSPEVE. These error analyses enable us to produce constant-factor quantum resource estimates for both std-EVE and QSP-EVE across a variety of molecular systems and observables. For the systems considered, we show that QSP-EVE reduces (Toffoli) gate counts by up to three orders of magnitude and reduces qubit width by up to 25% compared to std-EVE. While estimated resource counts remain far too high for the first generations of fault-tolerant quantum computers, our estimates mark a first of their kind for both the application of expectation value estimation and modern QSP-based techniques

    Chromatic Chords in Theory and Practice

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    "Chromatic harmony" is seen as a fundamental part of (extended) tonal music in the Western classical tradition (c.1700–1900). It routinely features in core curricula. Yet even in this globalised and data-driven age, 1) there are significant gaps between how different national "schools" identify important chords and progressions, label them, and shape the corresponding curricula; 2) even many common terms lack robust definition; and 3) empirical evidence rarely features, even in in discussions about "typical", "representative" practice. This paper addresses those three considerations by: 1) comparing English- and German-speaking traditions as an example of this divergence; 2) proposing a framework for defining common terms where that is lacking; and 3) surveying the actual usage of these chromatic chord categories using a computational corpus study of human harmonic analyses

    Deep Generative Modelling of Human Behaviour

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    Human action is naturally intelligible as a time-varying graph of connected joints constrained by locomotor anatomy and physiology. Its prediction allows the anticipation of actions with applications across healthcare, physical rehabilitation and training, robotics, navigation, manufacture, entertainment, and security. In this thesis we investigate deep generative approaches to the problem of understanding human action. We show that the learning of generative qualities of the distribution may render discriminative tasks more robust to distributional shift and real-world variations in data quality. We further build, from the bottom-up, a novel stochastically deep generative modelling model taylored to the problem of human motion and demonstrate many of it’s state-of-the-art properties such as anomaly detection, imputation in the face of incomplete examples, as well as synthesis—and conditional synthesis—of new samples on massive open source human motion datasets compared to multiple baselines derived from the most relevant pieces of literature

    A Tale of Two Approaches: Comparing Top-Down and Bottom-Up Strategies for Analyzing and Visualizing High-Dimensional Data

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    The proliferation of high-throughput and sensory technologies in various fields has led to a considerable increase in data volume, complexity, and diversity. Traditional data storage, analysis, and visualization methods are struggling to keep pace with the growth of modern data sets, necessitating innovative approaches to overcome the challenges of managing, analyzing, and visualizing data across various disciplines. One such approach is utilizing novel storage media, such as deoxyribonucleic acid~(DNA), which presents efficient, stable, compact, and energy-saving storage option. Researchers are exploring the potential use of DNA as a storage medium for long-term storage of significant cultural and scientific materials. In addition to novel storage media, scientists are also focussing on developing new techniques that can integrate multiple data modalities and leverage machine learning algorithms to identify complex relationships and patterns in vast data sets. These newly-developed data management and analysis approaches have the potential to unlock previously unknown insights into various phenomena and to facilitate more effective translation of basic research findings to practical and clinical applications. Addressing these challenges necessitates different problem-solving approaches. Researchers are developing novel tools and techniques that require different viewpoints. Top-down and bottom-up approaches are essential techniques that offer valuable perspectives for managing, analyzing, and visualizing complex high-dimensional multi-modal data sets. This cumulative dissertation explores the challenges associated with handling such data and highlights top-down, bottom-up, and integrated approaches that are being developed to manage, analyze, and visualize this data. The work is conceptualized in two parts, each reflecting the two problem-solving approaches and their uses in published studies. The proposed work showcases the importance of understanding both approaches, the steps of reasoning about the problem within them, and their concretization and application in various domains

    Brain-wide representations of behavior spanning multiple timescales and states in C. elegans.

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    Changes in an animal's behavior and internal state are accompanied by widespread changes in activity across its brain. However, how neurons across the brain encode behavior and how this is impacted by state is poorly understood. We recorded brain-wide activity and the diverse motor programs of freely moving C. elegans and built probabilistic models that explain how each neuron encodes quantitative behavioral features. By determining the identities of the recorded neurons, we created an atlas of how the defined neuron classes in the C. elegans connectome encode behavior. Many neuron classes have conjunctive representations of multiple behaviors. Moreover, although many neurons encode current motor actions, others integrate recent actions. Changes in behavioral state are accompanied by widespread changes in how neurons encode behavior, and we identify these flexible nodes in the connectome. Our results provide a global map of how the cell types across an animal's brain encode its behavior

    Deep Learning, Shallow Dips: Transit light curves have never been so trendy

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    At the crossroad between photometry and time-domain astronomy, light curves are invaluable data objects to study distant events and sources of light even when they can not be spatially resolved. In particular, the field of exoplanet sciences has tremendously benefited from acquired stellar light curves to detect and characterise a majority of the outer worlds that we know today. Yet, their analysis is challenged by the astrophysical and instrumental noise often diluting the signals of interest. For instance, the detection of shallow dips caused by transiting exoplanets in stellar light curves typically require a precision of the order of 1 ppm to 100 ppm in units of stellar flux, and their very study directly depends upon our capacity to correct for instrumental and stellar trends. The increasing number of light curves acquired from space and ground-based telescopes—of the order of billions—opens up the possibility for global, efficient, automated processing algorithms to replace individual, parametric and hard-coded ones. Luckily, the field of deep learning is also progressing fast, revolutionising time series problems and applications. This reinforces the incentive to develop data-driven approaches hand-in-hand with existing scientific models and expertise. With the study of exoplanetary transits in focus, I developed automated approaches to learn and correct for the time-correlated noise in and across light curves. In particular, I present (i) a deep recurrent model trained via a forecasting objective to detrend individual transit light curves (e.g. from the Spitzer space telescope); (ii) the power of a Transformer-based model leveraging whole datasets of light curves (e.g. from large transit surveys) to learn the trend via a masked objective; (iii) a hybrid and flexible framework to combine neural networks with transit physics

    SoK:Delay-based Cryptography

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    The black hole information paradox in a brane world

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    Recent progress in our understanding of the black hole information paradox has led to a new prescription for calculating entanglement entropy, which involves special subsystems in regions where gravity is dynamical, called quantum extremal islands. We present a simple holographic framework where the emergence of quantum extremal islands can be understood in terms of the standard Ryu-Takayanagi prescription, used for calculating entanglement entropy under the anti-de Sitter (AdS)/conformal field theory (CFT) correspondence. Our setup describes a d-dimensional boundary CFT coupled to a (d-1)-dimensional defect, which are dual to a (d+1)-dimensional global AdS spacetime containing a codimension-one brane. Through the Randall-Sundrum mechanism, graviton modes become localized at the brane and, in a certain parameter regime, an effective description of the brane is given by Einstein gravity on a d-dimensional AdS background coupled to two copies of the boundary CFT. Within this effective description, the standard Ryu-Takayanagi formula implies the existence of quantum extremal islands in the gravitating region, whenever Ryu-Takayanagi surfaces cross the brane. Considered with Rindler and Poincaré coordinates respectively, our setup may be viewed as a special class of non-extremal and extremal black holes on the brane, in equilibrium with non-gravitational bath systems. For non-extremal black holes in any dimension, the appearance of quantum extremal islands has the right behaviour to avoid the information paradox and we show that the calculation of the full Page curve is possible. In the case of extremal black holes in higher dimensions, we find no quantum extremal islands for a wide range of parameters. The main benefit of our setup is that it allows for a high degree of analytic control as compared to previous work in higher dimensions. In two dimensions, we find agreement with previous work at leading order; however, a finite ultraviolet cutoff introduced by the brane results in subleading corrections
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