Photonic quantum information processing based on directionally-unbiased linear-optical multiports

The progress in modern quantum information processing (QIP) strongly depends on new algorithms and on the development of novel quantum entanglement processing elements enabling to perform quantum computation and quantum simulation effectively. Several examples of quantum information processing applications based on freshly designed linear-optics devices are presented. A beam splitter (BS) is a central device in linear-optical quantum information processing because it can split the incoming photon amplitudes into spatially distinct modes to establish conditions for quantum superposition. The BS naturally possesses directional-bias in a sense that incoming photons can only propagate in a forward manner. When the execution of certain quantum information tasks would require multiple operations, this directionality condition becomes a serious obstacle by creating significant overhead in the number of needed elements and other supporting devices. We introduce a family of amplitude-controllable fully-reversible linear-optical quantum information processors, called directionally-unbiased linear-optical multiports, in order to achieve significant reduction in the number of required hardware. The theoretical analysis of the device design as well as the experimental realization of three-port unit using bulk linear optics is demonstrated. These devices offer several fresh approaches in quantum-walk-based applications such as quantum simulation of solid-state Hamiltonians, topological protection of polarization qubits against errors, and quantum communication. Topological photonics is an emerging and actively developing field because of its capability to stabilize and protect some quantum states from perturbation errors by ensuring the environment carries a distinct topological signature. Topology-dependent quantum information processing is globally stable due to the entire system being engaged in the information manipulation. We demonstrate suppression of quantum amplitude transfer between two distinct bulk regions of a system. This results in error avoidance for a two-photon polarization-entangled state under specific conditions. The goal of modern quantum communication is a reliable distribution of quantum entanglement between multiple nodes performing quantum operations such as quantum memories and quantum computers. We demonstrated that local quantum information processing using new fully-reversible four-port linear-optical structures could find an immediate application in quantum communication. A quantum information routing device is introduced based on the use of four-dimensional Grover matrices and beam splitters. Several multiport-based units are developed to demonstrate new higher-dimensional Hong-Ou-Mandel (HOM) effect and directionally-controllable entangled state distribution while changing only phases in a waveguided unit. Several such operational elements could be linked to form a reconfigurable network of quantum users without losing control of quantum amplitudes. This allows controllable routing of entangled photons and sharing entanglement between any designated users in the future quantum computational networks.2022-05-15T00:00:00

International Congress of Mathematicians: 2022 July 6–14: Proceedings of the ICM 2022

Following the long and illustrious tradition of the International Congress of Mathematicians, these proceedings include contributions based on the invited talks that were presented at the Congress in 2022. Published with the support of the International Mathematical Union and edited by Dmitry Beliaev and Stanislav Smirnov, these seven volumes present the most important developments in all fields of mathematics and its applications in the past four years. In particular, they include laudations and presentations of the 2022 Fields Medal winners and of the other prestigious prizes awarded at the Congress. The proceedings of the International Congress of Mathematicians provide an authoritative documentation of contemporary research in all branches of mathematics, and are an indispensable part of every mathematical library

Local Cytoskeletal and Organelle Interactions Impact Molecular Motor-Driven Early Endosomal Trafficking

Molecular motors generate the force needed for long-distance transport of cargos and organelles in the cell. How motor proteins attach to a diverse array of cargos and navigate to the correct location in the cell with enough fidelity to maintain organelle integrity is only starting to be understood. Studying the properties of individual motors, and their fine-tuning by regulatory molecules, is one area of active investigation in vitro. However, the organization of the cell, and the variability of the environment within a single cell, cannot be fully reconstituted in vitro. We investigated the effects of the crowded intracellular environment on early endosomal trafficking. Live-cell imaging of an endosomal cargo (endocytosed epidermal growth factor-conjugated quantum dots) combined with high-resolution tracking was used to analyze the heterogeneous motion of individual endosomes. The motile population of endosomes moved towards the perinuclear region in directed bursts of microtubule-based, dynein-dependent transport interrupted by longer periods of diffusive motion. Actin network density did not affect motile endosomes during directed runs or diffusive interruptions. Simultaneous two-color imaging was used to correlate changes in endosomal movement with potential obstacles to directed runs. Termination of directed runs spatially correlated with microtubule-dense regions, encounters with other endosomes, and interactions with the endoplasmic reticulum, suggesting these interactions interrupt directed transport. Early endosomal and lysosomal interactions with the ER were characterized by dramatic deformation and tubulation of the ER. During a subset of run terminations, we also observed merging and splitting of endosomes, and reversals in direction at speeds up to ten-fold greater than characteristic in vitro motor velocities. These observations suggest endosomal membrane tension is high during directed run termination. Our results indicate that the crowded cellular environment significantly impacts the motor-driven motility of organelles. Rather than simply acting as impediments to movement, interactions of trafficking cargos with intracellular obstacles may facilitate communication between membrane-bound compartments or contribute to the generation of membrane tension necessary for fusion and fission of endosomal membranes or remodeling of the endoplasmic reticulum

Non-Abelian Anyons and Topological Quantum Computation

Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as {\it Non-Abelian anyons}, meaning that they obey {\it non-Abelian braiding statistics}. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations which are necessary for quantum computation are carried out by braiding quasiparticles, and then measuring the multi-quasiparticle states. The fault-tolerance of a topological quantum computer arises from the non-local encoding of the states of the quasiparticles, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the \nu=5/2 state, although several other prospective candidates have been proposed in systems as disparate as ultra-cold atoms in optical lattices and thin film superconductors. In this review article, we describe current research in this field, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. We address both the mathematical underpinnings of topological quantum computation and the physics of the subject using the \nu=5/2 fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.Comment: Final Accepted form for RM

Application and Development of Mechanoresponsive Polymer Structures

Mechanoresponsive Systeme antworten auf mechanische Reize mit einer Eigenschaftsänderung. Diese Dissertation umfasst die Arbeiten mit zwei mechanoresponsiven Systemen, die optisch auf mechanische Reize antworten. Sie basieren auf polymeren Strukturen, einer Polymerbürste und einem Hydrogelnetzwerk. Ihr optischer Antwortmechanismus ermöglicht die Beobachtung wirkender Kräfte als ein Ansatz zur in situ-Kraftmessung. Im ersten Teil wird ein existierendes, mechanoresponsives System zur Anwendung gebracht, das auf einer mit Fluoreszenzfarbstoff markierten Polyelektrolytbürste basiert. Die Ladungen des Polyelektrolyts können die Fluoreszenz des Farbstoffs unterdrücken, sodass lokale Kompression und Zugspannung über die Fluoreszenzintensität unterschieden werden können. Die mechanoresponsive Polymerbürste wurde als mechanosensitive Oberflächenbeschichtung angewandt, um Unterschiede in der Kontaktspannungsverteilung von Gecko-inspirierten adhäsiven Mikrostempelstrukturen aufzuklären. Die erarbeiteten Ergebnisse und daraus abgeleiteten Ablösemechanismen der Mikrostempeltypen deckten sich qualitativ mit Vorhersagen aus theoretischen Ansätzen. Aufgrund geometrischer Einschränkungen einer planaren Oberflächenbeschichtung zielt der zweite Teil darauf ab, dieses mechanoresponsive Prinzip in ein dreidimensionales Netzwerk zu überführen und ein mechanoresponsives Hydrogelnetzwerk als Plattform zur Kraftmessung zu entwickeln. Konzeptionell besitzt ein homogenes Netzwerk vorhersagbare mechanische Eigenschaften, sodass lokale optische Antworten auf mechanische Kräfte ermöglichen könnten, die wirkenden Kräfte zu lokalisieren und quantifizieren. Basierend auf einer Gestaltung nach der Flory-Rehner-Theorie wurden Präkursoren mit vordefinierter Größe und Architektur für die Hydrogelherstellung eingesetzt, um auf ein homogenes Netzwerk abzuzielen. Zu diesem Zweck wurde das Mischungsvolumen durch Tropfenmikrofluidik reduziert. Für den optischen Antwortmechanismus wurden die Hydrogelnetzwerk-Präkursoren mit zwei verschiedenen Fluorophoren markiert, die sich durch abstandsabhängige Emission über Förster-Resonanzenergietransfer auszeichnen. Die Funktionalität des optischen Antwortmechanismus wurde auf globaler Ebene durch Kollabieren und kontrolliertes Quellen des Netzwerks, dann auf lokalisierter Ebene durch definierte mechanische Belastung mit Rasterkraftmikroskopie gezeigt. Durch ihre Anpassbarkeit könnte die Hydrogelplattform zukünftig verschiedenste Anwendungen im Bereich intrisischer Kraftmessung weicher Materie bedienen.Mechanoresponsive systems respond to mechanical triggers by changes in a certain property. This thesis covers the work conducted with two mechanoresponsive systems that respond optically to mechanical triggers. These two systems are based on polymer structures, a polymer brush and a hydrogel network. Thus, the optical response mechanism allows observing acting forces as an approach to force sensing in situ. In the first part, an existing mechanoresponsive system based on a polyelectrolyte brush labeled with a fluorescent dye is engaged in application. The charges of the polyelectrolyte are able to quench the fluorescence of the dye so that local compression or tension can be distinguished from the local fluorescence intensity. The mechanoresponsive polymer brush was applied as mechanosensitive surface coating to elucidate differences in the contact stress distributions of gecko-inspired adhesive micropillar structures. The determined results and the derived detachment mechanisms of the micropillar types were in qualitative accordance with predictions from theoretical approaches. Overcoming the geometrical limitations of a planar surface coating, the second part aims at translating the mechanoresponse principle to a three-dimensional network and developing a mechanoresponsive hydrogel as a platform for force sensing. Conceptually, a homogeneous network allows to predict mechanical properties so that localized optical mechanoresponses could enable locating and quantifying acting forces. Based on network design principles from the Flory-Rehner theory, precursors with predefined size and architecture were utilized in hydrogel preparation, aiming for a homogeneous network. Further in this regard, the mixing volume was reduced by employing droplet microfluidics. As optical response mechanism, the hydrogel network precursors were labeled with two kinds of fluorophore, featuring distance-dependent emission from Förster Resonance Energy Transfer. The functionality of the optical response mechanism was demonstrated on global level by collapsing and controlled swelling of the network, and on a localized level by defined mechanical stress, applied with Atomic Force Microscopy. Owing to its adjustability, the hydrogel platform might be employed in various applications that require intrinsic force sensing of soft matter in future

Discrete quantum geometries and their effective dimension

In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then how the smooth geometries of general relativity, expressed in terms of suitable geometric observables, arise from such discrete quantum geometries in some semiclassical and continuum limit. In this thesis I tackle the question of suitable observables focusing on the effective dimension of discrete quantum geometries. For this purpose I give a purely combinatorial description of the discrete structures which these geometries have support on. As a side topic, this allows to present an extension of group field theory to cover the combinatorially larger kinematical state space of loop quantum gravity. Moreover, I introduce a discrete calculus for fields on such fundamentally discrete geometries with a particular focus on the Laplacian. This permits to define the effective-dimension observables for quantum geometries. Analysing various classes of quantum geometries, I find as a general result that the spectral dimension is more sensitive to the underlying combinatorial structure than to the details of the additional geometric data thereon. Semiclassical states in loop quantum gravity approximate the classical geometries they are peaking on rather well and there are no indications for stronger quantum effects. On the other hand, in the context of a more general model of states which are superposition over a large number of complexes, based on analytic solutions, there is a flow of the spectral dimension from the topological dimension $d$ on low energy scales to a real number $0<\alpha<d$ on high energy scales. In the particular case of $\alpha=1$ these results allow to understand the quantum geometry as effectively fractal.Comment: PhD thesis, Humboldt-Universit\"at zu Berlin; urn:nbn:de:kobv:11-100232371; http://edoc.hu-berlin.de/docviews/abstract.php?id=4204

Hypersweeps, Convective Clouds and Reeb Spaces

Isosurfaces are one of the most prominent tools in scientific data visualisation. An isosurface is a surface that defines the boundary of a feature of interest in space for a given threshold. This is integral in analysing data from the physical sciences which observe and simulate three or four dimensional phenomena. However it is time consuming and impractical to discover surfaces of interest by manually selecting different thresholds. The systematic way to discover significant isosurfaces in data is with a topological data structure called the contour tree. The contour tree encodes the connectivity and shape of each isosurface at all possible thresholds. The first part of this work has been devoted to developing algorithms that use the contour tree to discover significant features in data using high performance computing systems. Those algorithms provided a clear speedup over previous methods and were used to visualise physical plasma simulations. A major limitation of isosurfaces and contour trees is that they are only applicable when a single property is associated with data points. However scientific data sets often take multiple properties into account. A recent breakthrough generalised isosurfaces to fiber surfaces. Fiber surfaces define the boundary of a feature where the threshold is defined in terms of multiple parameters, instead of just one. In this work we used fiber surfaces together with isosurfaces and the contour tree to create a novel application that helps atmosphere scientists visualise convective cloud formation. Using this application, they were able to, for the first time, visualise the physical properties of certain structures that trigger cloud formation. Contour trees can also be generalised to handle multiple parameters. The natural extension of the contour tree is called the Reeb space and it comes from the pure mathematical field of fiber topology. The Reeb space is not yet fully understood mathematically and algorithms for computing it have significant practical limitations. A key difficulty is that while the contour tree is a traditional one dimensional data structure made up of points and lines between them, the Reeb space is far more complex. The Reeb space is made up of two dimensional sheets, attached to each other in intricate ways. The last part of this work focuses on understanding the structure of Reeb spaces and the rules that are followed when sheets are combined. This theory builds towards developing robust combinatorial algorithms to compute and use Reeb spaces for practical data analysis