281 research outputs found

    Quantum Error Correction with the Toric-GKP Code

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    We examine the performance of the single-mode GKP code and its concatenation with the toric code for a noise model of Gaussian shifts, or displacement errors. We show how one can optimize the tracking of errors in repeated noisy error correction for the GKP code. We do this by examining the maximum-likelihood problem for this setting and its mapping onto a 1D Euclidean path-integral modeling a particle in a random cosine potential. We demonstrate the efficiency of a minimum-energy decoding strategy as a proxy for the path integral evaluation. In the second part of this paper, we analyze and numerically assess the concatenation of the GKP code with the toric code. When toric code measurements and GKP error correction measurements are perfect, we find that by using GKP error information the toric code threshold improves from 10%10\% to 14%14\%. When only the GKP error correction measurements are perfect we observe a threshold at 6%6\%. In the more realistic setting when all error information is noisy, we show how to represent the maximum likelihood decoding problem for the toric-GKP code as a 3D compact QED model in the presence of a quenched random gauge field, an extension of the random-plaquette gauge model for the toric code. We present a new decoder for this problem which shows the existence of a noise threshold at shift-error standard deviation σ00.243\sigma_0 \approx 0.243 for toric code measurements, data errors and GKP ancilla errors. If the errors only come from having imperfect GKP states, this corresponds to states with just 4 photons or more. Our last result is a no-go result for linear oscillator codes, encoding oscillators into oscillators. For the Gaussian displacement error model, we prove that encoding corresponds to squeezing the shift errors. This shows that linear oscillator codes are useless for quantum information protection against Gaussian shift errors.Comment: 50 pages, 14 figure

    Evolution of entanglement structure in open quantum systems

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    The thesis presents research related to the dynamics of quantum systems, both isolated and in the presence of interactions with their environment. Generally, I employ matrix product state (MPS) techniques to explore quantum dynamics in open and closed systems. In the first part I present a study of quantum chaos and how mapping to a MPS variational manifold allow the use of techniques developed in the study of classical many-body systems. Using code developed for this project the Lyapunov spectrum is extracted to give an alternative perspective on eigenstate thermalization, pre-thermalization and integrability. In the second part, I present a novel combination of MPS methods with a Langevin description of the open system. I use this to show how coupling to the environment restricts the growth of entanglement. The consequences of this are relevant for simulations of open quantum systems and their use in in quantum technologies. Finally I discuss applications of these ideas to quantum search. I consider adiabatic and quantum walk algorithms for optimal scaling quantum search algorithms, and hybridizations between the two. The robustness of the different underlying physical mechanisms is investigated in a simple infinite-temperature model, and in a low-temperature limit using the MPS Langevin equation

    Non-ergodic phenomena in many-body quantum systems

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    The assumption of ergodicity is the cornerstone of conventional thermodynamics, connecting the equilibrium properties of macroscopic systems to the chaotic nature of the underlying microscopic dynamics, which eventuates in thermalization and the scrambling of information contained in any generic initial condition. The modern understanding of ergodicity in a quantum mechanical framework is encapsulated in the so-called eigenstate thermalization hypothesis, which asserts that thermalization of an isolated quantum system is a manifestation of the random-like character of individual eigenstates in the bulk of the spectrum of the system's Hamiltonian. In this work, we consider two major exceptions to the rule of generic thermalization in interacting many-body quantum systems: many-body localization, and quantum spin glasses. In the first part, we debate the possibility of localization in a system endowed with a non-Abelian symmetry. We show that, in line with proposed theoretical arguments, such a system is probably delocalized in the thermodynamic limit, but the ergodization length scale is anomalously large, explaining the non-ergodic behavior observed in previous experimental and numerical works. A crucial feature of this system is the quasi-tensor-network nature of its eigenstates, which is dictated by the presence of nontrivial symmetry multiplets. As a consequence, ergodicity may only be restored by extensively large cascades of resonating spins, explaining the system's resistance to delocalization. In the second part, we study the effects of non-ergodic behavior in glassy systems in relation to the possibility of speeding up classical algorithms via quantum resources, namely tunneling across tall free energy barriers. First, we define a pseudo-tunneling event in classical diffusion Monte Carlo (DMC) and characterize the corresponding tunneling rate. Our findings suggest that DMC is very efficient at tunneling in stoquastic problems even in the presence of frustrated couplings, asymptotically outperforming incoherent quantum tunneling. We also analyze in detail the impact of importance sampling, finding that it does not alter the scaling. Next, we study the so-called population transfer (PT) algorithm applied to the problem of energy matching in combinatorial problems. After summarizing some known results on a simpler model, we take the quantum random energy model as a testbed for a thorough, model-agnostic numerical characterization of the algorithm, including parameter setting and quality assessment. From the accessible system sizes, we observe no meaningful asymptotic speedup, but argue in favor of a better performance in more realistic energy landscapes

    27th Annual European Symposium on Algorithms: ESA 2019, September 9-11, 2019, Munich/Garching, Germany

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    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    LIPIcs, Volume 248, ISAAC 2022, Complete Volume

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    LIPIcs, Volume 248, ISAAC 2022, Complete Volum

    Bio-sensing using toroidal microresonators & theoretical cavity optomechanics

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    In this thesis we report on two matters, (i) time-resolved single particle bio-sensing using a cavity enhanced refractive index sensor with unmatched sensitivity, and (ii) the theoretical analysis of parametric normal mode splitting in cavity optomechanics, as well as the quantum limit of a displacement transducer that relies on multiple cavity modes. It is the unifying element of these studies that they rely on a high-Q optical cavity transducer and amount to a precision measurement of an optical frequency. In the first part, we describe an experiment where a high-Q toroidal microcavity is used as a refractive index sensor for single particle studies. The resonator supports whispering gallery modes (WGM) that feature an evanescent fraction, probing the environment close to the toroid's surface. When a particle with a refractive index, different from its environment, enters the evanescent field of the WGM, the resonance frequency shifts. Here, we monitor the shift with a frequency resolution of df/f=7.7e-11 at a time resolution of 100µs , which constitutes a x10 improvement of the sensitivity and a x100 improvement in time resolution, compared to the state of the art. This unprecedented sensitivity is the key to real-time resolution of single lipid vesicles with 25nm radius adsorbing onto the surface. Moreover -- for the first time within one distinct measurement -- a record number of up to 200 identifiable events was recorded, which provides the foundation for a meaningful statistical analysis. Strikingly, the large number of recorded events and the high precision revealed a disagreement with the theoretical model for the single particle frequency shift. A correction factor that fully accounts for the polarizability of the particle, and thus corrects the deviation, was introduced and establishes a quantitative understanding of the binding events. Directed towards biological application, we introduce an elegant method to cover the resonator surface with a single lipid bilayer, which creates a universal, biomimetic interface for specific functionalization with lipid bound receptors or membrane proteins. Quantitative binding of streptavidin to biotinylated lipids is demonstrated. Moving beyond the detection limit, we provide evidence that the presence of single IgG proteins (that cannot be resolved individually) manifests in the frequency noise spectrum. The theoretical analysis of the thermo-refractive noise floor yields a fundamental limit of the sensors resolution. The second part of the thesis deals with the theoretical analysis of the coupling between an optical cavity mode and a mechanical mode of much lower frequency. Despite the vastly different resonance frequencies, a regime of strong coupling between the mechanics and the light field can be achieved, which manifests as a hybridization of the modes and as a mode splitting in the spectrum of the quadrature fluctuations. The regime is a precondition for coherent energy exchange between the mechanical oscillator and the light field. Experimental observation of optomechanical mode splitting was reported shortly after publication of our results [cf. Gröblacher et al., Nature 460, 724--727]. Dynamical backaction cooling of the mechanical mode can be achieved, when the optical mode is driven red-detuned from resonance. We use a perturbation and a covariance approach to calculate both, the power dependence of the mechanical occupation number and the influence of excess noise in the optical drive that is used for cooling. The result was one to one applied for data analysis in a seminal article on ground state cooling of a mechanical oscillator [cf. Teufel et al., Nature 475, 359--363]. In addition we investigate a setting, where multiple optical cavity modes are coupled to a single mechanical degree of freedom. Resonant build-up of the motional sidebands amplifies the mechanical displacement signal, such that the standard quantum limit for linear position detection can be reached at significantly lower input power.In dieser Dissertation werden zwei Themen behandelt. Im ersten Teil widmen wir uns experimentell der zeitaufgelösten Messung von Liposomen mit Hilfe eines Nahfeld-Brechungsindex-Sensors. Der zweite Teil handelt von der theoretischen Beschreibung des Regimes der starken Kopplung zwischen einem mechanischen Oszillator und dem Feld eines optischen Resonators. Des Weiteren erörtern wir ein Messschema, das es erlaubt eine mechanische Bewegung, mit Hilfe von mehreren optischen Resonatormoden genauer auszulesen. Die Gemeinsamkeit beider Arbeiten besteht darin, dass es sich jeweils um eine Präzisionsmessung einer optischen Frequenz handelt. Im experimentellen Teil benutzen wir Toroid-Mikroresonatoren mit extrem hoher optischer Güte als Biosensoren. Dabei handelt es sich um eine ringförmige Glasstruktur, entlang welcher Licht im Kreis geleitet wird. Dazu muss eine Resonanzbedingung erfüllt sein, die besagt, dass der (effektive) Umfang des Rings einem ganzzahligen Vielfachen der optischen Wellenlänge entspricht. Ein Teil des zirkulierenden Lichts ist als evaneszente Welle empfänglich für Brechungsindexänderungen nahe der Oberfläche des Resonators. Ein Partikel, dessen Brechungsindex sich von dem der Umgebung unterscheidet, induziert beim Eintritt in das evaneszente Feld eine Frequenzverschiebung der optischen Resonanz. Im Rahmen dieser Arbeit lösen wir relative Frequenzverschiebungen mit einer Genauigkeit von df/f=7.7e-11 und einer Zeitkonstante von 100µs auf. Dies stellt eine Verbesserung des derzeitigen Stands der Technik um einen Faktor x10 in der Frequenz und einen Faktor x100 in der Zeit dar. Diese bisher unerreichte Empfindlichkeit der Messmethode ist der Schlüssel zur Echtzeitdetektion einzelner Lipidvesikel mit einem Radius von 25nm . Zudem gelingt es uns innerhalb einer Messung, bis zu 200 Einzelteilchenereignisse aufzunehmen, welche die Basis für eine aussagekräftige Statistik liefern. Bemerkenswerterweise konnten wir Dank der außerordentlichen Präzision und der Vielzahl der Ereignisse eine Abweichung zur bis dato akzeptierten und angewandten Theorie feststellen. Wir ergänzen das Model um einen Korrekturfaktor, der die Polarisierbarkeit des Teilchens vollständig berücksichtigt und erlangen dadurch ein umfassendes und quantitatives Verständnis der Messergebnisse. Im Hinblick auf biologisch relevante Fragestellungen zeigen wir eine elegante Methode auf, die es erlaubt, den Resonator mit einer einzelnen Lipidmembran zu beschichten. Wir kreieren somit eine biomimetische Schnittstelle, welche das Grundgerüst für eine spezifische Funktionalisierung mit lipidgebundenen Rezeptoren, Antikörpern oder Membranproteinen darstellt. Des Weiteren zeigen wir, dass der Empfindlichkeit eine fundamentale Grenze durch thermische Brechungsindexfluktuationen gesetzt ist. Hierzu wird ein theoretisches Modell speziell für den relevanten niederfrequenten Bereich errechnet. Im zweiten Teil der Arbeit beschäftigen wir uns mit der theoretischen Beschreibung eines optischen Resonators, dessen Lichtfeld an eine mechanische Schwingung gekoppelt ist. Obwohl sich die Resonanzfrequenzen der Optik und der Mechanik typischerweise um mehrere Größenordnungen unterscheiden, existiert ein Regime der starken Kopplung, in dem die Fluktuationen des Lichts und die mechanischen Vibrationen hybridisieren. Dies offenbart sich zum Beispiel im Phasenspektrum, wo sich das ursprüngliche Maximum der Resonanz in zwei Maxima aufspaltet. Die starke Kopplung stellt die Grundlage für kohärenten Energie- und Informationsaustausch zwischen Licht und Mechanik dar und ist daher von besonderem technischen und wissenschaftlichen Interesse. Es ist anzumerken, dass die starke Kopplung und die einhergehende Aufspaltung der Resonanz bereits kurz nach Veröffentlichung unserer theoretischen Beschreibung im Experiment beobachtet wurde [vgl. Gröblacher et al., Nature 460, 724--727]. Wenn der optische Resonator (zur längeren Wellenlänge hin) verstimmt von der Resonanz angeregt wird, kann über dynamische Rückkopplung eine effektive Kühlung der mechanischen Schwingung erreicht werden. Wir berechnen die thermische Besetzungszahl der mechanischen Mode (und somit die Temperatur) mit Hilfe eines störungstheoretischen und eines Kovarianzansatzes. Dabei berücksichtigen wir sowohl ein klassisches Rauschen des optischen Feldes als auch den Einfluss der optomechanischen Kopplung auf die Grenztemperatur. Der hergeleitete Ausdruck für die finale Besetzungszahl wurde eins zu eins für die Datenanalyse in dem wegweisenden Artikel über das Kühlen eines mechanischen Oszillators in den Quantengrundzustand verwendet [vgl. Teufel et al., Nature 475, 359--363]. Abschließend betrachten wir ein Schema, bei dem die Lichtfelder mehrerer optischer Resonanzen an eine mechanischen Schwingung gekoppelt sind. Die resonante Verstärkung der Information über die mechanische Bewegung in den optischen Seitenbändern ermöglicht es, eine durch das Standard Quantenlimit begrenzte Empfindlichkeit bei signifikant niedriger Eingangsleistung zu erreichen

    Full stack development toward a trapped ion logical qubit

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    Quantum error correction is a key step toward the construction of a large-scale quantum computer, by preventing small infidelities in quantum gates from accumulating over the course of an algorithm. Detecting and correcting errors is achieved by using multiple physical qubits to form a smaller number of robust logical qubits. The physical implementation of a logical qubit requires multiple qubits, on which high fidelity gates can be performed. The project aims to realize a logical qubit based on ions confined on a microfabricated surface trap. Each physical qubit will be a microwave dressed state qubit based on 171Yb+ ions. Gates are intended to be realized through RF and microwave radiation in combination with magnetic field gradients. The project vertically integrates software down to hardware compilation layers in order to deliver, in the near future, a fully functional small device demonstrator. This thesis presents novel results on multiple layers of a full stack quantum computer model. On the hardware level a robust quantum gate is studied and ion displacement over the X-junction geometry is demonstrated. The experimental organization is optimized through automation and compressed waveform data transmission. A new quantum assembly language purely dedicated to trapped ion quantum computers is introduced. The demonstrator is aimed at testing implementation of quantum error correction codes while preparing for larger scale iterations.Open Acces

    LIPIcs, Volume 258, SoCG 2023, Complete Volume

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    LIPIcs, Volume 258, SoCG 2023, Complete Volum
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