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Sebastian Bock

Publications and source records attributed to Sebastian Bock.

14 recordsLinked to original sources

MUFASA: A Multi-Layer Framework for Slot Attention

Unsupervised object-centric learning (OCL) decomposes visual scenes into distinct entities. Slot attention is a popular approach that represents individual objects as latent vectors, called slots. Current methods obtain these slot representations solely from the last layer of a pre-trained vision transformer (ViT), ignoring valuable, semantically rich information encoded across the other layers. To better utilize this latent semantic information, we introduce MUFASA, a lightweight plug-and-play framework for slot-attention-based approaches to unsupervised object segmentation. Our model computes slot attention across multiple feature layers of the ViT encoder, fully leveraging their semantic richness. We propose a fusion strategy to aggregate slots obtained on multiple layers into a unified object-centric representation. Integrating MUFASA into existing OCL methods improves their segmentation results across multiple datasets, setting a new state of the art while simultaneously improving training convergence with only minor inference overhead.

cs.CV

Methods and Tools for Secure Quantum Clouds with a specific Case Study on Homomorphic Encryption

The rise of quantum computing/technology potentially introduces significant security challenges to cloud computing, necessitating quantum-resistant encryption strategies as well as protection schemes and methods for cloud infrastructures offering quantum computing time and services (i.e. quantum clouds). This research explores various options for securing quantum clouds and ensuring privacy, especially focussing on the integration of homomorphic encryption (HE) into Eclipse Qrisp, a high-level quantum computing framework, to enhance the security of quantum cloud platforms. The study addresses the technical feasibility of integrating HE with Qrisp, evaluates performance trade-offs, and assesses the potential impact on future quantum cloud architectures. The successful implementation and Qrisp integration of three post-quantum cryptographic (PQC) algorithms demonstrates the feasibility of integrating HE with quantum computing frameworks. The findings indicate that while the Quantum One-Time Pad (QOTP) offers simplicity and low overhead, other algorithms like Chen and Gentry-Sahai-Waters (GSW) present performance trade-offs in terms of runtime and memory consumption. The study results in an overall set of recommendations for securing quantum clouds, e.g. implementing HE at data storage and processing levels, developing Quantum Key Distribution (QKD), and enforcing stringent access control and authentication mechanisms as well as participating in PQC standardization efforts.

cs.CR

Solving Drone Routing Problems with Quantum Computing: A Hybrid Approach Combining Quantum Annealing and Gate-Based Paradigms

This paper presents a novel hybrid approach to solving real-world drone routing problems by leveraging the capabilities of quantum computing. The proposed method, coined Quantum for Drone Routing (Q4DR), integrates the two most prominent paradigms in the field: quantum gate-based computing, through the Eclipse Qrisp programming language; and quantum annealers, by means of D-Wave System's devices. The algorithm is divided into two different phases: an initial clustering phase executed using a Quantum Approximate Optimization Algorithm (QAOA), and a routing phase employing quantum annealers. The efficacy of Q4DR is demonstrated through three use cases of increasing complexity, each incorporating real-world constraints such as asymmetric costs, forbidden paths, and itinerant charging points. This research contributes to the growing body of work in quantum optimization, showcasing the practical applications of quantum computing in logistics and route planning.

quant-ph

Qrisp: A Framework for Compilable High-Level Programming of Gate-Based Quantum Computers

While significant progress has been made on the hardware side of quantum computing, support for high-level quantum programming abstractions remains underdeveloped compared to classical programming languages. In this article, we introduce Qrisp, a framework designed to bridge several gaps between high-level programming paradigms in state-of-the-art software engineering and the physical reality of today's quantum hardware. The framework aims to provide a systematic approach to quantum algorithm development such that they can be effortlessly implemented, maintained and improved. We propose a number of programming abstractions that are inspired by classical paradigms, yet consistently focus on the particular needs of a quantum developer. Unlike many other high-level language approaches, Qrisp's standout feature is its ability to compile programs to the circuit level, making them executable on most existing physical backends. The introduced abstractions enable the Qrisp compiler to leverage algorithm structure for increased compilation efficiency. Finally, we present a set of code examples, including an implementation of Shor's factoring algorithm. For the latter, the resulting circuit shows significantly reduced quantum resource requirements, strongly supporting the claim that systematic quantum algorithm development can give quantitative benefits.

quant-ph

Eclipse Qrisp QAOA: description and preliminary comparison with Qiskit counterparts

This paper focuses on the presentation and evaluation of the high-level quantum programming language Eclipse Qrisp. The presented framework, used for developing and compiling quantum algorithms, is measured in terms of efficiency for its implementation of the Quantum Approximation Optimization Algorithm (QAOA) Module. We measure this efficiency and compare it against two alternative QAOA algorithm implementations using IBM's Qiskit toolkit. The evaluation process has been carried out over a benchmark composed of 15 instances of the well-known Maximum Cut Problem. Through this preliminary experimentation, Eclipse Qrisp demonstrated promising results, outperforming both versions of its counterparts in terms of results quality and circuit complexity.

quant-ph

Uncomputation in the Qrisp high-level Quantum Programming Framework

Uncomputation is an essential part of reversible computing and plays a vital role in quantum computing. Using this technique, memory resources can be safely deallocated without performing a nonreversible deletion process. For the case of quantum computing, several algorithms depend on this as they require disentangled states in the course of their execution. Thus, uncomputation is not only about resource management, but is also required from an algorithmic point of view. However, synthesizing uncomputation circuits is tedious and can be automated. In this paper, we describe the interface for automated generation of uncomputation circuits in our Qrisp framework. Our algorithm for synthesizing uncomputation circuits in Qrisp is based on an improved version of "Unqomp", a solution presented by Paradis et. al. Our paper also presents some improvements to the original algorithm, in order to make it suitable for the needs of a high-level programming framework. Qrisp itself is a fully compilable, high-level programming language/framework for gate-based quantum computers, which abstracts from many of the underlying hardware details. Qrisp's goal is to support a high-level programming paradigm as known from classical software development.

quant-ph

Non-Convergence and Limit Cycles in the Adam optimizer

One of the most popular training algorithms for deep neural networks is the Adaptive Moment Estimation (Adam) introduced by Kingma and Ba. Despite its success in many applications there is no satisfactory convergence analysis: only local convergence can be shown for batch mode under some restrictions on the hyperparameters, counterexamples exist for incremental mode. Recent results show that for simple quadratic objective functions limit cycles of period 2 exist in batch mode, but only for atypical hyperparameters, and only for the algorithm without bias correction. %More general there are several more adaptive gradient methods which try to estimate a fitting learning rate and / or search direction from the training data to improve the learning process compared to pure gradient descent with fixed learningrate. We extend the convergence analysis for Adam in the batch mode with bias correction and show that even for quadratic objective functions as the simplest case of convex functions 2-limit-cycles exist, for all choices of the hyperparameters. We analyze the stability of these limit cycles and relate our analysis to other results where approximate convergence was shown, but under the additional assumption of bounded gradients which does not apply to quadratic functions. The investigation heavily relies on the use of computer algebra due to the complexity of the equations.

cs.LG

Efficient Floating Point Arithmetic for Quantum Computers

One of the major promises of quantum computing is the realization of SIMD (single instruction - multiple data) operations using the phenomenon of superposition. Since the dimension of the state space grows exponentially with the number of qubits, we can easily reach situations where we pay less than a single quantum gate per data point for data-processing instructions which would be rather expensive in classical computing. Formulating such instructions in terms of quantum gates, however, still remains a challenging task. Laying out the foundational functions for more advanced data-processing is therefore a subject of paramount importance for advancing the realm of quantum computing. In this paper, we introduce the formalism of encoding so called-semi-boolean polynomials. As it turns out, arithmetic $\mathbb{Z}/2^n\mathbb{Z}$ ring operations can be formulated as semi-boolean polynomial evaluations, which allows convenient generation of unsigned integer arithmetic quantum circuits. For arithmetic evaluations, the resulting algorithm has been known as Fourier-arithmetic. We extend this type of algorithm with additional features, such as ancilla-free in-place multiplication and integer coefficient polynomial evaluation. Furthermore, we introduce a tailor-made method for encoding signed integers succeeded by an encoding for arbitrary floating-point numbers. This representation of floating-point numbers and their processing can be applied to any quantum algorithm that performs unsigned modular integer arithmetic. We discuss some further performance enhancements of the semi boolean polynomial encoder and finally supply a complexity estimation. The application of our methods to a 32-bit unsigned integer multiplication demonstrated a 90\% circuit depth reduction compared to carry-ripple approaches.

quant-ph

Automatic Generation of Grover Quantum Oracles for Arbitrary Data Structures

The steadily growing research interest in quantum computing - together with the accompanying technological advances in the realization of quantum hardware - fuels the development of meaningful real-world applications, as well as implementations for well-known quantum algorithms. One of the most prominent examples till today is Grover's algorithm, which can be used for efficient search in unstructured databases. Quantum oracles that are frequently masked as black boxes play an important role in Grover's algorithm. Hence, the automatic generation of oracles is of paramount importance. Moreover, the automatic generation of the corresponding circuits for a Grover quantum oracle is deeply linked to the synthesis of reversible quantum logic, which - despite numerous advances in the field - still remains a challenge till today in terms of synthesizing efficient and scalable circuits for complex boolean functions. In this paper, we present a flexible method for automatically encoding unstructured databases into oracles, which can then be efficiently searched with Grover's algorithm. Furthermore, we develop a tailor-made method for quantum logic synthesis, which vastly improves circuit complexity over other current approaches. Finally, we present another logic synthesis method that considers the requirements of scaling onto real world backends. We compare our method with other approaches through evaluating the oracle generation for random databases and analyzing the resulting circuit complexities using various metrics.

quant-ph

Local Convergence of Adaptive Gradient Descent Optimizers

Adaptive Moment Estimation (ADAM) is a very popular training algorithm for deep neural networks and belongs to the family of adaptive gradient descent optimizers. However to the best of the authors knowledge no complete convergence analysis exists for ADAM. The contribution of this paper is a method for the local convergence analysis in batch mode for a deterministic fixed training set, which gives necessary conditions for the hyperparameters of the ADAM algorithm. Due to the local nature of the arguments the objective function can be non-convex but must be at least twice continuously differentiable. Then we apply this procedure to other adaptive gradient descent algorithms and show for most of them local convergence with hyperparameter bounds.

cs.LG

An improvement of the convergence proof of the ADAM-Optimizer

A common way to train neural networks is the Backpropagation. This algorithm includes a gradient descent method, which needs an adaptive step size. In the area of neural networks, the ADAM-Optimizer is one of the most popular adaptive step size methods. It was invented in \cite{Kingma.2015} by Kingma and Ba. The $5865$ citations in only three years shows additionally the importance of the given paper. We discovered that the given convergence proof of the optimizer contains some mistakes, so that the proof will be wrong. In this paper we give an improvement to the convergence proof of the ADAM-Optimizer.

cs.LG

Build-up of the Kondo effect from real-time 2PI effective action for the Anderson impurity model

The nonequilibrium time evolution of a quantum dot is studied by means of dynamic equations for time-dependent Greens functions derived from a two-particle-irreducible (2PI) effective action for the Anderson impurity model. Coupling the dot between two leads at different voltages, the dynamics of the current through the dot is investigated. We show that the 2PI approach is capable to describe the dynamical build-up of the Kondo effect, which shows up as a sharp resonance in the spectral function, with a width exponentially suppressed in the electron self coupling on the dot. An external voltage applied to the dot is found to deteriorate the Kondo effect at the hybridization scale. The dynamic equations are evaluated within different nonperturbative resummation schemes, within the direct, particle-particle, and particle-hole channels, as well as their combination, and the results compared with that from other methods.

cond-mat.mes-hall

Measuring Hidden Higgs and Strongly-Interacting Higgs Scenarios

Higgs couplings can be affected by physics beyond the Standard Model. We study modifications through interactions with a hidden sector and in specific composite Higgs models accessible at the LHC. Both scenarios give rise to congruent patterns of universal, or partially universal, shifts. In addition, Higgs decays to the hidden sector may lead to invisible decay modes which we also exploit. Experimental bounds on such potential modifications will measure the concordance of an observed Higgs boson with the Standard Model.

hep-ph

On a three dimensional analogue to the holomorphic z-powers

The main objective of this article is a constructive generalization of the holomorphic power and Laurent series expansions in C to dimension 3 using the framework of hypercomplex function theory. For this reason, deals the first part of this article with generalized Fourier & Taylor series expansions in the space of square integrable quaternion-valued functions which possess peculiar properties regarding the hypercomplex derivative and primitive. In analogy to the complex one-dimensional case, both series expansions are orthogonal series with respect to the unit ball in R^3 and their series coefficients can be explicitly (one-to-one) linked with each other. Furthermore, very compact and efficient representation formulae (recurrence, closed-form) for the elements of the orthogonal bases are presented. The latter results are then used to construct a new orthonormal bases of outer solid spherical monogenics in the space of square integrable quaternion-valued functions. This finally leads to the definition of a generalized Laurent series expansion for the spherical shell.

math.CV