Search

Tensor networks provide a powerful tool for studying many-body quantum systems, particularly making quantum simulations more efficient. In this article, we construct a tensor network representation of the spin network states, which correspond to $SU(2)$ gauge-invariant discrete field theories. Importantly, the spin network states play a central role in the Loop Quantum Gravity (LQG) approach to the Planck scale physics. Our focus is on the Ising-type spin networks, which provide a basic model of quantum space in LQG. It is shown that the tensor network approach improves the previously introduced methods of constructing quantum circuits for the Ising spin networks by reducing the number of qubits involved. It is also shown that the tensor network approach is convenient for implementing holographic states involving the bulk-boundary conjecture, which contributes to establishing a link between LQG and holographic duality., Comment: Article consists of 16 pages and 46 figures. Comments are welcome

Syntactic parsing is essential in natural-language processing, with constituent structure being one widely used description of syntax. Traditional views of constituency demand that constituents consist of adjacent words, but this poses challenges in analysing syntax with non-local dependencies, common in languages like German. Therefore, in a number of treebanks like NeGra and TIGER for German and DPTB for English, long-range dependencies are represented by crossing edges. Various grammar formalisms have been used to describe discontinuous trees - often with high time complexities for parsing. Transition-based parsing aims at reducing this factor by eliminating the need for an explicit grammar. Instead, neural networks are trained to produce trees given raw text input using supervised learning on large annotated corpora. An elegant proposal for a stack-free transition-based parser developed by Coavoux and Cohen (2019) successfully allows for the derivation of any discontinuous constituent tree over a sentence in worst-case quadratic time. The purpose of this work is to explore the introduction of supertag information into transition-based discontinuous constituent parsing. In lexicalised grammar formalisms like CCG (Steedman, 1989) informative categories are assigned to the words in a sentence and act as the building blocks for composing the sentence's syntax. These supertags indicate a word's structural role and syntactic relationship with surrounding items. The study examines incorporating supertag information by using a dedicated supertagger as additional input for a neural parser (pipeline) and by jointly training a neural model for both parsing and supertagging (multi-task). In addition to CCG, several other frameworks (LTAG-spinal, LCFRS) and sequence labelling tasks (chunking, dependency parsing) will be compared in terms of their suitability as auxiliary tasks for parsing., Comment: Bachelor's Thesis. Supervised by Dr. Kilian Evang and Univ.-Prof. Dr. Laura Kallmeyer

Quantum Machine Learning (QML) has gathered significant attention through approaches like Quantum Kernel Machines. While these methods hold considerable promise, their quantum nature presents inherent challenges. One major challenge is the limited resolution of estimated kernel values caused by the finite number of circuit runs performed on a quantum device. In this study, we propose a comprehensive system of rules and heuristics for estimating the required number of circuit runs in quantum kernel methods. We introduce two critical effects that necessitate an increased measurement precision through additional circuit runs: the spread effect and the concentration effect. The effects are analyzed in the context of fidelity and projected quantum kernels. To address these phenomena, we develop an approach for estimating desired precision of kernel values, which, in turn, is translated into the number of circuit runs. Our methodology is validated through extensive numerical simulations, focusing on the problem of exponential value concentration. We stress that quantum kernel methods should not only be considered from the machine learning performance perspective, but also from the context of the resource consumption. The results provide insights into the possible benefits of quantum kernel methods, offering a guidance for their application in quantum machine learning tasks., Comment: 18 + 13 pages, 8 figures. This manuscript is a first release that will be improved in future versions. We wanted to provide this preview now as we recently became aware of extensive modifications in arXiv:2208.11060

Retrieval Augmented Generation (RAG) techniques aim to mitigate hallucinations in Large Language Models (LLMs). However, LLMs can still produce information that is unsupported or contradictory to the retrieved contexts. We introduce LYNX, a SOTA hallucination detection LLM that is capable of advanced reasoning on challenging real-world hallucination scenarios. To evaluate LYNX, we present HaluBench, a comprehensive hallucination evaluation benchmark, consisting of 15k samples sourced from various real-world domains. Our experiment results show that LYNX outperforms GPT-4o, Claude-3-Sonnet, and closed and open-source LLM-as-a-judge models on HaluBench. We release LYNX, HaluBench and our evaluation code for public access.

In Nielsen's geometric approach to quantum complexity, the introduction of a suitable geometrical space, based on the Lie group formed by fundamental operators, facilitates the identification of complexity through geodesic distance in the group manifold. Earlier work had shown that the computation of geodesic distance can be challenging for Lie groups relevant to harmonic oscillators. Here, this problem is approached by working to leading order in an expansion by the structure constants of the Lie group. An explicit formula for an upper bound on the quantum complexity of a harmonic oscillator Hamiltonian with time-dependent frequency is derived. Applied to a massless test scalar field on a cosmological de Sitter background, the upper bound on complexity as a function of the scale factor exhibits a logarithmic increase on super-Hubble scales. This result aligns with the gate complexity and earlier studies of de Sitter complexity. It provides a proof of concept for the application of Nielsen complexity in cosmology, together with a systematic setting in which higher-order terms can be included., Comment: 32 pages including references and appendix

Background: Asymmetric fission is known to occur in two regions, the actinides and sub-lead, and is dependent on the fissioning system excitation energy. Experimental evidence in the sub-lead region show that this mode is surprisingly persistent with increasing energy and its origin is not fully understood. Purpose: To experimentally study the fusion-fission reaction of $^{215}$Fr at moderate excitation energy and determine previously unknown independent fission yields and other properties. Method: The compound nucleus was formed in the reaction $^{18}$O + $^{197}$Au. The prompt gamma-rays emitted during the reaction were measured with the high efficiency and high granularity $\nu$-ball2 spectrometer. Independent fission yields of even-even nuclei were determined by detecting triple-gamma cascades in the fission fragments. Results: The observed yields, although dominated by a symmetric peak, show maxima for heavy fragment of $Z \approx 54-56$, which is consistent with the known results in the actinide region but unexpected for the nuclide of interest, and at the studied excitation energy. Conclusions: The mode of asymmetric fission is present even at relatively high excitation energies in the system studied. This observation matches experimental findings in the sub-lead region, contrary to the actinides, and so far there is no well-developed explanation of this phenomenon.

The industry of quantum technologies is rapidly expanding, offering promising opportunities for various scientific domains. Among these emerging technologies, Quantum Machine Learning (QML) has attracted considerable attention due to its potential to revolutionize data processing and analysis. In this paper, we investigate the application of QML in the field of remote sensing. It is believed that QML can provide valuable insights for analysis of data from space. We delve into the common beliefs surrounding the quantum advantage in QML for remote sensing and highlight the open challenges that need to be addressed. To shed light on the challenges, we conduct a study focused on the problem of kernel value concentration, a phenomenon that adversely affects the runtime of quantum computers. Our findings indicate that while this issue negatively impacts quantum computer performance, it does not entirely negate the potential quantum advantage in QML for remote sensing., Comment: 2 pages, 2 figures. Presented at the Big Data from Space 2023 conference

In this article, the possibility of generating non-classical light due to Planck-scale effects is considered. For this purpose, a widely studied model of deformation of the Heisenberg uncertainty relation is applied to single-mode and multi-mode lights. The model leads to a deformed dispersion relation, which manifests in an advancement in the time of arrival of photons. The key finding is that the model also leads to an oscillatory pattern of squeezing of the state of light. Furthermore, while the amplitude of the oscillations is constant for energy eigenstates, it exhibits linear growth over time for coherent states with the annihilation operator eigenvalue $\alpha \neq0 $. This second case leads to the accumulation of squeezing and phase-space displacement, which can be significant for astrophysical photons. In particular, for $\alpha \sim 1$, coherent light in the optical spectrum emitted at megaparsec distances would acquire squeezing with the amplitude of the order unity. This suggests that measurements of the non-classical properties of light originating from distant astrophysical sources may open a window to test these predictions., Comment: 11 pages main text, 1 page appendix, 1 figure. Matches published version. Discussion about the dimension of $\beta$ below Eq. (1) extended. Bibliography reordered

According to the pioneering work of Nielsen and collaborators, the length of the minimal geodesic in a geometric realization of a suitable operator space provides a measure of the quantum complexity of an operation. Compared with the original concept of complexity based on the minimal number of gates required to construct the desired operation as a product, this geometrical approach amounts to a more concrete and computable definition, but its evaluation is nontrivial in systems with a high-dimensional Hilbert space. The geometrical formulation can more easily be evaluated by considering the geometry associated with a suitable finite-dimensional group generated by a small number of relevant operators of the system. In this way, the method has been applied in particular to the harmonic oscillator, which is also of interest in the present paper. However, subtle and previously unrecognized issues of group theory can lead to unforeseen complications, motivating a new formulation that remains on the level of the underlying Lie algebras for most of the required steps. Novel insights about complexity can thereby be found in a low-dimensional setting, with the potential of systematic extensions to higher dimensions as well as interactions. Specific examples include the quantum complexity of various target unitary operators associated with a harmonic oscillator, inverted harmonic oscillator, and coupled harmonic oscillators. The generality of this approach is demonstrated by an application to an anharmonic oscillator with a cubic term., Comment: Discussions added, improved plots, typos fixed, references added. Matches the published version

Support vector machines (SVMs) are a well-established classifier effectively deployed in an array of pattern recognition and classification tasks. In this work, we consider extending classic SVMs with quantum kernels and applying them to satellite data analysis. The design and implementation of SVMs with quantum kernels (hybrid SVMs) is presented. It consists of the Quantum Kernel Estimation (QKE) procedure combined with a classic SVM training routine. The pixel data are mapped to the Hilbert space using ZZ-feature maps acting on the parameterized ansatz state. The parameters are optimized to maximize the kernel target alignment. We approach the problem of cloud detection in satellite image data, which is one of the pivotal steps in both on-the-ground and on-board satellite image analysis processing chains. The experiments performed over the benchmark Landsat-8 multispectral dataset revealed that the simulated hybrid SVM successfully classifies satellite images with accuracy on par with classic SVMs., Comment: Prepared for IGARSS 2023 Proceedings, 4 pages, 2 figures

The optimization of Kernel-Target Alignment (TA) has been recently proposed as a way to reduce the number of hardware resources in quantum classifiers. It allows to exchange highly expressive and costly circuits to moderate size, task oriented ones. In this work we propose a simple toy model to study the optimization landscape of the Kernel-Target Alignment. We find that for underparameterized circuits the optimization landscape possess either many local extrema or becomes flat with narrow global extremum. We find the dependence of the width of the global extremum peak on the amount of data introduced to the model. The experimental study was performed using multispectral satellite data, and we targeted the cloud detection task, being one of the most fundamental and important image analysis tasks in remote sensing., Comment: Prepared for IGARSS 2023 Proceedings, 4 pages, 4 figures

Spin network states are a powerful tool for constructing the $SU(2)$ gauge theories on a graph. In loop quantum gravity (LQG), they have yielded many promising predictions, although progress has been limited by the computational challenge of dealing with high-dimensional Hilbert spaces. To explore more general configurations, quantum computing methods can be applied by representing spin network states as quantum circuits. In this article, we introduce an improved method for constructing quantum circuits for 4-valent Ising spin networks, which utilizes a smaller number of qubits than previous approaches. This has practical implications for the implementation of quantum circuits. We also demonstrate the procedure with various examples, including the construction of a 10-node Ising spin network state. The key ingredient of the method is the variational transfer of partial states, which we illustrate through numerous examples. Our improved construction provides a promising avenue for further exploring the potential of quantum computing methods in quantum gravity research., Comment: 16 pages, 33 figures

Support vector machines (SVMs) are a well-established classifier effectively deployed in an array of classification tasks. In this work, we consider extending classical SVMs with quantum kernels and applying them to satellite data analysis. The design and implementation of SVMs with quantum kernels (hybrid SVMs) are presented. Here, the pixels are mapped to the Hilbert space using a family of parameterized quantum feature maps (related to quantum kernels). The parameters are optimized to maximize the kernel target alignment. The quantum kernels have been selected such that they enabled analysis of numerous relevant properties while being able to simulate them with classical computers on a real-life large-scale dataset. Specifically, we approach the problem of cloud detection in the multispectral satellite imagery, which is one of the pivotal steps in both on-the-ground and on-board satellite image analysis processing chains. The experiments performed over the benchmark Landsat-8 multispectral dataset revealed that the simulated hybrid SVM successfully classifies satellite images with accuracy comparable to the classical SVM with the RBF kernel for large datasets. Interestingly, for large datasets, the high accuracy was also observed for the simple quantum kernels, lacking quantum entanglement., Comment: 12 pages, 10 figures

Quantum networks open the way to an unprecedented level of communication security. However, due to physical limitations on the distances of quantum links, current implementations of quantum networks are unavoidably equipped with trusted nodes. As a consequence, the quantum key distribution can be performed only on the links. Due to this, some new authentication and key exchange schemes must be considered to fully benefit from the unconditional security of links. One such approach uses Multiple Non-Overlapping Paths (MNOPs) for key exchange to mitigate the risk of an attack on a trusted node. The scope of the article is to perform a security analysis of this scheme for the case of both uncorrelated attacks and correlated attacks with finite resources. Furthermore, our analysis is extended to the case of Multiple Overlapping Paths (MOPs). We prove that introducing overlapping paths allows one to increase the security of the protocol, compared to the non-overlapping case with the same number of additional links added. This result may find application in optimising architectures of large-scale (hybrid) quantum networks., Comment: 18 pages, 12 figures

The exploration of the universe has recently entered a new era thanks to the multi-messenger paradigm, characterized by a continuous increase in the quantity and quality of experimental data that is obtained by the detection of the various cosmic messengers (photons, neutrinos, cosmic rays and gravitational waves) from numerous origins. They give us information about their sources in the universe and the properties of the intergalactic medium. Moreover, multi-messenger astronomy opens up the possibility to search for phenomenological signatures of quantum gravity. On the one hand, the most energetic events allow us to test our physical theories at energy regimes which are not directly accessible in accelerators; on the other hand, tiny effects in the propagation of very high energy particles could be amplified by cosmological distances. After decades of merely theoretical investigations, the possibility of obtaining phenomenological indications of Planck-scale effects is a revolutionary step in the quest for a quantum theory of gravity, but it requires cooperation between different communities of physicists (both theoretical and experimental). This review is aimed at promoting this cooperation by giving a state-of-the art account of the interdisciplinary expertise that is needed in the effective search of quantum gravity footprints in the production, propagation and detection of cosmic messengers., Comment: This review was written by participants of the COST Action CA18108. Further information on the review can be found at https://qg-mm.unizar.es/review/, updated to published version

One of the central difficulties in the quantization of the gravitational interactions is that they are described by a set of constraints. The standard strategy for dealing with the problem is the Dirac quantization procedure, which leads to the Wheeler-DeWitt equation. However, solutions to the equation are known only for specific symmetry-reduced systems, including models of quantum cosmology. Novel methods, which enable solving the equation for complex gravitational configurations are, therefore, worth seeking. Here, we propose and investigate a new method of solving the Wheeler-DeWitt equation, which employs a variational quantum computing approach, and is possible to implement on quantum computers. For this purpose, the gravitational system is regularized, by performing spherical compactification of the phase space. This makes the system's Hilbert space finite-dimensional and allows to use $SU(2)$ variables, which are easy to handle in quantum computing. The validity of the method is examined in the case of the flat de Sitter universe. For the purpose of testing the method, both an emulator of a quantum computer and the IBM superconducting quantum computer have been used. The advantages and limitations of the approach are discussed., Comment: 15 pages

An accumulation of theoretical evidence contribute to the picture of gravity as a manifestation of quantum entanglement in a certain many-body quantum system. This is in particular expresses in the ER=EPR conjecture, which relates gravitational Einstein-Rosen (ER) bridge with the Einstein-Podolsky-Rosen (EPR) quantum entangled pairs or, more generally, with the so-called Thermofield Double State. In this letter, the ER=EPR conjecture is employed to introduce unitary quantum teleportation protocol, which \emph{recycles} the entanglement forming traversable generalization of the Einstein-Rosen bridge. In consequence, the wormhole remains unaffected by the quantum teleportation. Furthermore, it is shown that the protocol guarantees the unconditional security of the quantum communication. Performance of the protocol is demonstrated in a simple setting with the use of 5-qubit Santiago IBM quantum computer, giving fidelities above the $2/3$ classical limit for a representative set of teleported states. Security of the protocol has been supported by experimental studies performed with the use of the noisy quantum processor. Possible generalization of the protocol, which may have relevance in the context of macroscopic gravitational configurations, is also considered., Comment: 6 pages

The European Spallation Source (ESS) accelerator is composed of superconducting elliptical cavities. When the facility is running, the cavities are fed with electrical field from klystrons. Parameters of this field are monitored and controlled by the Low-Level Radio Frequency (LLRF) system. Its main goal is to keep the amplitude and phase at a given set-point. The LLRF system is also responsible for the reference clock distribution. During machine operation the cavities are periodically experiencing strain caused by the Lorentz force, appearing when the beam is passing through the accelerating structures. Even small changes of the physical dimensions of the cavity cause a shift of its resonance frequency. This phenomenon, called detuning, causes significant power losses. It is actively compensated by the LLRF control system, which can physically tune lengths of the accelerating cavities with stepper motors (slow, coarse grained control) and piezoelements (active compensation during operation state). The paper describes implementation and tests of the software supporting various aspects of the LLRF system and cavities management. The Piezo Driver management and monitoring tool is dedicated for piezo controller device. The LO Distribution application is responsible for configuration of the local oscillator. The Cavity Simulator tool was designed to provide access to properties of the hardware device, emulating behaviour of elliptical cavities. IPMI Manager software was implemented to monitor state of MicroTCA.4 crates, which are major part of the LLRF system architecture. All applications have been created using the Experimental Physics and Industrial Control System (EPICS) framework and built in ESS EPICS Environment (E3)., Comment: Real Time conference reference: https://indico.cern.ch/event/737461/contributions/4000912/

Digital cameras are commonly used for diagnostic purposes in large-scale physics experiments. A typical image diagnostic system consists of an optical setup, digital camera, frame grabber, image processing CPU, and data analysis tool. The standard architecture of the imaging system has a number of disadvantages. Data transmitted from a camera are buffered multiple times and must be converted between various protocols before they are finally transmitted to the host memory. Such an architecture makes the system quite complicated, limits its performance and, in consequence, increases its price. The limitations are even more critical for control or protection systems operating in real-time. Modern megapixel cameras generate large data throughput, easily exceeding 10 Gb/s, which often requires some additional processing on the host side. The optimal system architecture should assure low overhead and high performance of the data transmission and processing. It is particularly important during the processing of data streams from several imaging devices, which can be as high as several terabits per second. A novel architecture of image acquisition and processing system based on the PCI Express interface was proposed to meet the requirements of real-time imaging systems applied in large-scale physics experiments. The architecture allows to transfer an image stream directly from the camera to the data processing unit and therefore significantly decreases the overhead and improves performance., Comment: 2 pages, 3 figures, presented on 22nd IEEE Real Time Conference

The models of spin systems defined on Euclidean space provide powerful machinery for studying a broad range of condensed matter phenomena. While the non-relativistic effective description is sufficient for most of the applications, it is interesting to consider special and general relativistic extensions of such models. Here, we introduce a framework that allows us to construct theories of continuous spin variables on a curved spacetime. Our approach takes advantage of the results of the non-linear field space theory, which shows how to construct compact phase space models, in particular for the spherical phase space of spin. Following the methodology corresponding to a bosonization of spin systems into the spin wave representations, we postulate a representation having the form of the Klein-Gordon field. This representation is equivalent to the semi-classical version of the well-known Holstein-Primakoff transformation. The general-relativistic extension of the spin wave representation is then performed, leading to the general-relativistically motivated modifications of the Ising model coupled to a transversal magnetic field. The advantage of our approach is its off-shell construction, while the popular methods of coupling fermions to general relativity usually depend on the form of Einstein field equations with matter. Furthermore, we show equivalence between the considered spin system and the Dirac-Born-Infeld type scalar field theory with a specific potential, which is also an example of k-essence theory. Based on this, the cosmological consequences of the introduced spin field matter content are preliminarily investigated., Comment: 19 pages, 3 figures v2 rewritten parts of Secs. I-III, some clarifications elsewhere, typos corrected, references added, 1 extra figure

In loop quantum gravity approach to Planck scale physics, quantum geometry is represented by superposition of the so-called spin network states. In the recent literature, a class of spin networks promising from the perspective of quantum simulations of quantum gravitational systems has been studied. In this case, the spin network states are represented by graphs with four-valent nodes, and two dimensional intertwiner Hilbert spaces (qubits of space) attached to them. In this article, construction of quantum circuits for a general intertwiner qubit is presented. The obtained circuits are simulated on 5-qubit (Yorktown) and 15-qubit (Melbourne) IBM superconducting quantum computers, giving satisfactory fidelities. The circuits provide building blocks for quantum simulations of complex spin networks in the future. Furthermore, a class of maximally entangled states of spin networks is introduced. As an example of application, attempts to determine transition amplitudes for a monopole and a dipole spin networks with the use of superconducting quantum processor are made., Comment: 17 pages. Matches the version published in PRD

In the recent article Phys. Rev. D 100, no. 4, 043533 (2019) a compact phase space generalization of the flat de Sitter cosmology has been proposed. The main advantages of the compactification is that physical quantities are bounded, and the quantum theory is characterized by finite dimensional Hilbert space. Furthermore, by considering the $\mathbb{S}^2$ phase space, quantum description is constructed with the use $SU(2)$ representation theory. The purpose of this article is to apply effective methods to extract semi-classical regime of the quantum dynamics. The analysis is performed both without prior solving of the quantum constraint and by extracting physical Hamiltonian of the model. At the effective level, the results of the two procedures are shown to be equivalent. We find a nontrivial behavior of the fluctuations around the recollapse of the universe, which is distinct from what is found after quantization with the standard flat phase space. The behavior is reflected at the level of the modified Friedmann equation with quantum back-reaction effects, which is derived. Finally, an unexpected relation between the quantum fluctuations of the cosmological sector and the holographic Bousso bound is shown., Comment: 13 pages, 4 figures

Electro-optical detection has proven to be a valuable technique to study temporal profiles of THz pulses with pulse durations down to femtoseconds. As the Coulomb field around a relativistic electron bunch resembles the current profile, electro-optical detection can be exploited for non-invasive bunch length measurements at accelerators. We have developed a very compact and robust electro-optical detection system based on spectral decoding for bunch length monitoring at the European XFEL with single-shot resolution better than 200~fs. Apart from the GaP crystal and the corresponding laser optics at the electron beamline, all components are housed in 19\" chassis for rack mount and remote operation inside the accelerator tunnel. An advanced laser synchronization scheme based on radio-frequency down-conversion has been developed for locking a custom-made Yb-fiber laser to the radio-frequency of the European XFEL accelerator. In order to cope with the high bunch repetition rate of the superconducting accelerator, a novel linear array detector (KALYPSO) has been employed for spectral measurements of the Yb-fiber laser pulses at frame rates of up to 2.26~MHz. In this paper, we describe all sub-systems of the electro-optical detection system as well as the measurement procedure in detail, and discuss first measurement results of longitudinal bunch profiles of around 400~fs (rms) with an arrival-time jitter of 35~fs (rms).

The purpose of this letter is to explore the relation between gauge fields, which are at the base of our understanding of fundamental interactions, and the quantum entanglement. To this end, we investigate the case of ${\rm SU}(2)$ gauge fields. It is first argued that holonomies of the ${\rm SU}(2)$ gauge fields are naturally associated with maximally entangled two-particle states. Then, we provide some evidence that the notion of such gauge fields can be deduced from the transformation properties of maximally entangled two-particle states. This new insight unveils a possible relation between gauge fields and spin systems, as well as contributes to understanding of the relation between tensor networks (such as MERA) and spin network states considered in loop quantum gravity. In consequence, our results turn out to be relevant in the context of the emerging Entanglement/Gravity duality., Comment: 6 pages, 3 figures, v2 introduction and crucial statements refined, additional results (eqs. (20-27)), typos corrected, references added, 2 extra figures

Detailed applications of minisuperspace methods are presented and compared with results obtained in recent years by means of causal dynamical triangulations (CDTs), mainly in the form of effective actions. The analysis sheds light on conceptual questions such as the treatment of time or the role and scaling behavior of statistical and quantum fluctuations. In the case of fluctuations, several analytical and numerical results show agreement between the two approaches and offer possible explanations of effects that have been seen in causal dynamical triangulations but whose origin remained unclear. The new approach followed here suggests `CDT experiments' in the form of new simulations or evaluations motivated by theoretical predictions, testing CDTs as well as the minisuperspace approximation., Comment: 51 pages, 16 figures

The kinematical phase space of classical gravitational field is flat (affine) and unbounded. Because of this, field variables may tend to infinity leading to appearance of singularities, which plague Einstein's theory of gravity. The purpose of this article is to study the idea of generalizing the theory of gravity by compactification of the phase space. We investigate the procedure of compactification of the phase space on a minisuperspace gravitational model with two dimensional phase space. In the affine limit, the model reduces to the flat de Sitter cosmology. The phase space is generalized to the spherical case, and the case of loop quantum cosmology is recovered in the cylindrical phase space limit. Analysis of the dynamics reveals that the compactness of the phase space leads to both UV and IR effects. In particular, the phase of re-collapse appears, preventing the universe from expanding to infinite volume. Furthermore, the quantum version of the model is investigated and the quantum constraint is solved. As an example, we analyze the case with the spin quantum number $s=2$, for which we determine transition amplitude between initial and final state of the classical trajectory. The probability of the transition is peaked at $\Lambda=0$., Comment: 13 pages, 5 figures