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.

The basic tenet of the present work is the assumption of the lack of external and fixed time in the Universe. This assumption is best embodied by general relativity, which replaces the fixed space-time structure with the gravitational field, which is subject to dynamics. The lack of time does not imply the lack of evolution but rather brings to the forefront the role of internal clocks which are some largely arbitrary internal degrees of freedom with respect to which the evolution of timeless systems can be described. We take this idea seriously and try to understand what it implies for quantum mechanics when the fixed external time is replaced by an arbitrary internal clock. We put the issue in a solid, mathematically rigorous framework. We find that the dynamical interpretation of a quantum state of a timeless system depends on the employed internal clock. In particular, we find that the continuous spectra of well-known dynamical observables like the position of a free particle on the real line may turn discrete if measured in unusual clocks. We discuss the meaning of our result for attempts at quantization of global gravitational degrees of freedom.

Quantum cosmological models are commonly described by means of semiclassical approximations in which a smooth evolution of the expectation values of elementary geometry operators replaces the classical and singular dynamics. The advantage of such descriptions is that they are relatively simple and display the classical behavior for large universes. However, they may smooth out an important inner structure and to include it a more detailed treatment is needed. The purpose of the present work is to investigate quantum uncertainty in the basic background variables and its influence on primordial gravitational waves. To this end we quantize a model of the Friedmann-Lemaitre-Robertson-Walker universe filled with a linear barotropic cosmological fluid and with gravitational waves. We carefully derive the dynamical equations for the perturbations in quantum spacetime. The quantization yields an equation of motion for the Fourier modes of gravitational radiation, which is a quantum extension to the usual parametric oscillator equation for gravitational waves propagating in an expanding universe. The two quantum effects from the cosmological background that enter the enhanced equation of motion are (i) a repulsive potential resolving the big bang singularity and replacing it with a big bounce and (ii) uncertainties in the numerical values for the background spacetime dynamical variables. First we study the former effect and its consequences for the primordial amplitude spectrum and carefully discuss the relation between the bounce scale and the physical predictions of the model. Next we investigate the latter effect, in particular, the extent to which it may affect the primordial amplitude of gravitational waves. Making use of the WKB approximation, we find an analytical formula for the amplitude spectrum as a function of the quantum dispersion of the background spacetime.

We develop an approach to quantum dynamics based on quantum phase space trajectories. The latter are built from a unitary irreducible representation of the symmetry group of the respective classical phase space. We use a quantum action functional to derive the basic equations. In principle, our formulation is equivalent to the Hilbert space formulation. However, the former allows for consistent truncations to reduced phase spaces in which approximate quantum dynamics can be derived. We believe that our approach can be very useful in the domain of quantum cosmology and therefore, we use the cosmological phase space example to establish the basic equations of this formalism.

The analysis of satellite images has attracted significant research interest due to its numerous applications and unparalleled scalability in Earth observation (EO). Although artificial intelligence (AI) algorithms for EO emerge at a steady pace, the community still needs to address many practical challenges that are concerned with such highly dimensional and unprecedentedly large volumes of image data. Quantum machine learning (QML) is a promising research avenue here. Despite the growing interest and funding in the field, current results remain inconclusive, shifting focus toward understanding the strengths and limitations of QML rather than solely expanding the applications of such methods. This article addresses a critical gap by consolidating advancements in QML, with a special focus on quantum kernel methods—which already proved their value in EO—to evaluate their role in advancing state-of-the-art (SOTA) EO solutions and exploring the potential quantum advantage via identifying their benefits and shortcomings in an unbiased and thorough way.