This is the fourth event by the Quantum Gravity Gatherings (QGG) Study Group at RIKEN iTHEMS. For this event we have invited Prof. Yuki Sato, National Institute of Technology, Tokuyama College, to give pedagogical lectures on the causal dynamical triangulations approach to quantum gravity. We wish this event to provide insights to researchers in related fields.

The causal dynamical triangulations formalism appears to be one of the most promising constructive approaches to quantum gravity: possessing deep links with the asymptotic safety programme and Hořava-Lifshitz gravity, causal dynamical triangulations appears to avoid many of the well-known pathologies characteristic of its Euclidean analogue. As an example the emergence of spacetime geometry remains possible in various spacetime dimensions. While many of the results in higher dimensions are understood only at the numerical level, the analytical study of the approach in two spacetime dimensions is relatively well developed; Yuki Sato is a leading expert on these latter developments and we are very lucky he has agreed to present the understanding of 2D causal spacetime coming from this approach in a manner consistent with the Quantum Gravity Gatherings philosophy.

This intensive lecture series is intended to be a lively and participatory event, not just a listening experience. For this reason, the number of participants will be limited to about 30 with priority given to graduate students and young post-docs; the intensive talk will be given in a face-to-face blackboard style (in English, no online streaming) to allow for informal and lively Q&A discussions. The program will also include short talk sessions, where interested participants can give a 5 min talk on a topic of their choice (their research, reviews on some works, what they want to study in the future, etc.). Registration is available via the dedicated website.

As all biological and many artificial systems, hosts and their parasites are most often spatially structured. Besides this highly relevant spatial context, parasites may change through time due to to evolutionary processes, including mutation and selection. These facts imply that we must study host-parasite systems taking into account space and evolution. Past work has mainly focused on simple spatial structures, but how parasites evolve in realistically complex landscapes remains unclear, hampering the translation of theoretical predictions to real ecological systems.Therefore, we here develop an eco-evolutionary metapopulation model of host-parasite interactions in which hosts and parasites disperse through realistically complex spatial graphs. Parasite virulence, a parasite life-history trait of central importance that here impacts host reproduction, is able to evolve. Our model therefore captures the eco-evolutionary feedback loop between host demography and parasite evolution in space. In order to gain a general understanding of parasite eco-evolution in space, we analyse our model for spatial networks that represent terrestrial (represented by random-geometric graphs; RGG) and riverine aquatic (represented by optimal channel networks; OCN) landscapes. We find that evolved virulence is generally a function of host dispersal, with a unimodal relationship in aquatic and a saturating relationship in terrestrial landscape, and this is driven by higher order network properies. Consistent with previous work, we show that our results are driven by kin selection, because dispersal and landscape structure impact both patterns of relatedness and availability of susceptible hosts. Our model yields readily testable predictions, including that terrestrial parasites should be more virulent than aquatic parasites are low dispersal rates and vice versa as dispersal increases. These differences in evolved virulence directly lead to differences in system stability, with more virulent parasites more often leading to host extinction. Thus, in this study we highlight the role of landscape structure in driving eco-evolutionary dynamics of parasites.

We introduce the first large-scale dataset, MNISQ, for both the Quantum and the Classical Machine Learning community during the Noisy Intermediate-Scale Quantum era. MNISQ consists of 4,950,000 data points organized in 9 subdatasets. Building our dataset from the quantum encoding of classical information (e.g., MNIST dataset), we deliver a dataset in a dual form: in quantum form, as circuits, and in classical form, as quantum circuit descriptions (quantum programming language, QASM). In fact, also Machine Learning research related to quantum computers undertakes a dual challenge: enhancing machine learning by exploiting the power of quantum computers, while also leveraging state-of-the-art classical machine learning methodologies to help the advancement of quantum computing. Therefore, we perform circuit classification on our dataset, tackling the task with both quantum and classical models. In the quantum endeavor, we test our circuit dataset with Quantum Kernel methods, and we show excellent results with up to 97% accuracy. In the classical world, the underlying quantum mechanical structures within the quantum circuit data are not trivial. Nevertheless, we test our dataset on three classical models: Structured State Space sequence model (S4), Transformer, and LSTM. In particular, the S4 model applied on the tokenized QASM sequences reaches an impressive 77% accuracy. These findings illustrate that quantum circuit-related datasets are likely to be quantum advantageous, but also that state-of-the-art machine learning methodologies can competently classify and recognize quantum circuits. We finally entrust the quantum and classical machine learning community.

The thermal plasma in the early universe produced a guaranteed stochastic gravitational wave (GW) background, which peaks today in the microwave regime and was dubbed the cosmic gravitational microwave background (CGMB). I show that the CGMB spectrum encodes fundamental information about particle physics and gravity at ultra high energies. In particular, one can determine from the CGMB spectrum the maximum temperature of the universe and the effective degrees of freedom at the maximum temperature. I also discuss briefly how quantum gravity effects arise in the CGMB spectrum as corrections to the leading order result.

Cosmological observations have led to an extremely precise understanding of the large-scale structure of the Universe. A common assumption is to extrapolate large-scale properties to smaller scales; however, whether this is correct or not is unknown and many well-motivated early Universe scenarios predict substantially different structure formation histories. In this seminar I will discuss two scenarios where nonlinear structures form much earlier than is typically assumed. In the first case, the initial fluctuations are enhanced on small scales leading to either primordial black holes clusters or WIMP minihalos right after matter-radiation equality. In the second, I will show that an additional attractive dark force leads to structure formation even in the radiation dominated Universe. I will furthermore discuss possible observations of such early structure formation including changes to the cosmic microwave background, dark matter annihilation, and when the first galaxies form.