Scientific Series

In this talk, we develop a systematic framework for understanding symmetries in topological phases in \(2+1\) dimensions using the string-net model, encompassing both gauge symmetries that preserve anyon types and global symmetries permuting anyon types, including both invertible symmetries describable by groups and noninvertible symmetries described by categories. As an archetypal example, we reveal the first noninvertible categorical gauge symmetry of topological orders in \(2+1\) dimensions: the Fibonacci gauge symmetry of the doubled Fibonacci topological order, described by the Fibonacci fusion \(2\)-category. Our approach involves two steps: first, establishing duality between different string-net models with Morita equivalent input UFCs that describe the same topological order; and second, constructing symmetry transformations within the same string-net model when the dual models have isomorphic input UFCs, achieved by composing duality maps with isomorphisms of degrees of freedom between the dual models.

We present a tensorization algorithm for constructing tensor train representations of functions, drawing on sketching and cross interpolation ideas. The method only requires black-box access to the target function and a small set of sample points defining the domain of interest. Thus, it is particularly well-suited for machine learning models, where the domain of interest is naturally defined by the training dataset. We show that this approach can be used to enhance the privacy and interpretability of neural network models. Specifically, we apply our decomposition to (i) obfuscate neural networks whose parameters encode patterns tied to the training data distribution, and (ii) estimate topological phases of matter that are easily accessible from the tensor train representation. Additionally, we show that this tensorization can serve as an efficient initialization method for optimizing tensor trains in general settings, and that, for model compression, our algorithm achieves a superior trade-off between memory and time complexity compared to conventional tensorization methods of neural networks.

I plan to review several ways of testing if the gravitational field has quantum aspects in the low energy regime.  I explain why the hybrid (half quantum/half classical) models are inadequate and how they could be ruled out. Furthermore, I maintain that there is no prima facie reason to expect problems when quantizing gravity in the linear regime; I summarise the main perceived difficulties only to dismiss them as irrelevant. Going beyond the linear regime is challenging in the lab, and one might have to look towards astrophysics and cosmology of the early universe instead.  Finally, many interesting features of quantum field theory could be explored in the low-energy regime that may not necessarily be specific to gravity.

Gravitational waves were detected in 2015 after 100 years of their prediction. Coalescence of black holes and neutron stars have been studied giving birth to a new way of studying our Universe. The coincidence of the gravitational signal with a gamma ray burst has been identified as the beginning of multi-messenger astronomy. In order to move from the limited statistics, allowed by the actually running interferometers (LIGO and VIRGO), to a huge sample a new generation of detectors has to be designed , built and operated. Einstein Telescope is the project for a third generation detector, supported by a large European collaboration. It is going to be formed by a combination of a Low Frequency Cryogenic interferometer and an High Frequency high laser power interferometer both located underground in order to minimise the noise. Laser technology, seismic noise attenuation, quantim squeezing are a few of the keys to success. The experiment is going to produce results in several field of research like astronomy, astrophysics, nuclear physics, cosmology. It is going to be in competition and cooperation with the US project Cosmic Explorer.

I will give a general method for producing a process theory of local spacetime events and higher-order transformations from any base process theory of first-order maps. This process theory models events as intervention-context pairs, uniting the local actions by agents with the structure of the spacetime around them. I will show how this theory is richer than a standard process theory by permitting additional ways of composing agents beyond the usual tensor product, thereby capturing various strengths of possible spatio-temporal correlations. I will also explain the connection between these compositions and the logic "system BV".

High-rate quantum low-density parity-check (qLDPC) codes offer significantly lower encoding overhead compared to their topological counterparts by relaxing locality constraints. However, achieving full-fledged logical computation with these codes in physical systems with low space-time costs remains a formidable challenge. In the first part of this talk, I will provide an overview of recent advancements in implementing qLDPC codes as quantum memories on realistic platforms, such as reconfigurable atom arrays. Next, I will present a new scheme for performing parallelizable and locally addressable logical operations on homological product codes. This scheme extends the transversal CNOT gate from two identical CSS codes to two distinct, yet structurally similar, qLDPC codes, enabling efficient local addressing of collectively encoded information. We demonstrate that this approach achieves lower overhead in not only the space- but also the overall space-time overhead compared to surface-code-based computations. Finally, I will discuss new strategies for achieving highly space-time-efficient computations with qLDPC codes by leveraging algorithm-specific fault tolerance, designing tailored protocols for structured quantum algorithms.

Recent efforts to formulate a unified, causally neutral approach to quantum theory have highlighted the need for a framework treating spatial and temporal correlations on an equal footing. Building on this motivation, we propose operationally inspired axioms for quantum states over time, demonstrating that, unlike earlier approaches, these axioms yield a unique quantum state over time that is valid across both bipartite and multipartite spacetime scenarios. In particular, we show that the Fullwood-Parzygnat state over time uniquely satisfies these axioms, thus unifying bipartite temporal correlations and extending seamlessly to any number of temporal points. In particular, we identify two simple assumptions—linearity in the initial state and a quantum analog of conditionability—that single out a multipartite extension of bipartite quantum states over time, giving rise to a canonical generalization of Kirkwood-Dirac type quasi-probability distributions. This result provides a new characterization of quantum Markovianity, advancing our understanding of quantum correlations across both space and time.

In this talk, I will explain the concept of fault tolerance, which ensures reliable quantum computation. Building on recent advancements in mixed-state phases of matter, I introduce a new diagnostic called the spacetime Markov length. The divergence of this length scale signals the intrinsic breakdown of fault tolerance.