Keynote lectures will be 45 minutes + 15 minutes questions.

Research talks will be 25 minutes + 5 minutes questions.

Francesco Plastina — Keynote Lecture

**Quantum Coherence and Thermodynamics**

In the quantum regime, finite-time controlled evolutions (transformations) typically lead to the generation of energetic coherence in the state of the dynamical system. Exploiting the relative entropy of coherence, it is possible to isolate a coherent contribution in the energetics of a driven nonequilibrium quantum system, leading one to identify that part of the irreversible entropy that is produced because of coherence generation. On the other hand, coherence is connected also to the non-adiabaticity of a processes, for which it gives the dominant contribution for slow-enough transformations. With the help of fluctuation theorems, we will provide a full characterization of the irreversible entropy being generated because of both deviation from adiabaticity, and coherence production. Besides the coherence that is generated *during* time evolution, *initial* coherence plays a distiguished role in the thermodynamics of quantum systems, as, e.g., thermodynamic cycles can, in principle, be designed to extract work from such a nonequilibrium resource. In this context, we will discuss the connection between coherence and ergotropy (the maximum amount of unitarily extractable work via cyclical variation of Hamiltonian parameters), and, using similar tools, its role in other information-thermodynamic processes, such as Landauer erasure.

Francesco Plastina — Research Talk

**A hybrid classical–quantum approach to speed-up Q-learning**

We introduce a classical–quantum hybrid approach to computation, allowing for a quadratic performance improvement in the decision process of a learning agent. Using the paradigm of quantum accelerators, we introduce a routine that runs on a quantum computer, which allows for the encoding of probability distributions. This quantum routine is then employed, in a reinforcement learning set-up, to encode the distributions that drive action choices. Our routine is well-suited in the case of a large, although finite, number of actions and can be employed in any scenario where a probability distribution with a large support is needed. We describe the routine and assess its performance in terms of computational complexity, needed quantum resource, and accuracy. Finally, we design an algorithm showing how to exploit it in the context of Q-learning.

Salvatore Lorenzo — Keynote Lecture

**Quantum Collision models**

An old, but always topical, quantum mechanics problem, consists in studying the dynamics of systems interacting with an external environment. Finding a general master equation to describe the dynamics of such systems is a challenging task, and to date, no truly general equation exists except for a few limited classes of dynamics. One conventional approach to address this problem is to decompose the bath into a continuum of normal modes and let them interact with the system according to some physically motivated coupling model.

The last few years have yet seen a growing use of a less conventional class of system–bath models known as quantum collision models (CMs) or repeated interaction schemes.

Quantum collision models view the system-bath dynamics as a sequence of two-body unitary collisions between the system and ancillas. In its most basic formulation, a CM model imagines the bath as a large collection of smaller subunits (ancillas) with which the open system interacts one at a time through a sequence of pairwise, short unitary interactions (collisions). Compared to the conventional system-bath modeling, CMs differ in many respects. First, they are intrinsically discrete, where continuous time is effectively replaced by a step number. Second, the system interacts with a single little portion of the bath at a time, which decomposes the extremely complex system-bath dynamics into simple elementary contributions.

In conclusion, quantum collision models offer an alternative to the conventional approach to tackle system-bath dynamics at a microscopic level. CMs are a natural framework for introducing a class of weak quantum measurements and have become a standard approach in quantum thermodynamics, quantum non-Markovian dynamics, and quantum optics.

We first analyze the basic properties of CMs and then consider the major areas of application of CMs to date: quantum trajectories/weak measurements, non-equilibrium quantum thermodynamics, non-Markovian extensions of CMs and white-noise microscopic models.

Salvatore Lorenzo — Research Talk

**State estimation via QELM**

We present a complete characterization of the information that can be exactly retrieved from linear post-processing of measurement probabilities in quantum extreme learning machine (QELM) schemes. Our analysis sheds light on the relationship between the ability of a device to retrieve nonlinear functionals of input states and the memory of the associated quantum channel. Our framework can be extended to analyze time-dependent signals encoded in quantum states in quantum reservoir computing (QRC).

We found that the efficiency of QELM protocols depends on the properties of an effective positive operator valued measurement (POVM) describing the entire apparatus, comprising of a dynamical evolution and a measurement stage. Our work also shows that the sampling noise, inherent in any measurement data obtained from a quantum device, significantly affects estimation performances and cannot be ignored.

Our study provides insight into the performance factors of QELMs and QRCs in experimental scenarios, and identifies ways to counter them. It also opens up avenues for future research, including the extension of our analysis to time-trace signals for dynamical QRCs and the optimization of POVMs for quantum state estimation.

Antonio Acín — Keynote Lecture

**The device-independent scenario: quantum information processing based on Bell’s Theorem**

The 2022 Nobel prize in Physics has acknowledged the fundamental role of Bell’s theorem in physics. It is well understood that the experimental demonstration of the theorem implies the existence of quantum correlations, often known as nonlocal, that cannot be described by classical theories, in which measurement outcomes are predetermined. In recent years, Bell nonlocal correlations have also acquired the status of information resource, as they are crucial for the construction of quantum information protocols in the device-independent scenario, where no modelling of the devices is assumed in the implementation. Because of this absence of modelling, device-independent protocols offer the strongest form of security attainable in quantum theory. The talk provides an introduction to all these concepts, going from quantum foundations to quantum information science and back. The main concepts and tools in the device-independent formalism are explained, together with an overview of the main results and remaining challenges.

Antonio Acín — Research Talk

**Certifying ground-state properties of many-body systems**

A ubiquitous problem in physics is to understand the ground-state properties of classical and quantum many-body systems. It is also one of the main applications of first-generation of quantum computing devices, such as quantum optimisers or simulators. Since an exact solution soon becomes too costly when increasing the system size, variational approaches are often employed as a scalable alternative: energy is minimised over a subset of all possible states and then different physical quantities are computed over the solution state. However, strictly speaking, all what these methods provide are provable upper bounds on ground-state energy. Relaxations to the ground-state problem based on semi-definite programming represent a complementary approach, providing lower bounds to the ground- state energy but, again, no provable bound on any other relevant quantity. We first discuss how these relaxations can be useful to benchmark the performance of quantum optimisers. After that, we show how relaxations, when assisted with an energy upper bound, can be used to derive certifiable bounds on the value of any physical parameter, such as correlation functions of arbitrary degree or structure factors, at the ground state. We illustrate the approach in paradigmatic examples of 1D and 2D spin-one-half systems.

Karol Życzkowski — Keynote Lecture

**Voting in the European Union: A Mathematical Approach**

Two major mathematical issues related to the governance in European Union are discussed:

a) Voting rules in the European Council,

b) Allocation of seats in the European Parliament.

Each member state is represented in the European Council by a single representative, which takes part in weighted voting with a qualified majority. We review the theory of Penrose, according to which the voting power of any citizen of any state is equal, if the voting weights are proportional to the square root of the population of each Member State. The proposed voting system, called Jagiellonian Compromise (JagCom), is based on the Penrose law. For EU-27 the value of the optimal threshold of qualified majority is around 61%.

In the case of the European Parliament, each Member State sends several of their representatives. They vote separately, so their votes can differ to optimally represent the point of views of their electorate. This assumption leads to the linear dependence between the population of a given state and the number of Parliament members representing this state. We review certain apportionment functions and show that the constitutional constraints are so strong that admissible functions lead to rather similar solutions. In particular, we discuss the partition of 705 MP adopted by the European Parliament after Brexit in January 2020, equivalent to a fixed base plus a term proportional to the population.

Karol Życzkowski — Research Talk

**Thirty-six Entangled Officers of Euler: Quantum Solution of a Classically Impossible Problem**

Negative solution to the famous problem of 36 officers of Euler implies that there are no two orthogonal Latin squares of order six. We show that the problem has a solution, provided the ranks and units of the officers are allowed to be entangled, and construct orthogonal quantum Latin squares of this size. The solution can be visualized on a chessboard of size six, which shows that 36 officers are split into nine groups, each containing four entangled states. It allows us to find an absolutely maximally entangled state of four subsystems with six levels each and to construct a pure nonadditive quhex quantum error detection code.