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Scientific and technological advances in medicine and systems biology have unequivocally shown that health and disease must be viewed in the context of the interplay among multiple molecular and environmental factors. Understanding the effects of cellular interconnection on disease progression may lead to the identification of novel disease genes and pathways, and hence influence precision diagnostics and therapeutics. To accomplish this goal, the emerging field of network medicine applies network science approaches to investigate disease pathogenesis, integrating information from relevant Omics databases, including protein-protein interaction, correlation-based, gene regulatory, and Bayesian networks. However, this requires analysing and computing large amounts of data. Moreover, if we are to efficiently search for new drugs and new drug combinations, there is a pressing need for computational methods that could allow us to access the immense chemical compound space until now largely unexplored. Finally, at the microscopic level, drug-target chemistry simulation is ultimately a quantum problem, and hence it requires a quantum solution. As we will discuss, quantum computing may be a key ingredient in enabling the full potential of network medicine. We propose to combine network medicine and quantum algorithms in a novel research field, quantum network medicine, to lay the foundations of a new era of disease prevention and drug design.

In this article, we provide an extensive overview of a wide range of quantum games and interactive tools that have been employed by the community in recent years. The paper presents selected tools, as described by their developers. The list includes Hello Quantum, Hello Qiskit, Particle in a Box, Psi and Delta, QPlayLearn, Virtual Lab by Quantum Flytrap, Quantum Odyssey, ScienceAtHome, and The Virtual Quantum Optics Laboratory. Additionally, we present events for quantum game development: hackathons, game jams, and semester projects. Furthermore, we discuss the Quantum Technologies Education for Everyone (QUTE4E) pilot project, which illustrates an effective integration of these interactive tools with quantum outreach and education activities. Finally, we aim at providing guidelines for incorporating quantum games and interactive tools in pedagogic materials to make quantum technologies more accessible for a wider population., Comment: 39 pages, 17 figures

We draw a picture of physical systems that allows us to recognize what is this thing called "time" by requiring consistency not only with our notion of time but also with the way time enters the fundamental laws of Physics, independently of one using a classical or a quantum description. Elements of the picture are two non-interacting and yet entangled quantum systems, one of which acting as a clock, and the other one doomed to evolve. The setting is based on the so called "Page and Wootters (PaW) mechanism", and updates, with tools from Lie-Group and large-$N$ quantum approaches. The overall scheme is quantum, but the theoretical framework allows us to take the classical limit, either of the clock only, or of the clock and the evolving system altogether; we thus derive the Schr\"odinger equation in the first case, and the Hamilton equations of motion in the second one. Suggestions about possible links with general relativity and gravity are also put forward.

We present and discuss a formal approach for describing the quantum to classical crossover based on the group-theoretic construction of generalized coherent states. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories, and has been recently used for studying open quantum systems whose environment, while becoming macroscopic, may or may not display a classical behaviour. Referring to these recent developments, in this paper we provide the essential elements of Yaffes's approach in the framework of standard quantum mechanics, so as to clarify how the approach can be used without referring to quantum field theory. Moreover, we address the role played by a possible global symmetry in making the large-$N$ limit of the original quantum theory to flow into a formally well defined classical theory, and we specifically consider the quantum-to-classical crossover of angular momentum. We also give details of a paradigmatic example, namely that of $N$ free one-dimensional spinless particles. Finally, we discuss upon the foundational requirement that any classical description should ultimately be derived from an underlying quantum theory, that however is not, and should never be confused with, the one obtained via some quantization procedure of the classical description itself., Comment: 13 pages. Accepted for publication in Soft Computing

We study the dynamics of a quantum system $\Gamma$ with an environment $\Xi$ made of $N$ elementary quantum components. We aim at answering the following questions: can the evolution of $\Gamma$ be characterized by some general features when $N$ becomes very large, regardless of the specific form of its interaction with each and every component of $\Xi$? In other terms: should we expect all quantum systems with a macroscopic environment to undergo a somehow similar evolution? And if yes, of what type? In order to answer these questions we use well established results from large-$N$ quantum field theories, particularly referring to the conditions ensuring a large-$N$ quantum model to be effectively described by a classical theory. We demonstrate that the fulfillment of these conditions, when properly imported into the framework of the open quantum systems dynamics, guarantees that the evolution of $\Gamma$ is always of the same type of that expected if $\Xi$ were a measuring apparatus, no matter the details of the actual interaction. On the other hand, such details are found to determine the specific basis w.r.t. which $\Gamma$ undergoes the decoherence dictated by the dynamical description of the quantum measurement process. This result wears two hats: on the one hand it clarifies the physical origin of the formal statement that, under certain conditions, any channel from $\rho_\Gamma$ to $\rho_\Xi$ takes the form of a measure-and-prepare map, as recently shown in Ref. [1]; on the other hand, it formalizes the qualitative argument that the reason why we do not observe state superpositions is the continual measurement performed by the environment.

We address the dynamics of a bosonic system coupled to either a bosonic or a magnetic environment, and derive a set of sufficient conditions that allow one to describe the dynamics in terms of the effective interaction with a classical fluctuating field. We find that for short interaction times the dynamics of the open system is described by a Gaussian noise map for several different interaction models and independently on the temperature of the environment. In order to go beyond a qualitative understanding of the origin and physical meaning of the above short-time constraint, we take a general viewpoint and, based on an algebraic approach, suggest that any quantum environment can be described by classical fields whenever global symmetries lead to the definition of environmental operators that remain well defined when increasing the size, i.e. the number of dynamical variables, of the environment. In the case of the bosonic environment this statement is exactly demonstrated via a constructive procedure that explicitly shows why a large number of environmental dynamical variables and, necessarily, global symmetries, entail the set of conditions derived in the first part of the work., Comment: 9 pages, close to published version

We study the dynamics of a bipartite quantum system in a way such that its formal description keeps holding even if one of its parts becomes macroscopic: the problem is related with the analysis of the quantum-to-classical crossover, but our approach implies that the whole system stays genuinely quantum. Aim of the work is to understand 1) if, 2) to what extent, and possibly 3) how, the evolution of a macroscopic environment testifies to the coupling with its microscopic quantum companion. To this purpose we consider a magnetic environment made of a large number of spin-1/2 particles, coupled with a quantum mechanical oscillator, possibly in the presence of an external magnetic field. We take the value of the total environmental-spin S constant and large, which allows us to consider the environment as one single macroscopic system, and further deal with the hurdles of the spin-algebra via approximations that are valid in the large-S limit. We find an insightful expression for the propagator of the whole system, where we identify an effective "back-action" term, i.e. an operator acting on the magnetic environment only, and yet missing in the absence of the quantum principal system. This operator emerges as a time-dependent magnetic anisotropy whose character, whether uniaxial or planar, also depends on the detuning between the level-splitting in the spectrum of the free magnetic system, induced by the possible presence of the external field, and the frequency of the oscillator. The time-dependence of the anisotropy is analysed, and its effects on the dynamics of the magnet, as well as its relation with the entangling evolution of the overall system, are discussed.