**Scientific activities of the various Research Units**

The outstanding developments of the last two decades, known as second quantum revolution, have given birth to the emerging fields of Quantum Information and Quantum Technologies. Combined theoretical and experimental efforts, as well as the progress in simulation techniques, have led to the concrete possibility of quantum-based technological advances, with the development of devices capable of reaching unprecedented performances. The related novel physical phenomena, as well as the astounding possibilities in controlling, addressing and manipulating single (real and artificial) atoms, atom arrays, spin systems, and superconducting circuits, and the increasing accuracy in interferometric techniques motivate novel theoretical ideas, as well as reliable and precise analyses.

The major objectives of the QUANTUM collaboration are the investigation of typical quantum mechanical effects and phenomena via three major, interrelated avenues:

*1. Entanglement and other Quantum Correlations (ENT);*

*2. Quantum Simulation (SIM);*

*3. Quantum Control (CTRL)*.

The theoretical effort is highly synergic, involving close collaborations among the partners, exchange of students, post-docs and young researchers. We detail in the following the activities of the different research units and their joint collaborations.

**INFN Section: Bari [BA]**

* ENT* – In collaboration with CT and NA, the Bari unit is investigating phase transitions of Renyi entropies in many-body systems and the role of frustration in multipartite entanglement. Dynamical mechanisms of entanglement generation is analyzed in systems of quantum emitters, characterizing the relaxation process towards nontrivial bound states in the continuum, and in clouds of cold gases, analyzing the role of quantum correlations in collective sub-radiant and super-radiant states. We also study the possibility to develop imaging tasks based on photon entanglement and thermal correlations of light.

* SIM* – In collaboration with the Bologna and Padova units, we are performing quantum simulations of non-Abelian lattice gauge theories in more than one dimensions. Analogous simulations will be done via integrated photonic devices for the time evolution of closed and open quantum systems.

* CTRL* – In collaboration with NA and TS, we are investigating quantum control of open quantum systems by strong coupling limits and adiabatic decoupling. The objective is to implement and optimize dynamically-controlled quantum interfaces between matter (atomic ensembles or ionic crystals) and photons. The role of quantum boundary conditions and non-trivial topological effects will be detailed.

**INFN Section: Bologna [BO] (Bologna and Camerino groups)**

* ENT* – In collaboration with NA and PD, we are examining two aspects that can provide excellent tools to study topological phases of matter: i) the role of multipartite entanglement by looking at indicators such as Fisher information for non-local order parameters; ii) the use of classical machine learning techniques for the analysis of correlators and topological invariants. In Camerino, we are considering applications to the expansion of the universe when including anisotropy and non-homogeneity, so that multimode entanglement is expected to arise. Attention is also put to entanglement properties of scalar and Dirac fields, when torsion terms are present.

__SIM__* – *In collaboration with BA, CT and PD, we want to generalize our previous results for the construction of a Hamiltonian description for lattice gauge theories: i) in higher dimensions and ii) in the non-abelian case, starting from discrete groups such the finite subgroups of SU(n). Then we will couple this theory to fermionic matter, in order to study the full model in the case of finite densities, considering also the possibility of describing out-of-equilibrium phenomena.

__CTRL__*– *In collaboration with TS, to control entanglement, we go beyond Markovian quantum feedback by looking at a setup based on the Bayesian one, with a filtering process of the measurement record. This can be regarded as a learning process and revisited in the light of Quantum Machine Learning. Also, we are examining strategies to enhance data retrieval, by using quantum correlations and adaptive techniques: an array of cells, containing an unknown quantum channel labelled by a classical bit, will be regarded as an optical memory, with information encoded by means of error correcting codes.

**INFN Section: Catania [CT] ( Catania and Palermo groups)**

__ENT__** **– In collaboration with BA, the group in Palermo is studying the role of quantum correlations in specific collective behaviors such as the raise of synchronization in quantum networks. We carry out the analysis how the synchronized phases depend on quantum noise and coupling parameters. Attention is given also to chiral waveguides to realize one-direction connections between the nodes.

* SIM* – In collaboration with BO and NA, we are studying the persistent current of SU(N) fermions confined in a ring-shape potential. Both repulsive and attractive interaction are considered. We are also considering ring-shaped fermionic systems in the presence of a localized barrier interrupting the ring (emulating f.i. Kondo systems). With this approach, we will put the basis for a quantum simulator for SU(N) fermions based current flows. At the same time, we will provide the proof of concept for devices/sensors with enhanced control and performances.

__CTRL__ – In collaboration with NA, PD and TS, the group in Catania is studying Machine Learning engineering of atomtronic circuits*.* The main objective is to develop ML based control on simple integrated atomtronic circuits with lumped parameters. The simplest instances are provided by ring-lattices of bosonic/fermionic degenerate gases. Specifically, we resort to our first study in [arXiv:1911.09578] to generate currents on demand by suitable local driving of the circuits. We can generate current states without synthetic fields and therefore our systems can define atomic SQUID’s or atomtronic flux qubits but with new specifications and simplified architectures [Nature **506**, 200 (2014), NJP **17**, 045023 (2015)]. At the same time, fundamental aspects of many-body physics and macroscopic phase coherence can be explored with the new twist provided by the atomtronic platform. The group in Palermo is investigating control protocols through time-dependent Hamiltonians, especially in the adiabatic regime. Shortcuts to adiabaticity will be analyzed as well. Decoherence and dissipation will be taken into account through master equations or non-Hermitian Hamiltonians, where applicable. The group in Messina is investigating a consistent statistical theory of quantum-classical systems with a discrete number of energy levels embedded in a continuum described by non-Hermitian Hamiltonians, with applications in entanglement generation via stroboscopic measurements and in quantum transport.

**INFN Section: Milano [MI] ( Como)**

__ENT__*, CTRL* – In collaboration with PD and NA, we are studying state transfer, entanglement generation, and quantum gates in the ultra-strong coupling regime, using adiabatic switching of the light-matter coupling. Preliminary results with a STIRAP (stimulated Raman adiabatic passage) protocol showed that very large fidelities in state transfer can be obtained at coupling strengths corresponding to clock rates much larger than those in the strong coupling regime [MDPI Proceedings 12, 35 (2019)]. We are investigating the resilience of STIRAP protocols and more generally of optimal control protocols, under the main sources of errors in the ultra-strong coupling regime, that is, the production of photon pairs due to the modulation of the light-matter coupling (a manifestation of the dynamical Casimir effect), and cavity losses.

* CTRL* – In collaboration with TS, we are exploring the fundamental bounds on the efficiency of quantum thermal machines. In particular, we will explore the trade-off between power, efficiency and fluctuations, both in steady-state and in periodically driven heat engines. Indeed, a heat engine should ideally have large power, operate close to the Carnot efficiency, and exhibit small fluctuations around its mean value. Having in mind fundamental bounds proposed by Seifert and coworkers [PRL 120, 190602 (2018); PRL 122, 230601 (2019)] within the framework of stochastic thermodynamics, we are investigating whether quantum coherence, quantum correlations, and non-Markovian effects might lead to a violation of such bounds, thus improving the performance of heat engines. We will also work on heat management, and in particular on heat flow control and thermal rectification in quantum systems.

**INFN Section: Napoli [NA] ( Napoli and Salerno groups)**

* ENT*— In collaboration with BA, BO and MI, we are studying purification and squashing protocols of quantum information and their applications to quantum matter at equilibrium and out of equilibrium, as well as to holographic entanglement in quantum field theory. We will also characterize entanglement in terms of positive definite functions. As for quantum theory of probability, we are going to consider a representation of generic quantum states in terms of dichotomic probabilities or stochastic products and characterize quantum observables and covariant quantum channels. We are investigating monotonic quantum metrics emerging from relative entropies considered as potential functions. In the quantum field theory context, we are conducting studies on geometry and quantum tomography, by employing covariant phase-space formulation and Peierls brackets.

* SIM* – In collaboration with CT and PD, we are investigating topological states in spin-orbit coupled Bose-Einstein condensates and the effects of curved geometries on global topological orders along with the effect of geometric frustration and disorder. Regarding systems with long-range interactions, e.g. dipolar BECs, we plan to study many-body localization and thermalization, as well as the supersolidity phenomenon.

* CTRL* – In collaboration with BA, CT and MI, we are interested in the study of open quantum systems for understanding the evolution of quantum entropies, decoherence effects induced by quantum gravity, non-Markovian master equations. Regarding quantum and thermal fluctuations of the electromagnetic field, we plan to apply new powerful surface-current methods to investigate the non-trivial geometry dependence of the Casimir force and radiative heat-transfer between two closely spaced bodies of different shapes.

**INFN Section: Padova [PD]**

* ENT*,

*– In collaboration with BA and BO, the Padova unit is developing and exploring the application of tensor networks methods for lattice gauge theories, which promise to be a revolutionary tool to attack some of the most long-standing problems in theoretical physics, characterizing fundamental phenomena of fundamental theories as string breaking, confinement or scattering with new numerical and theoretical tools, e.g., studying their entanglement properties. Moreover, these novel tensor network simulations will play a key role in supporting the development, the validating and the benchmarking of future quantum simulators for lattice gauge theories [Phys. Rev. Res.*

__SIM__**2**, 013288 (2020)]. The optimal control tools for many-body systems will play here a fundamental role in terms of preparation of initial states optimal readout.

* CTRL* – In collaboration with CT and MI, the Padova unit is exploring the application of tensor network methods to machine learning, that promise to open new paths towards the interpretability of machine learning applications, and novel structures and time-efficient process. They are pursuing the recent applications of quantum-inspired tensor network machine learning to high-energy physics data, along the lines of the recent classification of b-bbar events at LHCb data [arXiv:2004.13747]. They will provide the knowhow and software suites the Padova unit has developed in the last ten years to support the project activities and guide their application to relevant problems.

**INFN Section: Trieste [TS]**

__ENT__*, CTRL* – The description of mesoscopic quantum systems must take into account the noise and dissipation due to their environment. In collaboration with BA, CT and MI, we plan to study the open dynamics of the collective fluctuations operators in systems as ultracold atomic ensembles, for which quantum correlations can be engineered and controlled. The aim is to analyze mesoscopic entanglement generation at the level of quantum fluctuations and its behavior under irreversible open quantum dynamics, with and without memory and feed-back effects. Such investigations are relevant for quantum control and quantum sensing, specifically, in the development of new quantum devices, as e.g. many-body energy harvesting and storage devices (quantum batteries).

__SIM__*, CTRL* – The classical techniques related to MDLP has not yet been applied to either quantum state or quantum channel reconstruction or to the emerging field of Quantum Machine Learning. Also, the attempts at extending Kolmogorov algorithmic complexity to quantum systems have not yet been confronted with the formulation of truly quantum inductive inference schemes based on entirely quantum tools. In collaboration with BO and MI, we plan 1) to test MDLP in the characterization of quantum processes where one can control the degree of Markovianity and insert feedback effects and 2) to study the possible formulation of a quantum MDLP basing on the identification of learning with compressibility and on the existing proposals of algorithmic quantum complexities. In such a case, a natural arena is offered by quantum perceptrons and quantum neural network.