Valentina Brosco

Non-Abelian gauge symmetries are cornerstones of modern theoretical physics, underlying fundamental interactions and the geometric structure of quantum mechanics. However, their potential to control quantum coherence, entanglement, and transport in engineered quantum systems remains to a large extent unexplored. In this work, we propose utilizing non-Abelian Thouless pumping to realize one-dimensional discrete-time quantum walks on topological lattices characterized by degenerate flat bands. Through carefully designed pumping cycles, we implement different classes of holonomic coin and shift operators. This framework allows for the construction of quantum walks that encode the topological and geometric properties of the underlying system. Remarkably, the resulting evolution exhibits parity symmetry breaking and gives rise to a dynamical process governed by a Weyl-like equation, highlighting the deep connection between parity and time-reversal symmetry breaking in quantum walks.

Topology and nonlinearity are deeply connected. However, whether topological effects can arise solely from the structure of nonlinear interaction terms, and the nature of the resulting topological phases, remain to large extent open questions. Here we consider a chain of parametrically driven quantum resonators coupled only via weak nearest-neighbor cross-Kerr interaction, without any quadratic tunneling term. We show that, when the drive overcomes a critical threshold value, the system undergoes a transition from the atomic limit of decoupled oscillators to a symmetry-broken topological phase. The topology is determined by the interplay of local and nearest-neighbor Kerr nonlinearities, yielding a nontrivial bulk-boundary correspondence. In the topological phase, we derive analytical approximations for the low-energy spectrum, identifying the conditions to observe topological edge modes.

Non-Abelian Thouless pumping intertwines adiabatic quantum control and topological quantum transport, and it holds potential for quantum metrology and computing. In this work, we introduce a ladder model featuring two doubly degenerate bands and we show that adiabatic manipulation of the lattice parameters results in non-Abelian Thouless pumping, inducing both the displacement of an initially localized state and a geometric unitary transformation within the degenerate subspace. Additionally, we show that the structure and symmetry of the ladder model can be understood through its connection to a Yang monopole model. The proposed Hamiltonian can be realized using cold atoms in optical lattices, enabling the experimental demonstration of non-Abelian Thouless pumping in a genuinely quantum many-body system.

Recent advances in the manipulation of complex oxide layers, particularly the fabrication of atomically thin cuprate superconducting films via molecular beam epitaxy, have revealed new ways in which nanoscale engineering can govern superconductivity and its interwoven electronic orders. In parallel, the creation of twisted cuprate heterostructures through cryogenic stacking techniques marks a pivotal step forward, exploiting cuprate superconductors to deepen our understanding of exotic quantum states and propel next‐generation quantum technologies. This review explores over three decades of research in the emerging field of cuprate twistronics, examining both experimental breakthroughs and theoretical progress. It also highlights the methodologies poised to surmount the outstanding challenges in leveraging these complex quantum materials, underscoring their potential to expand the frontiers of quantum science and technology.

Non-Abelian evolution is a landmark in modern theoretical physics. But if noncommutative dynamics has a significant impact in the control of entanglement and transport in quantum systems is an open question. Here we propose to utilize non-Abelian Thouless pumping in one-dimensional discrete-time quantum walks in lattices with degenerate Bloch-bands. We show how the interplay of non-commutativity and topology enables geometrically protected quantum coin and shift operators. By composing different non-Abelian pumping cycles, different classes of tunable protected quantum walks arise. Surprisingly, the walks break parity symmetry and generate a dynamic process described by a Weyl-like equation.

Critical systems represent a valuable resource in quantum sensing and metrology. Critical quantum sensing (CQS) protocols can be realized using finite-component phase transitions, where criticality arises from the rescaling of system parameters rather than the thermodynamic limit. Here, we show that a collective quantum advantage can be achieved in a multipartite CQS protocol using a chain of parametrically coupled critical resonators in the weak-nonlinearity limit. We derive analytical solutions for the low-energy spectrum of this unconventional quantum many-body system, which is composed of locally critical elements. We then assess the scaling of the quantum Fisher information with respect to fundamental resources. We demonstrate that the coupled chain outperforms an equivalent ensemble of independent critical sensors, achieving quadratic scaling in the number of resonators. Finally, we show that even with finite Kerr nonlinearity or Markovian dissipation, the critical chain retains its advantage, making it relevant for implementing quantum sensors with current microwave superconducting technologies.

Non-Abelian Thouless pumping intertwines adiabatic quantum control and topological quantum transport and it holds potential for quantum metrology and computing. In this work, we introduce a ladder model featuring two doubly-degenerate bands and we show that adiabatic manipulation of the lattice parameters results in non-Abelian Thouless pumping, inducing both the displacement of an initially localized state and a geometric unitary transformation within the degenerate subspace. Additionally, we show that the structure and symmetry of the ladder model can be understood through its connection to a Yang monopole model. The proposed Hamiltonian can be realized using cold atoms in optical lattices, enabling the experimental demonstration of non-Abelian Thouless pumping in a genuinely quantum many-body system.

Van der Waals assembly allows for the creation of Josephson junctions in an atomically sharp interface between two exfoliated Bi2Sr2CaCu2O8+δ (Bi-2212) flakes that are twisted relative to each other. In a narrow range of angles close to 45°, the junction exhibits a regime where time-reversal symmetry can be spontaneously broken, and it can be used to encode an inherently protected qubit called flowermon. In this work, we investigate the physics emerging when two such junctions are integrated in a superconducting quantum interference device circuit threaded by a magnetic flux. We show that the flowermon qubit regime is maintained up to a finite critical value of the magnetic field, and, under appropriate conditions, it is protected against both charge and flux noise. For larger external fluxes, the interplay between the inherent twisted d-wave nature of the order parameter and the external magnetic flux enables the implementation of different artificial atoms, including a flux-biased protected qubit and a supersymmetric quantum circuit.

The rate and security of quantum communications between users placed at arbitrary points of a quantum communication network depend on the structure of the network, on its extension and on the nature of the communication channels. In this work we propose a strategy for the optimization of trusted-relays based networks that intertwines classical network approaches and quantum information theory. Specifically, by suitably defining a quantum communication efficiency functional, we identify the optimal quantum communication connections through the network by balancing security and the quantum communication rate. The optimized network is then constructed as the network of the maximal quantum communication efficiency connections and its performance is evaluated by studying the scaling of average properties as functions of the number of nodes and of the network spatial extension.