Quantum Simulation
Several scientific disciplines, ranging from quantum chemistry to condensed matter physics, face the challenge of understanding the properties of quantum systems composed of many interacting particles. Quantum technologies offer a unique opportunity to tackle this problem from a fundamentally different perspective through the use of quantum simulators.
Unlike universal quantum computers, quantum simulators are designed and optimized to solve specific classes of problems. By exploiting the intrinsic dynamics of controllable quantum systems, they enable the study of phenomena that are often inaccessible to classical computers.
The research group has extensive expertise in this area and has recently focused on extending the application of quantum simulation techniques to quantum field theories and high-energy physics, opening new avenues for the investigation of fundamental physical processes.
Quantum Complexity and Algorithms
There are numerous quantum systems whose properties we would like to compute efficiently. However, in many situations of practical and theoretical interest, these calculations become extraordinarily difficult due to the exponential growth of the Hilbert space with system size. This computational barrier prevents an accurate description of many important processes occurring in nature.
A fundamental question is whether we can identify the ultimate source of this computational complexity. Feynman’s seminal insight pointed directly to the heart of the problem: quantum systems are difficult to simulate because the mathematical structures that describe them, such as wave functions and operators, are fundamentally different from and often much more complex than their classical counterparts.
This perspective naturally leads to viewing many-body quantum systems as specific instances of quantum computations. What types of computations do these systems perform? Under what conditions can their behavior be efficiently described by classical methods, and when does genuine quantum complexity emerge? Addressing these questions is of critical importance in the context of modern quantum simulation experiments.
The research group investigates these issues through the tools of quantum complexity theory, quantum algorithms, and many-body physics, aiming to deepen our understanding of the computational power and limitations of quantum systems.
Quantum Entanglement in Many-Body Systems
Quantum entanglement was identified by Schrödinger in 1935 as the defining feature of quantum mechanics, responsible for its profound departure from classical physics. Today, entanglement is regarded as the fundamental resource underlying quantum computation and quantum communication, motivating intense theoretical and experimental research.
Among the most significant developments in this field are the characterization and quantification of entanglement in many-body systems through von Neumann and Rényi entropies, its role in quantum error correction, and its use in the classification of topological phases of matter. Entanglement has also become a central concept in the design of variational ansätze based on tensor networks, which provide efficient representations of ground states of local Hamiltonians.
The research group has a long and distinguished track record in these areas, as reflected in its extensive publication record.
Tensor Networks
Typical states in the Hilbert space of many-body systems exhibit extremely high levels of entanglement. However, an important class of physically relevant states displays much lower entanglement. This class generally includes ground states and low-lying excitations of local Hamiltonians, whose entanglement is predominantly short-ranged.
Tensor networks provide a powerful variational framework for representing the wave functions of such systems. By construction, they efficiently explore the low-entanglement sector of Hilbert space, allowing accurate descriptions of quantum states that would otherwise be inaccessible through conventional methods. The connectivity of the network encodes the underlying entanglement structure of the state.
The research group has developed a sustained research activity in this field, including extensions of tensor-network methods to quantum field theories, as well as applications to integrable systems and related areas of mathematical physics.
Noise Characterization and Quantum Error Correction
The so-called Second Quantum Revolution has led to the development of several technologies that exploit the laws of quantum mechanics to perform specific tasks more efficiently than their classical counterparts. The flagship example is the quantum computer, which can offer substantial, and in some cases exponential, advantages for particular computational problems.
Quantum computing is a strategic research priority within major international initiatives, including the European Quantum Flagship, and is actively pursued by leading industrial stakeholders such as Google, Amazon, IBM, and Microsoft.
Achieving practical quantum advantage in real-world applications requires addressing the unavoidable errors arising from imperfect device control and from the degradation of quantum information caused by interactions with the environment. Developing effective strategies to mitigate and correct these errors is therefore essential for the realization of large-scale quantum computing.
One of the research group’s main lines of activity focuses on the development of quantum error mitigation techniques, quantum error correction protocols, and hybrid approaches that combine both strategies. This work is carried out within realistic models of the dominant noise sources affecting current quantum computing platforms, particularly trapped-ion processors and superconducting quantum circuits.