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Testing and exploiting macroscopic quantum physics

The research in the group is focused on developing methods from quantum information and quantum many-body physics for problems relevant in experiment or theoretical physics.

Research Areas

Topological Data Analysis

Topological Data Analysis (TDA) is a rapidly growing field that applies concepts from topology—the mathematical study of shape and space—to uncover the underlying structure in complex datasets. By focusing on features like connected components, loops, and voids, TDA provides robust, multi-scale insights that are often resilient to noise and deformations in data. In our group, we are considering a reformulation of TDA as a fermionic many-body problem. In this perspective, the combinatorial structure of data (e.g., simplicial complexes) is mapped to the Hilbert space of fermionic states. This connection allows tools from many-body quantum physics like
tensor networks to be applied to problems in data analysis, opening up new computational strategies and theoretical insights.

Lattice Gauge Theories

Lattice Gauge Theories (LGTs) are a cornerstone of modern theoretical physics, providing a non-perturbative framework for studying gauge theories—such as quantum chromodynamics—by discretizing spacetime into a lattice. This approach preserves local gauge symmetry while
rendering complex quantum field theories amenable to numerical simulation and analytical insight. In the Hamiltonian formulation of LGTs, the focus shifts from path integrals to quantum states in a Hilbert space. This perspective is particularly well-suited to quantum simulation and the application of variational many-body methods. We combine a certain class of tensor networks, so-called Gauged Gaussian Projected Entangled Pair States (GGPEPS), with a variational Monte Carlo procedure to find the ground states of lattice gauge theories.

Quantum Networks

Quantum networks are engineered systems for distributing and processing quantum information across distant nodes, enabling tasks such as quantum communication, distributed quantum computing, and secure information transfer. At the heart of these networks is entanglement, a uniquely quantum resource that allows for correlations stronger than any classical system can support.

A central challenge in building large-scale quantum networks is the distribution of entanglement over long distances: quantum information cannot be copied and thus, quantum repeaters are fundamentally different from commonly used amplifiers in fiber networks.

By considering a quantum network as a genuine quantum many-body system, we can apply techniques from statistical mechanics and machine learning to optimize the topology and the operation of the network.

Nonlocality Detection

Bell nonlocality is a fundamental feature of quantum mechanics that reveals the impossibility of explaining quantum correlations through any local hidden variable theory. Demonstrated through violations of Bell inequalities, nonlocality highlights the intrinsic quantum nature of entanglement—showing that measurements on spatially separated particles can exhibit correlations that defy classical intuition.

Traditionally, Bell nonlocality is tested through statistical violations of specific inequalities. However, finding these inequalities for many-party settings like modern quantum processors is extremely challenging. By assuming a less strict certification scenario, a powerful alternative approach has emerged: detecting nonlocality via energy minimization. In this framework, one constructs a Bell operator—analogous to a Hamiltonian—whose expectation value is bounded for all local (classical) strategies. A quantum system exhibits nonlocality if its ground-state energy falls below this classical threshold.

This energy-based perspective connects Bell nonlocality to methods from many-body physics and optimization, allowing the use of variational techniques, semidefinite programming, and even tensor networks to detect nonlocal correlations. It also enables the exploration of nonlocality in more complex systems, such as spin chains or lattice models, where traditional Bell tests are difficult to
implement.

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