
Prof. Dr. Joachim Ankerhold
Prof. Dr. Joachim Ankerhold
Topological Data Analysis (TDA)
Topological Data Analysis (TDA for short) uses topology to reveal structure in complex datasets by analyzing features like loops and voids, offering robust, noise-resistant insights. Our group reformulates TDA as a fermionic many-body problem, mapping data structures to fermionic Hilbert spaces. This enables the use of quantum many-body tools for novel data analysis approaches.
Lattice Gauge Theory (LGT)
Lattice Gauge Theories discretize spacetime to study gauge theories like quantum chromodynamics, preserving local gauge symmetry and enabling simulations. The Hamiltonian approach focuses on quantum states, ideal for quantum simulation. We use Gauged Gaussian Projected Entangled Pair States, a special tensor network construction, with variational Monte Carlo methods to efficiently find ground states of these theories using tensor network techniques.
Quantum Networks
Quantum networks enable quantum communication, distributed computing, and secure data transfer by linking distant nodes using entanglement. A key challenge is distributing entanglement over long distances, requiring quantum repeaters unlike classical amplifiers. We view the network as a quantum many-body system which allows the use of statistical mechanics and machine learning to optimize its structure and performance.
Nonlocality Detection
Bell nonlocality reveals that quantum correlations can't be explained by local hidden variable theories. Traditionally tested via Bell inequalities, it's hard to extend to many-body systems. In our group, we use energy minimization as an alternative: a Bell operator's ground-state energy signals nonlocality if it drops below a classical bound. This connects quantum nonlocality with many-body physics and optimization techniques like tensor networks.