Physicist German F R Sborlini uses quantum algorithms to optimize Feynman integrals, a complex Quantum Field Theory (QFT) aspect. His work uses quantum computing to solve Directed Acyclic Graph (DAG) detection, which could significantly speed up high-precision predictions in QFT. Sborlini’s approach involves promoting the vertices and edges of a directed graph to a Hilbert space, which could potentially expedite the calculation of Feynman integrals. This development in quantum computing could lead to more precise predictions in high-energy physics.
Quantum Algorithms for Feynman Integrals
German F R Sborlini, a physicist from the Department of Fundamental Physics and IUFFyM at the University of Salamanca and the School of Science, Engineering, and Design at the European University of Valencia, has been exploring the use of quantum algorithms to optimize Feynman integrals. These integrals are a significant challenge in high-precision Quantum Field Theory (QFT) predictions.
Quantum Computing in High Energy Physics
Quantum computing has shown potential in various fields, including high-energy physics. It has been applied to scattering amplitude calculations, jet clustering, and recently, to perform the causal reconstruction of scattering amplitudes within LoopTree Duality (LTD). Sborlini’s work uses quantum computing to solve Directed Acyclic Graph (DAG) detection and exploits this information to bootstrap the causal LTD representation of multiloop multileg scattering amplitudes.
Causal LoopTree Duality from Geometry
The LTD theorem relies on the iterative application of Cauchy’s residue theorem to remove one degree of freedom per loop. This theorem allows the loops to be opened and recasts the virtual contributions in terms of tree-level-like amplitudes integrated over a real radiation phase space. The geometrical formulation of causal LTD implies that the causal representation can be bootstrapped from DAGs.
Quantum Algorithms for LTD
The problem of finding a causal representation has been partially reduced to identifying DAGs. Classical algorithms rely on construction strategies and the direct evaluation of acyclicity conditions. However, these methods have almost exponential scaling in the number of edges for dense graphs. On the other hand, Quantum algorithms can efficiently parallelize the evaluation of the acyclicity condition, leading to a significant speedup.
Quantum Algorithms and Feynman Integrals
Sborlini’s work involves promoting the vertices and edges of a directed graph to a Hilbert space. The Hamiltonian, an operator acting on the space of edges, is then built and minimized. This process results in a degenerated ground state with zero energy composed of all the possible acyclic configurations of the graph. This approach could potentially speed up the calculation of Feynman integrals, a significant bottleneck in high-precision predictions in QFT.
Quantum Computing and the Future of High Energy Physics
The exploration of quantum computing in high-energy physics could lead to significant advancements in the field. The potential speedup in database searching, factorization, and solving minimization/optimization problems could overcome the precision frontier. This development could lead to very precise predictions from the Standard Model and other quantum field theories for collider phenomenology.
In the article “Tackling Feynman integrals with quantum minimization algorithms,” author Germán F. R. Sborlini explores the application of quantum minimization algorithms to Feynman integrals. The paper was published on January 31, 2024. The full article can be accessed through its DOI: https://doi.org/10.22323/1.449.0501.
