Berlin 2024 – scientific programme
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QI: Fachverband Quanteninformation
QI 17: Quantum Information: Concept and Methods I
QI 17.5: Talk
Wednesday, March 20, 2024, 10:30–10:45, HFT-TA 441
Imaginary Time Evolution: A Lie-theoretic study with applications to Quantum Algorithms and Statistical Physics — •Roberto Gargiulo1, Matteo Rizzi1,2, and Robert Zeier1 — 1Forschungszentrum Jülich GmbH, Peter Grünberg Institute, Quantum Control (PGI-8), Jülich 52425, Germany — 2University of Cologne, Institute for theoretical physics (THP), 50937 Cologne, Germany
The imaginary time evolution has long been used in physics to relate dynamical and equilibrium properties. We discuss this duality in the case of variational quantum algorithms, where a systematic study of symmetries via Lie theory can be used to relate compact real Lie algebras (such as su(n), so(n), sp(n)) to the their noncompact “imaginary-time” counterparts.
This connection is exemplified for the transfer-matrix method in classical spin systems, especially for the two-dimensional Ising model. This is also related to the standard ansatz for the quantum approximate optimization algorithm aimed at solving the maximum-cut graph problem. By leveraging this Lie-theoretic approach, we study similarities and differences between the two counterparts and explore potential applications.
Keywords: Symmetries; Variational Quantum Algorithms; Lie Algebra; Statistical Physics; Thermodynamics