Quantum 2025 – wissenschaftliches Programm
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MON: Monday Contributed Sessions
MON 2: Quantum Control
MON 2.5: Vortrag
Montag, 8. September 2025, 15:15–15:30, ZHG002
Riemannian quantum circuit optimization based on matrix product operators — •Isabel Nha Minh Le1,2, Shuo Sun1,2, and Christian B. Mendl1,2,3 — 1Technical University of Munich, School of Computation, Information and Technology, 85748 Garching, Germany — 2Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany — 3Technical University of Munich, Institute for Advanced Study, 85748 Garching, Germany
We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods. Unlike previous approaches, our method imposes no symmetry assumptions, such as translational invariance, on the quantum systems. This technique is scalable to large systems through the use of a matrix product operator representation of the reference time evolution propagator. Our optimization routine is applied to various spin chains and fermionic systems described by the transverse-field Ising Hamiltonian, the Heisenberg Hamiltonian, and the spinful Fermi-Hubbard Hamiltonian. In these cases, our approach achieves a relative error improvement of up to four orders of magnitude for systems of 50 qubits. Furthermore, we demonstrate the versatility of our method by applying it to molecular systems, specifically lithium hydride, achieving an error improvement of up to eight orders of magnitude. This proof of concept highlights the potential of our approach for broader applications in quantum simulations.
Keywords: Quantum circuits; Quantum circuit compression; Hamiltonian simulation; Tensor networks; Quantum-classical hybrid methods