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Variational quantum simulation of U(1) lattice gauge theories with qudit systems
Pavel P. Popov (Institute of Photonic Sciences, Barcelona Institute of Science and Technology), M. Meth (Universität Innsbruck), Maciej Lewenstein (Institució Catalana de Recerca i Estudis Avançats, Institute of Photonic Sciences), Philipp Hauke (University of Trento, Istituto Nazionale di Fisica Nucleare, Trento Institute for Fundamental Physics And Applications), Martin Ringbauer (Universität Innsbruck), Erez Zohar (Hebrew University of Jerusalem), Valentin Kasper (Institute of Photonic Sciences, Barcelona Institute of Science and Technology)
Résumé : Lattice gauge theories are fundamental to various fields, including particle physics, condensed matter, and quantum information theory. Recent progress in the control of quantum systems allows for studying Abelian lattice gauge theories in table-top experiments. However, several challenges remain, such as implementing dynamical fermions in higher spatial dimensions and magnetic field terms. Here, we map U(1) Abelian lattice gauge theories in arbitrary spatial dimensions onto qudit systems with local interactions. We propose a variational quantum simulation scheme for the qudit system with a local Hamiltonian, that can be implemented on a universal qudit quantum device as the one developed in []. We describe how to implement the variational imaginary-time evolution protocol for ground-state preparation as well as the variational real-time evolution protocol to simulate nonequilibrium physics on universal qudit quantum computers, supplemented with numerical simulations. Our proposal can serve as a way of simulating lattice gauge theories, particularly in higher spatial dimensions, with minimal resources, regarding both system sizes and gate count. Published by the American Physical Society 2024