Erbium-tweezer arrays for quantum computation

The past two decades have demonstrated the unprecedented control over external and internal degrees of freedom that the scientific community has reached. Among these advances are discovery of Bose-Einstein condensates (1995), degenerate Fermi gases (1999), visualization of single atoms with quantum-gas microscope (2009) and atom-by-atom assembly of complex arrays (2016, 2018). These achievements resulted in Nobel prizes (2001, 2012) and laid the groundwork for quantum simulators analog of computers allowing scientists to explore complex quantum phenomena otherwise inaccessible. Our project focuses on developing a cutting-edge quantum simulator based on erbium atoms, which are uniquely suited for this purpose due to their extraordinary properties. Erbium atoms have a complex electronic structure and strong magnetic interactions, which enable the exploration of phenomena like quantum droplets and supersolid states. Central to this effort is the development of an erbium-tweezer array, where erbium atoms are trapped in laser-controlled optical tweezers. Unlike standard qubits, which are limited to two states, erbium enables the use of high-dimensional quditssuperpositions of up to 96 states. This significantly expands computational capacity and opens new possibilities for solving complex quantum problems. Coupling erbium atoms with Rydberg states, high-energy configurations of atoms, enables the creation of universal quantum gates for digital quantum simulations. Advances in optical-tweezer technology enable the creation of large, organized arrays of neutral atoms, approaching record numbers of qubits. These developments, combined with erbiums unique properties, make this platform a game-changer in quantum research. From superconductivity to the forces that shape the universe, this research brings us closer to solving some of the most profound mysteries of quantum physics. One major application of this technology is the simulation of lattice-gauge theories, essential for understanding fundamental forces such as electromagnetism and the strong nuclear force. By arrang- ing erbium atoms in a lattice and assigning them roles as matter or field, we can mimic these interactions in a controlled environment, allowing the investigation of energy states, phase transitions, and emergent quantum behaviors.