Neutral atom quantum computers for the applications in condensed matter physics

Quantum computers have the potential to solve problems that are difficult or impossible to address using classical modes of computation. Laser cooled neutral atoms at ultracold temperatures offer unique possibilities to study interacting many-body quantum systems which is at the heart of various quantum condensed matter phenomena. The first-generation neutral atom quantum computers for performing special purpose quantum computations was realized by trapping ultracold atoms in optical lattices. These tunable and scalable machines provided tremendous opportunities to study various quantum phases of Bose and Fermi Hubbard models, topological phases, and non-equilibrium dynamics, with control over key system parameters enabling insightful explorations within specific quantum models. In a more recent advent, arrays of single neutral atoms trapped in optical tweezers have emerged as dark horse candidate for universal and fault tolerant quantum computing. Here, we review recent advances and achievements obtained with this platform and discuss future perspectives.