Maximizing entanglement entropy and minimizing thermal entropy with an optical tweezer array

Here we discuss two new paradigms of studying quantum simulation with atom arrays. In the first, we use an array with as many as 60 Rydberg atoms to quantitatively compare the ability for classical and quantum devices to reproduce some idealized quantum dynamics. We find the cost of the classical simulation increases by orders-of-magnitude with incremental experimental improvements, and show the quantum experiment can outperform the classical computer in finite sampling from maximum entanglement entropy states. Next, we discuss a new approach to quantum simulation with optical tweezer arrays by exerting control over the motional pure state. We show results in cooling to the absolute ground state via a novel form of measurement based cooling, and work towards generating Bell states between the low-lying motional levels of atoms in adjacent optical tweezers. We discuss the potential for full control of the motional degree of freedom for atoms trapped in optical tweezers, including efforts to generate the states necessary for bosonic quantum error correction.