  Rydberg atom arrays are a leading platform for quantum computing and
simulation, combining strong interactions with highly coherent operations and
flexible geometries. However, the achievable fidelities are limited by the
finite lifetime of the Rydberg states, as well as technical imperfections such
as atomic motion. In this work, we propose a novel approach to Rydberg atom
arrays using long-lived circular Rydberg states in optical traps. Based on the
extremely long lifetime of these states, exceeding seconds in cryogenic
microwave cavities that suppress radiative transitions, and gate protocols that
are robust to finite atomic temperature, we project that arrays of hundreds of
circular Rydberg atoms with two-qubit gate errors around $10^{-5}$ can be
realized using current technology. This approach combines several key elements,
including a quantum nondemolition detection technique for circular Rydberg
states, local manipulation using the ponderomotive potential of focused optical
beams, a gate protocol using multiple circular levels to encode qubits, and
robust dynamical decoupling sequences to suppress unwanted interactions and
errors from atomic motion. This represents a significant improvement on the
current state-of-the-art in quantum computing and simulation with neutral
atoms.
