  Suppressing errors is the central challenge for useful quantum computing,
requiring quantum error correction for large-scale processing. However, the
overhead in the realization of error-corrected ``logical'' qubits, where
information is encoded across many physical qubits for redundancy, poses
significant challenges to large-scale logical quantum computing. Here we report
the realization of a programmable quantum processor based on encoded logical
qubits operating with up to 280 physical qubits. Utilizing logical-level
control and a zoned architecture in reconfigurable neutral atom arrays, our
system combines high two-qubit gate fidelities, arbitrary connectivity, as well
as fully programmable single-qubit rotations and mid-circuit readout. Operating
this logical processor with various types of encodings, we demonstrate
improvement of a two-qubit logic gate by scaling surface code distance from d=3
to d=7, preparation of color code qubits with break-even fidelities,
fault-tolerant creation of logical GHZ states and feedforward entanglement
teleportation, as well as operation of 40 color code qubits. Finally, using
three-dimensional [[8,3,2]] code blocks, we realize computationally complex
sampling circuits with up to 48 logical qubits entangled with hypercube
connectivity with 228 logical two-qubit gates and 48 logical CCZ gates. We find
that this logical encoding substantially improves algorithmic performance with
error detection, outperforming physical qubit fidelities at both cross-entropy
benchmarking and quantum simulations of fast scrambling. These results herald
the advent of early error-corrected quantum computation and chart a path toward
large-scale logical processors.
