At University of Maryland, we have constructed a fully programmable, ion-based quantum computer with the goal of realizing an error-corrected logical quantum bit. I will report on the performance of our integrated device, including operation with more than 20 ion qubits, fidelities of single-and two-qubit gates, and their dominant errors. I will present the implementation of the building blocks of error correction in our system, and its first applications to the simulation of quantum many-body physics. I will conclude with a discussion of the physical limitations of our approach, as well as ways to address these and build a 50+-qubit quantum simulation platform based on trapped ions. This work is supported by the ARO with funding from the IARPA LogiQ program, the NSF Practical Fully-Connected Quantum Computer program, the DOE program on Quantum Computing in Chemical and Material Sciences, the AFOSR MURI on Quantum Measurement and Verification, and the AFOSR MURI on Interactive Quantum Computation and Communication Protocols.