are largely set by this task. Tailoring next-generation processors for joint measurements, therefore, could result in improvements to speed, accuracy, or cost — accelerating the development large-scale quantum computers. Here, we motivate such explorations by analyzing an unconventional surface code based on multi-body interactions between superconducting transmon qubits. Our central consideration, Hardware Optimized Parity (HOP) gates, achieves stabilizer-type measurements through simultaneous multi-qubit conditional phase accumulation. Despite the multi-body effects that underpin this approach, our estimates of logical faults suggest that this design can be at least as robust to realistic noise as conventional designs. We show a higher threshold of 1.25×10−3 compared to the standard code’s 0.79×10−3. However, in the HOP code the logical error rate decreases more slowly with decreasing physical error rate. Our results point to a fruitful path forward towards extending gate-model platforms for error correction at the dawn of its empirical development.