Practical quantum error correction with exchange-only silicon qubits

Quantum Error Correction (QEC) is essential for achieving the low error rates needed for teraquop-scale computations. This study investigates the utility of exchange-only qubits for QEC. Two dimensional arrays of exchange-only qubits in silicon offer flexible connectivity due to the triple-dot encoding, a plethora of native 2-qubit gates using only baseband exchange pulses, cost-effective dot-specific state transfer techniques, and compatibility with multiple measurement technologies. Given the large design space, we explore two routes: mapping a distance-3 surface code onto various physical topologies, and mapping various codes onto a single candidate topology. We also tailor topologies to address critical cost factors such as the number of dot rows or the total number of dots. Software tools are then used to extrapolate to large code distances, and to evaluate dot utilization efficiency and wiring overhead. This work aims to inspire the QEC community to explore the extensive design space of QEC with silicon quantum dots.