Investigating effects of increased connectivity on superconducting qubit gate speed limits

Fast two-qubit entangling gates are essential for quantum computers with finite coherence times. Due to the limit of interaction strength among qubits, there exists a theoretical speed limit for a given two-qubit entangling gate. This speed limit has been explicitly found only for a two-qubit system and under the assumption of negligible single qubit gate time. We demonstrate such a speed limit experimentally using optimal control on two superconducting transmon qubits with a fixed capacitive coupling. We then investigate the effect of additional couplings on the speed limit, both through introduction of an ancillary qubit as well as through utilization of higher transmon energy states. Finally, we discuss the generalization to many qubit systems where properly leveraging all available couplings can provide dramatic speedups, thus necessitating the co-design of quantum computers from both theorists and experimentalists for optimal gate performance.