Demonstrating two-qubit gates at the quantum speed limit using superconducting qubits.

The speed of elementary quantum gates, particularly two-qubit gates, ultimately sets the limit on the speed at which quantum circuits can operate. In this work, we experimentally demonstrate commonly used two-qubit gates at nearly the fastest possible speed allowed by the physical interaction strength between two superconducting transmon qubits. We achieve this quantum speed limit by implementing experimental gates designed using a machine learning-inspired optimal control method. The machine learning-based algorithm can achieve the speed limit of various two-qubit gates in an N-qubit system through the optimization of single-qubit pulses, and this algorithm significantly outperforms standard optimal control algorithms such as GRAPE. Importantly, our method only requires the single-qubit drive strength to be moderately larger than the interaction strength to achieve an arbitrary two-qubit gate close to its analytical speed limit with high fidelity. Thus, the method is applicable to a variety of platforms including those with comparable single-qubit and two-qubit gate speeds, or those with always-on interactions.