The cross-resonant gate is an entangling gate for fixed frequency superconducting qubits introduced for untunable qubits. While being simple and extensible, it suffers from long durationand limited fidelity. Using two different optimal control algorithms, we probe the quantum speed limit for a CNOT gate in this system. We show that the ability to approach this limit depends strongly on the ansatz used to describe the optimal control pulse. A piecewise constant ansatz with a single carrier leads to an experimentally feasible pulse shape, shorter than the one currently used in experiments, but that remains relatively far from the speed limit. On the other hand, an ansatz based on the two dominant frequencies involved in the optimal control problem allows to generate an optimal solution more than twice as fast, in under 30ns. This comes close to the theoretical quantum speed limit, which we estimate at 15ns for typical circuit-QED parameters, which is more than an order of magnitude faster than current experimental microwave-driven realizations, and more than twice as fast as tunable direct-coupling experimental realizations.
We use quantum optimal control theory to systematically map out the experimentally reachable parameter landscape of superconducting transmon qubits. With recent improvements in decoherencetimes, transmons have become a promising platform for quantum computing. They can be engineered over a wide range of parameters, giving them great flexibility, but also requiring us to identify good regimes to operate at. Using state-of-the-art control techniques, we exhaustively explore the landscape for the potential creation and distribution of entanglement, for a wide range of system parameters and applied microwave fields. We find the greatest success outside the usually considered dispersive regime. A universal set of gates is realized for gate durations of 50 ns, with gate errors approaching the theoretical limit. Our quantum optimal control approach is easily adapted to other platforms for quantum technology.
The creation of a quantum network requires the distribution of coherent information across macroscopic distances. We demonstrate the entanglement of two superconducting qubits, separatedby more than a meter of coaxial cable, by designing a joint measurement that probabilistically projects onto an entangled state. By using a continuous measurement scheme, we are further able to observe single quantum trajectories of the joint two-qubit state, confirming the validity of the quantum Bayesian formalism for a cascaded system. Our results allow us to resolve the dynamics of continuous projection onto the entangled manifold, in quantitative agreement with theory.