Superconducting gmon qubits allow for highly tuneable quantum computing devices. Optimally controlled evolution of these systems is of considerable interest. We determine the optimaldynamical protocols for the generation of the maximally entangled W state of three qubits from an easily prepared initial product state. These solutions are found by simulated annealing. Using the connection to the Pontryagin’s minimum principle, we fully characterize the patterns of these „bang-bang“ protocols, which shortcut the adiabatic evolution. The protocols are remarkably robust, facilitating the development of high-performance three-qubit quantum gates.
We apply the theory of optimal control to the dynamics of two „Gmon“ qubits, with the goal of preparing a desired entangled ground state from an initial unentangled one.Given an initial state, a target state, and a Hamiltonian with a set of permissible controls, can we reach the target state with coherent quantum evolution and, in that case, what is the minimum time required? The adiabatic theorem provides a far from optimal solution in the presence of a spectral gap. Optimal control yields the fastest possible way of reaching the target state and helps identify unreachable states. In the context of a simple quantum system, we provide examples of both reachable and unreachable target ground states, and show that the unreachability is due to a symmetry. We find the optimal protocol in the reachable case using three different approaches: (i) a brute-force numerical minimization (ii) an efficient numerical minimization using the bang-bang ansatz expected from the Pontryagin minimum principle, and (iii) direct solution of the Pontryagin boundary value problem, which yields an analytical understanding of the numerically obtained optimal protocols. Interestingly, our system provides an example of singular control, where the Pontryagin theorem does not guarantee bang-bang protocols. Nevertheless, all three approaches give the same bang-bang protocol.