Optimal control of superconducting gmon qubits using Pontryagin's minimum principle: preparing a maximally entangled state with singular bang-bang protocols

Understand

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.