Gradient-based quantum optimal control on superconducting qubit systems

Quantum technologies are expected to help solve many of today's global challenges, revolutionizing several fields such as computing, sensing and secure communications. In this regard, the need for precise manipulation of the dynamics of a quantum system and its optimization has given rise to the field of quantum control theory. In the search for optimal controls, accurate derivatives are a possible method to traverse and ultimately converge in quantum optimization landscapes. In this work we study an efficient algorithm for computing analytically-exact derivatives by formulating the control problem in the basis that diagonalizes the control Hamiltonian and applying a specific Trotterized time propagation scheme. The method is numerically verified for a system of superconducting transmon qubits in the few- and many body regime using matrix product states. The comparison between the results obtained using an exact dynamics via Krylov subspace methods shows how the approximate dynamics ultimately sets a trade-off between computational complexity and quality of the final solutions.