Quantum Optimal Control Using High Performance Computing
N. Anders Petersson, USDOE National Nuclear Security Administration (NNSA) · 2019
This feasibility study developed numerical methods for the optimal control problem for realizing logical gates in closed quantum systems, where the evolution of the state vector is governed by the time dependent Schrodinger equation. The number of parameters in the control functions is made independent of the number of time steps by expanding them in terms of B-spline basis functions, with and without carrier waves. We use an interior point gradient-based technique from the IPOPT package to minimize the gate infidelity subject to amplitude constraints on the control functions. The symplectic Stromer-Verlet scheme is used to integrate a real-valued formulation of Schrodinger's equation in time and the gradient of the gate infidelity is obtained by solving the corresponding adjoint equation. This allows all components of the gradient to be calculated at the cost of solving three Schrodinger systems, independently of the number of parameters in the control functions. The correctness of the method is verified and applied to Hamiltonians that model the dynamics of coupled super-conducting qubits.