Discrete Adjoints for Accurate Numerical Optimization with Application to Quantum Control

Understand

This paper considers the optimal control problem for realizing logical gates in a closed quantum system.

• The quantum state is governed by Schrodinger's equation, which we formulate as a time-dependent Hamiltonian system in terms of the real and imaginary parts of the state vector.
• The system is discretized with the Stormer-Verlet scheme, which is a symplectic partitioned Runge-Kutta method.
• Our main theoretical contribution is the derivation of a compatible time-discretization of the adjoint state equation, such that the gradient of the discrete objective function can be calculated exactly, at a computational cost of solving two Schr\"odinger systems, independently of the number of parameters in the control functions.