Engineering Effective Hamiltonians

Understand

In the field of quantum control, effective Hamiltonian engineering is a powerful tool that utilises perturbation theory to mitigate or enhance the effect that a variation in the Hamiltonian has on the evolution of the system.

• Here, we provide a general framework for computing arbitrary time-dependent perturbation theory terms, as well as their gradients with respect to control variations, enabling the use of gradient methods for optimizing these terms.
• In particular, we show that effective Hamiltonian engineering is an instance of a bilinear control problem - the same general problem class as that of standard unitary design - and hence the same optimization algorithms apply.
• We demonstrate this method in various examples, including decoupling, recoupling, and robustness to control errors and stochastic errors.