Continuous rotation schemes to map the objective Hamiltonian to its negative

Develop alternative continuous rotation schemes that transform the objective Hamiltonian H_obj into −H_obj over the evolution parameter in Q-CHOP for arbitrary objectives, beyond the specific global and local rotations proposed, and assess their efficiency and overhead for gate-based implementations.

Background

The paper proposes a specific construction to continuously rotate one qubit per Pauli-Z string term in the objective Hamiltonian to ensure H_obj(θ) changes sign across the evolution. The authors also mention an alternative strategy that splits the objective into even and odd parts.

They explicitly leave the broader design space of such rotations to future work, indicating that improved schemes could reduce overhead or better suit discretized implementations.