Imposing Constraints on Driver Hamiltonians and Mixing Operators: From Theory to Practical Implementation
The paper develops algebraic methods to create quantum driver Hamiltonians and unitary mixers that satisfy classical constraints. It proves that finding such operators is generally NP-Complete but provides polynomial-time algorithms for finding local, constant-locality operators. These tools are then used to build improved ansatzes for QAOA and CQA, showing new approaches outperform existing mixers on problems like 1-in-3 SAT.