Speaker
Description
We present a general algebraic framework for constructing constraint preserving driver Hamiltonians and mixing operators, a central challenge in constrained quantum optimization. We characterize the operators that preserve embedded classical constraints, establish the computational complexity of finding them, and then develop practical algorithms for constructing them when locality bounds are known or desired.
We prove that deciding whether constraint preserving operators exist is NP-complete in the general case, while showing that operators with constant locality can be found in worst-case polynomial time. Since many practical optimization problems admit local constraint preserving operators, these results provide an efficient route to ansatz construction despite the intractability of the unrestricted problem.
Building on this framework, we develop algorithmic procedures that transform these algebraic primitives into driver Hamiltonians and mixing operators suitable for Constrained Quantum Annealing (CQA) and the Quantum Alternating Operator Ansatz (QAOA), providing a systematic alternative to handcrafted constructions.
| Topic | Hybrid quantum-classical approaches for learning and optimization |
|---|---|
| Additional Topic | Quantum variational circuits and their applications |