Abstract
The quantum alternating operator ansatz (QAOA) is a promising gate-model metaheuristic for combinatorial optimization. Applying the algorithm to problems with constraints presents an implementation challenge for near-term quantum resources. This paper explores strategies for enforcing hard constraints by using Hamiltonians as mixing operators (mixers). Despite the complexity of simulating the model, we demonstrate that, for an integer variable admitting discrete values represented through one-hot encoding, certain classes of the mixer Hamiltonian can be implemented without Trotter error in depth . We also specify general strategies for implementing QAOA circuits on all-to-all connected hardware graphs and linearly connected hardware graphs inspired by fermionic simulation techniques. Performance is validated on graph-coloring problems that are known to be challenging for a given classical algorithm. The general strategy of using mixers is borne out numerically, demonstrating a significant improvement over the general mixer, and moreover the generalized state yields better performance than easier-to-generate classical initial states when mixers are used.
5 More- Received 1 August 2019
DOI:https://doi.org/10.1103/PhysRevA.101.012320
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