Rethinking Parity Check Enhanced Symmetry-Preserving Ansatz

With the arrival of the Noisy Intermediate-Scale Quantum (NISQ) era, Variational Quantum Algorithms (VQAs) have emerged to obtain possible quantum advantage. In particular, how to effectively incorporate hard constraints in VQAs remains a critical and open question. In this paper, we manage to seamlessly combine the Hamming Weight Preserving ansatz with a topological-aware parity check on physical qubits to enforce error mitigation and further hard constraints. We demonstrate such a combination significantly outperforms peer VQA methods on both quantum chemistry problems and constrained combinatorial optimization problems e.g.