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. Quadratic Assignment Problem. Our extensive experimental results on both simulators and superconducting quantum processors verify that the combination of HWP ansatz with parity check is among the most promising candidates to show quantum advantages in the NISQ era to solve more realistic problems.