Evolving Hardware-Efficient Grover Circuits via Grammatical Evolution

Grover’s algorithm offers a quadratic speedup for unstructured search problems, but its standard implementation becomes highly resource-intensive when deployed on real quantum hardware. In this work, we demonstrate that quantum circuits evolved through grammatical evolution (GE) can outperform the canonical Grover design on noisy intermediate-scale quantum (NISQ) devices. Using a symbolic BNF grammar and a hardware-aware fitness function, we evolved Grover-like circuits for all 8 basis states of a 3-qubit system. On IBM’s ibm_brisbane backend, our best evolved circuit achieved 97.9% fidelity (for |000), and even the lowest-performing evolved circuit reached 89.1% fidelity (for |011). In contrast, standard Grover circuits achieved only 44.2% to 47.6% fidelity under the same conditions. Evolved solutions also achieved up to 93.3% reduction in depth and 92.7% reduction in gate count, making them significantly more hardware efficient. These findings highlight the potential of symbolic AI techniques, like grammatical evolution, to discover performant, compact quantum programs that are better suited to near-term hardware than traditional, hand-crafted designs.