Quantum circuits are essential for executing quantum algorithms, and quantum gates must be reversible. Many algorithms rely on Boolean functions, which therefore need reversible implementation within the circuit. Reversible circuit synthesis translates such functions into reversible networks. Binary decision diagrams (BDDs) offer a scalable representation, yet the resulting BDDs and circuits are highly sensitive to variable ordering. Existing ordering heuristics typically minimize BDD size because it correlates with circuit size, but BDD size is an imperfect proxy for the quantum cost (QCC) of the synthesized circuit.
We introduce QuantumEvo, an evolutionary framework that employs a large language model (LLM) to generate QCC‑aware BDD variable‑ordering heuristics. Instead of directly predicting an ordering, QuantumEvo initializes a population of candidate heuristics drawn from several heuristic families and evolves them by manipulating variable orders through standard BDD operations. The downstream QCC metric selects the most effective heuristics. The discovered heuristic, HGA‑QE, modifies the sifting step inside a genetic algorithm to align the search more closely with QCC.
Across a benchmark suite, HGA‑QE achieves a 70.9% tie‑or‑win rate against the per‑function best baseline and is strictly best on 13.5% of the functions. Its advantage is especially pronounced on two benchmark collections sourced from data sets different from those used for heuristic discovery, indicating strong generalization.
Review: QuantumEvo leverages the generative power of LLMs together with evolutionary search, moving beyond the traditional proxy of BDD size. By directly optimizing heuristics for quantum cost, it delivers notable improvements in reversible circuit synthesis and opens a promising direction for scaling quantum algorithm implementation.