This paper proposes a training-free quantum architecture search (TF-QAS) method that uses two proxies—path-based and expressibility-based—to rank quantum circuits without requiring circuit training. The path-based proxy, which is zero-cost, estimates the topological complexity of a quantum circuit by counting the number of paths in a directed acyclic graph (DAG) representation. The expressibility-based proxy evaluates the circuit's ability to uniformly reach the entire Hilbert space, reflecting its performance in variational quantum algorithms (VQAs). These proxies enable a two-stage progressive TF-QAS, where the path-based proxy is used first to filter out unpromising circuits, followed by the expressibility-based proxy to identify high-performance circuits. Simulations on three VQE tasks for the transverse field Ising model (TFIM), Heisenberg model, and BeH₂ molecule show that TF-QAS achieves a significant improvement in sampling efficiency, ranging from 5 to 57 times compared to state-of-the-art QAS, while also being 6 to 17 times faster. The results demonstrate that TF-QAS is more efficient and effective than training-based QAS methods, making it suitable for large-scale quantum circuits. The paper also discusses the challenges of training-free QAS and the importance of developing effective proxies for quantum circuit design.This paper proposes a training-free quantum architecture search (TF-QAS) method that uses two proxies—path-based and expressibility-based—to rank quantum circuits without requiring circuit training. The path-based proxy, which is zero-cost, estimates the topological complexity of a quantum circuit by counting the number of paths in a directed acyclic graph (DAG) representation. The expressibility-based proxy evaluates the circuit's ability to uniformly reach the entire Hilbert space, reflecting its performance in variational quantum algorithms (VQAs). These proxies enable a two-stage progressive TF-QAS, where the path-based proxy is used first to filter out unpromising circuits, followed by the expressibility-based proxy to identify high-performance circuits. Simulations on three VQE tasks for the transverse field Ising model (TFIM), Heisenberg model, and BeH₂ molecule show that TF-QAS achieves a significant improvement in sampling efficiency, ranging from 5 to 57 times compared to state-of-the-art QAS, while also being 6 to 17 times faster. The results demonstrate that TF-QAS is more efficient and effective than training-based QAS methods, making it suitable for large-scale quantum circuits. The paper also discusses the challenges of training-free QAS and the importance of developing effective proxies for quantum circuit design.