Diagnosing Quantum Circuits: Noise Robustness, Trainability, and Expressibility

Parameterized quantum circuits are central to near-term quantum algorithms, and serve as the foundation for many quantum machine learning frameworks, which should be robust to noise, maintain trainability, and exhibit sufficient expressibility. Here we introduce 2MC-OBPPP, a polynomial-time classical estimator that quantifies the three aforementioned diagnostics for a given parameterized quantum circuit. As a demonstration of the power of our approach, we show that moderate amplitude damping noise can reduce the severity of vanishing gradients, but at the cost of lowered expressibility. In particular, our approach can yield a spatiotemporal "noise-hotspot" map that pinpoints the most noise-sensitive qubits/gates in parameterized quantum circuits. Applying this map to a specific circuit, we show that implementing interventions on fewer than 2% of the qubits is sufficient to mitigate up to 90% of the errors. Therefore, 2MC-OBPPP is not only an efficient, hardware-independent tool for pre-execution circuit evaluation but also enables targeted strategies that significantly reduce the cost of noise suppression.