Diagnosing Quantum Circuits: Noise Robustness, Trainability, and Expressibility

Abstract

Achieving practical quantum advantage on near-term noisy hardware is a central goal of quantum computation. However, without efficient pre-execution diagnostics, circuit design and scheme selection often rely on costly hardware-in-the-loop trial-and-error, inflating experimental overhead and impeding progress. To address this challenge, we introduce 2MC-OBPPP, a polynomial-time classical estimator that, for parameterized quantum circuits, jointly estimates trainability, expressibility, and robustness to noise. For example, our approach visually demonstrates that moderate amplitude damping alleviates barren plateaus (improving trainability) while decreasing expressibility. Moreover, the method produces a spatiotemporal ``noise-hotspot" map that pinpoints the most noise-sensitive qubits/gates, enabling targeted noise suppression. In a representative circuit, interventions on fewer than $2\%$ qubits reduce the error up to $90\%$. Together, before execution, our approach provides an efficient diagnostic benchmark for circuit/scheme design, and in deployment, guides for targeted interventions that substantially reduce the cost of error suppression.