End-to-End Fidelity Analysis of Quantum Circuit Optimization: From Gate-Level Transformations to Pulse-Level Control

Abstract

We present an analysis of quantum circuit fidelity across the full compilation stack, from high-level gate optimization through pulse-level control. We connect a C++ circuit optimizer to a per-gate Lindblad master-equation fidelity model whose decoherence channels are cross-validated against qiskit-dynamics and whose absolute predictions are benchmarked against execution on real hardware. Across a campaign of 4,452 experiment runs over 371 benchmark circuits, gate cancellation provides the dominant improvement ($d = 1.66$, 72% of circuits improved), while circuit size and pulse duration are the strongest negative predictors of process fidelity (input gates $r = -0.78$; pulse duration $r = -0.73$, $R^2 = 0.53$). A formal ablation study shows that pass ordering has no significant effect on two-qubit gate reduction (Kruskal--Wallis $p = 0.302$). Comparing against Qiskit transpilation levels, we show that two-qubit gate count, not total gate count, is the hardware-relevant metric: our optimizer attains superior two-qubit reduction on structured circuits (87.8% on QFT, 100% on QAOA) whereas Qiskit's larger total-gate reduction is dominated by single-qubit ($u_3$) consolidation. Finally, executing eight circuits on the IQM Resonance Garnet processor (8/8 jobs completed, job identifiers released) reveals that the model is a consistent upper bound: it preserves the relative difficulty ordering of circuits but overestimates absolute fidelity by a mean of 0.49, quantifying the error budget (crosstalk, leakage, readout) outside a $T_1$/$T_2$/depolarizing model. We release the framework, data, and scripts as open source.