A Fidelity-Aware Framework for Joint Circuit Knitting and Error Mitigation

Executing quantum circuits on current quantum Best Cut Identification devices is fundamentally limited by noise, decoherence, and hardware constraints. Circuit Knitting (CK) techniques enable the execution of larger circuits by decomposing them into smaller sub-circuits, at the cost of reconstruction overhead. At the same time, Quantum Error Mitigation (QEM) methods improve fidelity but introduce additional complexity. In this work, we propose a fidelity-aware framework that jointly optimizes circuit partitioning and error mitigation to maximize end-to-end execution fidelity. We introduce a unified model that captures the trade-off between sub-circuit operational fidelity, reconstruction penalties induced by cuts, and the impact of error mitigation. Based on this model, we formulate the cut placement problem as an optimization task and solve it to identify fidelity-optimal partitioning strategies accounting for error mitigation and under realistic hardware constraints. Notably, our framework integrates calibration-driven noise models and supports practical fidelity estimation using backend-specific parameters. We validate the proposed method on both noisy simulators (IBM Fake Backends) and real quantum hardware (IQM Lagrange), proving consistent improvements in execution fidelity with gains of up to 40% over standard circuit execution.