Constraint-Preserving Quantum Error Mitigation by Projection onto Admissible Residual Spaces

Quantum error mitigation (QEM) can improve target observables without ensuring that reconstructed experimental data satisfy known physical consistency conditions. We introduce a constraint-preserving QEM framework that represents reconstruction error in residual coordinates and projects the estimated residual onto the locally admissible tangent space defined by a differentiable physical constraint. The method removes the complete first-order constraint-violating component and suppresses generic constraint leakage to second order. We develop the construction analytically for CHSH correlations using no-signalling as the benchmark constraint and extend it to general smooth constraints. Deterministic and finite-shot simulations confirm the predicted suppression, including improved sampling behavior after projection. The method composes with calibrated readout mitigation and zero-noise extrapolation, while covariance-informed metrics provide optional task-dependent refinements. Real-device experiments on IBM quantum hardware validate the approach across eight disjoint physical qubit pairs and 24 pair-block realizations. After readout mitigation, projection reduces the no-signalling residual in all 24 realizations, with a mean paired reduction of 96.61% and negligible additional change in CHSH. A separate shot-count sweep improves all 15 hardware realizations, with a mean paired reduction of 97.38%, while revealing a hardware-limited residual floor at high shot count. Constraint-selectivity tests further show that different constraints remove different residual components. The method is entirely classical, requires no additional qubits, ancillas, or circuit depth, and provides a resource-efficient consistency layer for existing QEM pipelines.