Probabilistic Error Cancellation on Error-Detected Quantum Systems

Accurate estimation of quantum observables is crucial for diverse applications in quantum chemistry, optimization, and quantum machine learning, where small errors can diminish quantum advantages. We present a novel framework for combining probabilistic error cancellation (PEC) with quantum error detection (QED) using small CSS codes to improve the accuracy and resource overhead of quantum observable estimation. Our approach leverages the reduced error rates in post-selected QED channels to decrease the sampling overhead due to PEC implementation. We analyze this hybrid technique across various quantum circuits, including variational quantum algorithms such as QAOA and VQE circuits. Through Hamiltonian-level numerical simulations, we demonstrate that applying PEC to error-detected qubits yields significantly improved expectation value estimates compared to either technique alone with increased shot counts. Furthermore, our results show that this approach enables access to lower error regimes than previously achievable with comparable sampling resources. These findings establish a new frontier in the trade-off between sampling overhead and observable estimation accuracy, representing a significant advance in practical quantum error mitigation strategies.