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Real-time scattering calculations on a Noisy Intermediate Scale Quantum (NISQ) quantum computer are disrupted by errors that accumulate throughout the circuits. To improve the accuracy of such physics simulations, one can supplement the application circuits with a recent error mitigation strategy known as Noisy Output eXtrapolation (NOX). We tested these error mitigation protocols on a Transverse Field Ising model and improved upon previous calculations of the phase shift. Our proof-of-concept 4-qubit application circuits were run on several IBM quantum computing hardware architectures. Metrics were introduced that show between 21\% and 74\% error reduction for circuit depths ranging from 14 to 37 hard cycles, confirming that the NOX technique applies to circuits with a broad range of failure rates. This observation on different cloud-accessible devices further confirms that NOX provides performance improvements even in the advent where circuits are executed in substantially time-separated batches. Finally, we provide a heuristic method to obtain systematic error bars on the mitigated results, compare them with empirical errors and discuss their effects on phase shift estimates.