This paper presents a method for computing Fourier moments in the context of nuclear effective field theory on noisy intermediate-scale quantum (NISQ) devices. The study integrates echo verification (EV) and operator decoherence renormalization (ODR) into Hadamard tests with and without control reversal gates to mitigate quantum hardware decoherence. These techniques, combined with purification and error suppression methods, significantly reduce noise strength by two orders of magnitude. The analysis, conducted using noise models, shows that quantum circuits with up to 266 CNOT gates over five qubits achieve high accuracy on IBM superconducting quantum devices. The paper focuses on computing Fourier moments for the response function describing inelastic scattering between a Triton and a lepton on NISQ devices. The methods include error mitigation techniques such as EV and ODR, which are tailored to compute moments efficiently. The results demonstrate that purified EV and ODR strategies effectively reduce noise and improve the accuracy of quantum simulations. The study highlights the importance of Fourier moments in understanding physical properties and their utility in computing response functions and spectra. The experiments conducted on real IBM quantum devices show that error mitigation strategies are crucial for overcoming decoherence and extracting useful information from quantum simulations.This paper presents a method for computing Fourier moments in the context of nuclear effective field theory on noisy intermediate-scale quantum (NISQ) devices. The study integrates echo verification (EV) and operator decoherence renormalization (ODR) into Hadamard tests with and without control reversal gates to mitigate quantum hardware decoherence. These techniques, combined with purification and error suppression methods, significantly reduce noise strength by two orders of magnitude. The analysis, conducted using noise models, shows that quantum circuits with up to 266 CNOT gates over five qubits achieve high accuracy on IBM superconducting quantum devices. The paper focuses on computing Fourier moments for the response function describing inelastic scattering between a Triton and a lepton on NISQ devices. The methods include error mitigation techniques such as EV and ODR, which are tailored to compute moments efficiently. The results demonstrate that purified EV and ODR strategies effectively reduce noise and improve the accuracy of quantum simulations. The study highlights the importance of Fourier moments in understanding physical properties and their utility in computing response functions and spectra. The experiments conducted on real IBM quantum devices show that error mitigation strategies are crucial for overcoming decoherence and extracting useful information from quantum simulations.