This paper focuses on the computation of Fourier moments within the context of a nuclear effective field theory on superconducting quantum hardware. The study integrates echo verification and noise renormalization into Hadamard tests using control reversal gates. These techniques, combined with purification and error suppression methods, effectively address quantum hardware decoherence. The analysis, conducted using noise models, reveals a significant reduction in noise strength by two orders of magnitude. Moreover, quantum circuits involving up to 266 CNOT gates over five qubits demonstrate high accuracy under these methodologies when run on IBM superconducting quantum devices. The paper begins by introducing the concept of Fourier moments and their application in computing response functions, which are crucial for understanding the linear response of many-body systems. It then details the methods used to compute these moments, including the use of integral transforms and the Fourier basis. The response function is defined and its computation is explained, highlighting the challenges posed by the excitation operators. Error mitigation techniques, such as echo verification (EV) and operator decoherence renormalization (ODR), are tailored for computing expectation values via Hadamard tests. Echo verification involves verifying if an error occurred during circuit execution, discarding erroneous runs, and purifying the state before computing expectation values. Operator decoherence renormalization estimates the parameters of the noise model and uses them to correct the expectation values. Control reversal gates (CRG) are introduced to reduce the overhead of control operations, enabling toggling between forward and backward time evolution. This technique is particularly valuable for real devices, as it reduces the number of Trotter steps required for accurate results. The physical system considered is a nuclear lattice model inspired by a pionless lattice effective field theory, specifically a simplified model for a triton. The Hamiltonian of this model is equivalent to a 2D Fermi Hubbard model and is encoded into qubits using first quantization. The excitation operators and variational ground state preparation methods are also discussed. Finally, the results section presents the computation of the first few moments using the noise mitigation strategy. The performance of the techniques is evaluated on a superconducting quantum device, showing that purified EV and ODR significantly reduce noise and improve the accuracy of the results. The Trotter approximation remains accurate for longer times when using CRG, providing a significant advantage over direct implementations.This paper focuses on the computation of Fourier moments within the context of a nuclear effective field theory on superconducting quantum hardware. The study integrates echo verification and noise renormalization into Hadamard tests using control reversal gates. These techniques, combined with purification and error suppression methods, effectively address quantum hardware decoherence. The analysis, conducted using noise models, reveals a significant reduction in noise strength by two orders of magnitude. Moreover, quantum circuits involving up to 266 CNOT gates over five qubits demonstrate high accuracy under these methodologies when run on IBM superconducting quantum devices. The paper begins by introducing the concept of Fourier moments and their application in computing response functions, which are crucial for understanding the linear response of many-body systems. It then details the methods used to compute these moments, including the use of integral transforms and the Fourier basis. The response function is defined and its computation is explained, highlighting the challenges posed by the excitation operators. Error mitigation techniques, such as echo verification (EV) and operator decoherence renormalization (ODR), are tailored for computing expectation values via Hadamard tests. Echo verification involves verifying if an error occurred during circuit execution, discarding erroneous runs, and purifying the state before computing expectation values. Operator decoherence renormalization estimates the parameters of the noise model and uses them to correct the expectation values. Control reversal gates (CRG) are introduced to reduce the overhead of control operations, enabling toggling between forward and backward time evolution. This technique is particularly valuable for real devices, as it reduces the number of Trotter steps required for accurate results. The physical system considered is a nuclear lattice model inspired by a pionless lattice effective field theory, specifically a simplified model for a triton. The Hamiltonian of this model is equivalent to a 2D Fermi Hubbard model and is encoded into qubits using first quantization. The excitation operators and variational ground state preparation methods are also discussed. Finally, the results section presents the computation of the first few moments using the noise mitigation strategy. The performance of the techniques is evaluated on a superconducting quantum device, showing that purified EV and ODR significantly reduce noise and improve the accuracy of the results. The Trotter approximation remains accurate for longer times when using CRG, providing a significant advantage over direct implementations.