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The complex-scaling method can be used to calculate molecular resonances within the Born-Oppenheimer approximation, assuming the electronic coordinates are dilated independently of the nuclear coordinates. With this method, one will calculate the complex energy of a non-Hermitian Hamiltonian, whose real part is associated with the resonance position and the imaginary part is the inverse of the lifetime. In this study, we propose techniques to simulate resonances on a quantum computer. First, we transformed the scaled molecular Hamiltonian to second-quantization and then used the Jordan-Wigner transformation to transform the scaled Hamiltonian to the qubit space. To obtain the complex eigenvalues, we introduce the Direct Measurement method, which is applied to obtain the resonances of a simple one-dimensional model potential that exhibits pre-dissociating resonances analogous to those found in diatomic molecules. Finally, we applied the method to simulate the resonances of the H\(_2^-\) molecule. Numerical results from the IBM Qiskit simulators and IBM quantum computers verify our techniques.