  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.
