Subspace-Search for Excited State Quantum Imaginary Time Evolution

Calculating the ground state energies of quantum systems, such as molecules, is an area of expected computational advantage in the noisy intermediate-scale quantum era. Near term variational algorithms, such as the Variational Quantum Eigensolver (VQE), have been developed to determine the ground state energies of these systems. However, excited states have received relatively less attention. We propose a method to determine the excited states of quantum systems through adapting the Subspace-Search method from the Subspace-Search Variational Quantum Eigensolver (SSVQE) to Quantum Imaginary Time Evolution (QITE). As QITE is less susceptible to becoming trapped in local minima, SSQITE may be able to outperform SSVQE for certain systems and anstazes.