A method for calculating excited state properties of a molecular system using a hybrid classical-quantum computing system includes determining, using a quantum processor and memory, a ground state wavefunction of a combination of quantum logic gates. In an embodiment, the method includes forming a set of excitation operators. In an embodiment, the method includes forming a set of commutators from the set of excitation operators and a Hamiltonian operator. In an embodiment, the method includes mapping the set of commutators onto a set of qubit states, the set of qubit states corresponding to a set of qubits of the quantum processor. In an embodiment, the method includes evaluating, using the quantum processor and memory, the set of commutators. In an embodiment, the method includes causing a quantum readout circuit to measure an excited state energy from the set of computed commutators.
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