01313nas a2200145 4500008004100000245005400041210005400095260001500149490000600164520090100170100001901071700001801090700002201108856003701130 2019 eng d00aVariational Quantum Computation of Excited States0 aVariational Quantum Computation of Excited States c06/28/20190 v33 a
The calculation of excited state energies of electronic structure Hamiltonians has many important applications, such as the calculation of optical spectra and reaction rates. While low-depth quantum algorithms, such as the variational quantum eigenvalue solver (VQE), have been used to determine ground state energies, methods for calculating excited states currently involve the implementation of high-depth controlled-unitaries or a large number of additional samples. Here we show how overlap estimation can be used to deflate eigenstates once they are found, enabling the calculation of excited state energies and their degeneracies. We propose an implementation that requires the same number of qubits as VQE and at most twice the circuit depth. Our method is robust to control errors, is compatible with error-mitigation strategies and can be implemented on near-term quantum compute
1 aHiggott, Oscar1 aWang, Daochen1 aBrierley, Stephen uhttps://arxiv.org/abs/1805.08138