TY - JOUR T1 - Variational Quantum Computation of Excited States JF - Quantum Y1 - 2019 A1 - Oscar Higgott A1 - Daochen Wang A1 - Stephen Brierley AB -

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

VL - 3 UR - https://arxiv.org/abs/1805.08138 CP - 156 U5 - https://doi.org/10.22331/q-2019-07-01-156 ER -