Variational Quantum Computation of Excited States

By Oscar Higgott, Daochen Wang, Stephen Brierley. Quantum, 2018

500 citations recorded by the source corpus.

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 computers.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/eb656ed95f6db881f5650372170ea4ea7b04f7f5

Citations in the corpus

• Variational quantum algorithms (2020, unknown): “Then, H ′ = H + a|ψ̃G〉〈ψ̃G| is a Hamiltonian whose ground state is the first excited state of H [90].”
• Variational Quantum Linear Solver (2019, unknown): “[22] O.”