Variational Quantum Computation of Excited States

TL;DR

This paper introduces a quantum algorithm that efficiently computes excited state energies using overlap estimation, requiring minimal additional resources and being suitable for near-term quantum hardware.

Contribution

It presents a novel method for calculating excited states by deflating eigenstates with overlap estimation, avoiding high-depth controlled-unitaries.

Findings

Requires same number of qubits as VQE

At most twice the circuit depth of VQE

Compatible with error mitigation and robust to control errors

Abstract

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.