Quantum Computation of Electronic Transitions using a Variational Quantum Eigensolver (1901.01234v2)

Abstract: We develop an extension of the variational quantum eigensolver (VQE) algorithm - multistate, contracted VQE (MC-VQE) - that allows for the efficient computation of the transition energies between the ground state and several low-lying excited states of a molecule, as well as the oscillator strengths associated with these transitions. We numerically simulate MC-VQE by computing the absorption spectrum of an ab initio exciton model of an 18-chromophore light-harvesting complex from purple photosynthetic bacteria.

Quantum Computation of Electronic Transitions using a Variational Quantum Eigensolver

The paper presents an advancement in the application of quantum computing to electronic structure problems through the multistate, contracted variational quantum eigensolver (MC-VQE). The authors propose MC-VQE as an extension to the variational quantum eigensolver (VQE), aiming to compute electronic transition energies and corresponding oscillator strengths within molecular systems, especially focusing on efficiently handling both ground and excited states.

Key Methodological Advances

MC-VQE innovatively extends VQE by addressing the 'state-specific' limitations in conventional VQE approaches. Traditional VQE methods typically optimize quantum circuits for single states individually, posing difficulties when multiple states are of interest or when computational efficiency is paramount. MC-VQE, however, treats several states concurrently, utilizing a more compact representation of the electronic problem and minimizing the classical subspace required for diagonalization.

The algorithm begins by solving a classical electronic problem to establish a set of reference states — typically using configuration interaction singles (CIS). It then optimizes a VQE entangler operator in a state-averaged manner, providing uniform accuracy across ground and excited states. The classical post-processing of quantum data involves diagonalizing the entangled contracted Hamiltonian, which results in the identification of quantum approximations for electronic transition energies.

Numerical Simulation and Results

The authors simulated the absorption spectrum using MC-VQE for an 18-chromophore complex derived from purple photosynthetic bacteria, realizing quantum efficiencies competitive with full configuration interaction (FCI) methods. The MC-VQE approach yielded precise numerical results, with deviations in calculated excitation energies and oscillator strengths being minimal — on the order of $\mu$eV and less than 1% respectively, thus matching the FCI benchmark closely.

Implications and Future Work

This paper illustrates the substantial potential for MC-VQE in scaling quantum electronic structure calculations to sizes impractical for classical approaches. The algorithm’s qubit count, circuit depth, and its reliance solely on 1- and 2-body Pauli measurements, position MC-VQE as a promising candidate for execution on near-term quantum hardware.

Future exploration should focus on implementing MC-VQE on physical quantum devices, assessing robustness against noise and gate errors, and potentially extending the method to more complex electronic structure problems. Additionally, examining MC-VQE's applicability to fermionic systems could expand its utility in broader quantum chemistry contexts.

Conclusion

The paper successfully demonstrates MC-VQE as an efficient quantum algorithm capable of addressing the computational intensity associated with multi-state electronic structure problems. It lays a foundation for further development and application of quantum solutions to traditionally challenging quantum chemical computation tasks.