Classically Prepared, Quantumly Evolved: Hybrid Algorithm for Molecular Spectra

TL;DR

This paper presents a hybrid classical-quantum algorithm for calculating molecular spectra that leverages short quantum evolutions and classical processing to efficiently reconstruct high-resolution spectra.

Contribution

It introduces a novel hybrid approach combining classical state preparation with quantum evolution to improve spectral calculations in many-body systems.

Findings

Accurately reproduces molecular spectra with shallow quantum circuits.

Accesses dynamical timescales beyond classical computational limits.

Demonstrates excellent agreement with exact diagonalization.

Abstract

We introduce a hybrid classical-quantum algorithm to compute dynamical correlation functions and excitation spectra in many-body quantum systems, with a focus on molecular systems. The method combines classical preparation of a perturbed ground state with short-time quantum evolution of product states sampled from it. The resulting quantum samples define an effective subspace of the Hilbert space, onto which the Hamiltonian is projected to enable efficient classical simulation of long-time dynamics. This subspace-based approach achieves high-resolution spectral reconstruction using shallow circuits and few samples. Benchmarks on molecular systems show excellent agreement with exact diagonalization and demonstrate access to dynamical timescales beyond the reach of purely classical methods, highlighting its suitability for near-term and early fault-tolerant quantum hardware.