A unified quantum computing quantum Monte Carlo framework through structured state preparation
Abstract
We extend Quantum Computing Quantum Monte Carlo (QCQMC) beyond ground-state energy estimation by systematically constructing the quantum circuits used for state preparation. Replacing the original Variational Quantum Eigensolver (VQE) prescription with task-adapted unitaries, we show that QCQMC can address excited-state spectra via Variational Fast Forwarding and the Variational Unitary Matrix Product Operator (VUMPO), combinatorial optimization via a symmetry-preserving VQE ansatz, and finite-temperature observables via Haar-random unitaries. Benchmarks on molecular, condensed-matter, nuclear-structure, and graph-optimization problems demostrate that the QMC diffusion step consistently improves the energy accuracy of the underlying state-preparation method across all tested domains. For weakly correlated systems, VUMPO achieves near-exact energies with significantly shallower circuits by offloading optimization to a classical tensor-network pre-training step, while for strongly correlated systems, the QMC correction becomes essential. We further provide a proof-of-concept demonstration that Haar-random basis state preparation within QCQMC yields finite-temperature estimates from pure-state dynamics.
Cite
@article{arxiv.2603.25582,
title = {A unified quantum computing quantum Monte Carlo framework through structured state preparation},
author = {Giuseppe Buonaiuto and Antonio Marquez Romero and Brian Coyle and Annie E. Paine and Vicente P. Soloviev and Stefano Scali and Michal Krompiec},
journal= {arXiv preprint arXiv:2603.25582},
year = {2026}
}