A unified quantum computing quantum Monte Carlo framework through structured state preparation

TL;DR

This paper develops a versatile quantum Monte Carlo framework that enhances state preparation for various quantum computing tasks, improving accuracy and efficiency across multiple domains.

Contribution

It introduces task-adapted unitaries and extends QCQMC to excited states, optimization, and finite-temperature calculations, with demonstrated improvements in accuracy and circuit depth.

Findings

QMC diffusion step improves energy accuracy across domains.

VUMPO achieves near-exact energies with shallower circuits for weakly correlated systems.

Haar-random basis states enable finite-temperature estimates from pure states.

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.