Classically Driven Hybrid Quantum Algorithms with Sequential Givens Rotations for Reduced Measurement Cost
Abstract
Quantum algorithms for electronic-structure simulations are actively being developed, yet many hybrid quantum-classical approaches are bottlenecked by the measurement overhead associated with large molecular Hamiltonians. Here we introduce a diagonalization-driven framework that progressively drives the electronic Hamiltonian toward a (block-)diagonal form in the Slater-determinant basis using sequential Givens rotations. In contrast to Schr\"odinger-picture methods that variationally optimize a wave function, our approach adopts a Heisenberg-picture viewpoint: the Hamiltonian is iteratively transformed, and rotation angles are determined classically from low-dimensional effective blocks, reducing the quantum workload to a small, fixed set of matrix-element measurements per iteration. Candidate generators are estimated via approximate Baker-Campbell-Hausdorff updates with truncation and cumulant-based approximations that control Hamiltonian growth, complemented by stochastic selection to avoid stagnation. We further introduce an angle-merging procedure that reduces circuit depth by consolidating repeated small-angle rotations. We benchmark the framework on N and strongly correlated hydrogen systems, assessing convergence behavior, residual-structure diagnostics, measurement-accuracy trade-offs, circuit costs, and robustness under finite sampling.
Cite
@article{arxiv.2603.08025,
title = {Classically Driven Hybrid Quantum Algorithms with Sequential Givens Rotations for Reduced Measurement Cost},
author = {Benjamin Mokhtar and Noboru Inoue and Takashi Tsuchimochi},
journal= {arXiv preprint arXiv:2603.08025},
year = {2026}
}