Classically Driven Hybrid Quantum Algorithms with Sequential Givens Rotations for Reduced Measurement Cost

TL;DR

This paper presents a novel hybrid quantum algorithm that reduces measurement costs in electronic-structure simulations by iteratively transforming the Hamiltonian into a block-diagonal form using classical Givens rotations, improving efficiency and robustness.

Contribution

It introduces a diagonalization-driven, Heisenberg-picture framework with sequential Givens rotations and an angle-merging technique to lower measurement and circuit costs in quantum chemistry simulations.

Findings

Effective reduction in measurement overhead demonstrated on N₂ and hydrogen systems.

The approach achieves competitive convergence with fewer quantum measurements.

Circuit depth is reduced through angle-merging, maintaining accuracy.

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$_2$ and strongly correlated hydrogen systems, assessing convergence behavior, residual-structure diagnostics, measurement-accuracy trade-offs, circuit costs, and robustness under finite sampling.