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

• URL: http://arxiv.org/abs/2603.08025v1
• Date: Mon, 09 Mar 2026 07:01:16 GMT
• Title: Classically Driven Hybrid Quantum Algorithms with Sequential Givens Rotations for Reduced Measurement Cost
• Abstract summary: Quantum algorithms for electronic-structure simulations are actively being developed, yet many hybrid quantum-classical approaches are bottlenecked by measurement overhead associated with large molecular Hamiltonians.<n>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.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 Schrödinger-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.

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