Classically driven hybrid quantum algorithms with sequential Givens rotations for reduced measurement cost.

Area of Science:

• Quantum Computing
• Computational Chemistry
• Electronic Structure Theory

Background:

• Hybrid quantum-classical methods for electronic structure simulations face significant measurement overhead.
• This bottleneck hinders the application of quantum algorithms to large molecular systems.
• Existing Schrödinger-picture methods require variational wave function optimization.

Purpose of the Study:

• To introduce a novel diagonalization-driven framework to reduce measurement overhead in quantum electronic structure simulations.
• To transform the electronic Hamiltonian towards a diagonal form using sequential Givens rotations.
• To enable more efficient quantum computations by minimizing the quantum workload.

Main Methods:

• Employs a Heisenberg-picture approach, iteratively transforming the Hamiltonian.
• Determines rotation angles classically from low-dimensional effective blocks.
• Utilizes approximate Baker-Campbell-Hausdorff updates and cumulant-based approximations to control Hamiltonian growth, alongside stochastic selection.
• Introduces an angle-merging procedure to reduce quantum circuit depth.

Main Results:

• The framework successfully reduces the quantum workload to a fixed set of matrix-element measurements per iteration.
• Benchmarking on N2 and hydrogen systems demonstrates convergence behavior and residual-structure diagnostics.
• Analyzes measurement-accuracy trade-offs, circuit costs, and robustness under finite sampling.

Conclusions:

• The diagonalization-driven framework offers a promising solution to mitigate measurement overhead in quantum electronic structure simulations.
• The Heisenberg-picture approach and associated techniques provide a more efficient pathway for quantum computational chemistry.
• The method shows potential for accurate and robust simulations of molecular systems.