Geo-ADAPT-VQE: Quantum Information Metric-Aware Circuit Optimization for Quantum Chemistry

TL;DR

Geo-ADAPT-VQE introduces a geometry-aware adaptive quantum algorithm that leverages the natural gradient to improve convergence speed, stability, and ansatz compactness in quantum chemistry simulations.

Contribution

It proposes a novel geometry-aware operator selection method using natural gradients, enhancing convergence and efficiency over existing adaptive VQE algorithms.

Findings

Achieves up to 100-fold reduction in energy error.

Demonstrates faster and more stable convergence on five molecules.

Produces significantly shorter ansatz circuits.

Abstract

Adaptive ansatz construction has emerged as a powerful technique for reducing circuit depth and improving optimization efficiency in variational quantum eigensolvers. However, existing adaptive methods, including ADAPT-VQE, rely solely on first-order gradients and therefore ignore the underlying geometry of the quantum state space, limiting both convergence behavior and operator-selection efficiency. We introduce Geo-ADAPT-VQE, a geometry-aware adaptive VQE algorithm that selects operators from a pool using the natural gradient rule. The geometric operator-selection rule enables the ansatz to grow along directions aligned with the underlying quantum-state geometry, thereby improving convergence and reducing the algorithm's susceptibility to shallow local minima and saddle-point regions. We further provide an asymptotic convergence result. We present numerical simulations involving five molecules, which demonstrate that Geo-ADAPT-VQE achieves faster and more stable convergence compared to existing methods, while producing significantly shorter ansatz. In particular, Geo-ADAPT achieves up to 100-fold reduction in energy error compared to existing methods.