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

• URL: http://arxiv.org/abs/2603.10325v1
• Date: Wed, 11 Mar 2026 01:50:19 GMT
• Title: Geo-ADAPT-VQE: Quantum Information Metric-Aware Circuit Optimization for Quantum Chemistry
• Abstract summary: Geo-ADAPT-VQE is a geometry-aware adaptive VQE that selects operators from a pool using the natural gradient rule.<n>Geo-ADAPT-VQE achieves up to 100-fold reduction in energy error compared to existing methods.
• Score: 14.88416407274506
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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