Search papers, labs, and topics across Lattice.
The paper introduces Geo-ADAPT-VQE, a novel geometry-aware adaptive VQE algorithm that leverages the natural gradient rule for operator selection, addressing limitations of existing adaptive methods that rely solely on first-order gradients. By growing the ansatz along directions aligned with the quantum-state geometry, Geo-ADAPT-VQE improves convergence and reduces susceptibility to local minima. Numerical simulations on five molecules demonstrate that Geo-ADAPT-VQE achieves faster, more stable convergence and produces significantly shorter ansatz, achieving up to a 100-fold reduction in energy error compared to existing methods.
Forget first-order gradients: Geo-ADAPT-VQE slashes energy error by up to 100x in quantum chemistry calculations by intelligently navigating the quantum state space geometry.
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.
