Enhancing the reachability of variational quantum algorithms via input-state design

TL;DR

This paper introduces a framework for improving variational quantum algorithms by designing input states that expand their expressive power, leading to higher accuracy in quantum simulations without increasing circuit complexity.

Contribution

The authors propose a novel input-state design method that enhances the expressivity of VQAs, supported by rigorous proofs and broad applicability across various ansatz families.

Findings

Achieved higher accuracy in ground-state preparation tasks.

Demonstrated effectiveness across multiple quantum models.

Preserved efficiency while increasing expressive capacity.

Abstract

Variational quantum algorithms (VQAs) face an inherent trade-off between expressivity and trainability: deeper circuits can represent richer states but suffer from noise accumulation and barren plateaus, while shallow circuits remain trainable and implementable but lack expressive power. Here, we propose a general framework to address this challenge by enhancing the VQA performance with a specially designed input state constructed using a linear combination technique. This approach systematically modified the set of states reachable by the original circuit, enhancing accuracy while preserving efficiency. We provide a rigorous proof that such framework increases the expressive capacity of any given VQA ansatz, and demonstrate its broad applicability across different ansatz families. As applications, we apply the method to ground-state preparation of the transverse-field Ising, cluster-Ising, and Fermi-Hubbard models, achieving consistently higher accuracy under the same gate budget compared with standard VQAs. These results highlight input-state design as a powerful complement to circuit design in realizing VQAs that are both expressive and trainable.