Unitary Block-Correlated Coupled Cluster Ansatz Based on the Generalized Valence Bond Wave Function for Quantum...

Strongly correlated (SC) systems present significant challenges for classical quantum chemistry methods. Quantum computing, particularly the variational quantum eigensolver (VQE), offers a promising framework to address these challenges by inherently supporting exponentially large configuration spaces. However, its application to SC systems remains limited due to the single-reference nature of the widely used ansatzes such as unitary coupled cluster (UCC). To address this challenge, we propose the generalized valence bond-based unitary block correlated coupled cluster (GVB-UBCCC) method. This novel ansatz incorporates the multiconfigurational nature of generalized valence bond (GVB) and the accuracy of block correlated coupled cluster (BCCC) methods, making it well-suited for SC systems. We have implemented the GVB-UBCCC method with up to two-block correlation (GVB-UBCCC2) and applied it to investigate ground-state energies for several SC systems, including H₄, the water dimer, N₂H₂, and S₆, at most described by 24 qubits. Our approach demonstrates that for these systems, GVB-UBCCC2 can achieve more accurate ground-state energies than UCCSD in most cases while requiring only O(N²) quantum gates and parameters, as opposed to the O(N⁴) scaling of UCCSD. The results highlight the effectiveness and potential advantages of GVB-UBCCC in SC systems.