Reducing the Cost of Unitary Coupled Cluster via Active Space Partitioning

Unitary Coupled Cluster (UCC) theory is a promising variational method for electronic structure calculations, particularly for systems that exhibit strong electronic correlation and for implementation on quantum computers. However, its practical application is limited to small chemical systems with small basis sets due to its steep computational scaling, which results from its nonterminating Baker-Campbell-Hausdorff expansion. Here, we introduce an active space UCCSD(4)/MP2 approach that leverages a fourth-order many-body perturbation theory truncation of UCCSD within a selected active space while treating external excitations at the MP2 level. We explore two variants: a composite method that sums separate internal and external contributions and an interacting method that couples the amplitudes for potentially greater accuracy. We test our approach on a range of systems, including molecules from the GW100 data set in their equilibrium geometries, a moderately correlated metaphosphate hydrolysis reaction, and the strongly correlated torsion of ethylene. Our results suggest that the interacting method with canonical orbitals is robust and stable for both weakly and moderately correlated systems and accurately reproduces the full UCCSD(4) potential energy curves, including only 15-25% of the virtual orbitals in its active space. In comparison, the composite formulation exhibits greater sensitivity to the choice of orbital basis and active space size, leading to less systematic behavior across the benchmark set. For ethylene torsion, a system dominated by strong static correlation, both the composite and interacting formulations employing canonical orbitals closely track the full UCCSD(4) reference while preserving the qualitative behavior of the parent method, including the breakdown in strongly multireference regimes. This active space framework offers a computationally tractable approach for modeling correlated molecules and reactions on classical computers and provides a viable path for scaling UCC calculations for resource-constrained quantum hardware.