Beyond real: alternative unitary cluster Jastrow models for molecular electronic structure calculations on near-term quantum computers

Near-term quantum devices require wavefunction ansätze that are expressive while also of shallow circuit depth in order to both accurately and efficiently simulate molecular electronic structure. While the unitary coupled cluster ansatz (<i>e.g.</i>, UCCSD) has become a standard, the high gate count associated with the implementation of this limits its feasibility on noisy intermediate-scale quantum (NISQ) hardware. <i>k</i>-Fold unitary cluster Jastrow (uCJ) ansätze mitigate this challenge by providing O(<i>kN</i> ²) circuit scaling and favorable linear depth circuit implementation. Previous work has focused on the real orbitalrotation (Re-uCJ) variant of uCJ, which allows an exact (Trotter-free) implementation. Here we extend and generalize the <i>k</i>-fold uCJ framework by introducing two new variants, Im-uCJ and g-uCJ, which incorporate imaginary and fully complex orbital rotation operators, respectively. Similar to Re-uCJ, both of the new variants achieve quadratic gate-count scaling. Our results focus on the simplest <i>k</i> = 1 model, and show that the uCJ models frequently maintain energy errors within chemical accuracy (∼1 kcal mol^-1). Both g-uCJ and Im-uCJ are more expressive in terms of capturing electron correlation and are also more accurate than the earlier Re-uCJ ansatz. We further show that Im-uCJ and g-uCJ circuits can also be implemented exactly, without any Trotter decomposition. Numerical tests using <i>k</i> = 1 on H₂, H₃ ⁺, Be₂, C₂H₄, C₂H₆ and C₆H₆ in various basis sets confirm the practical feasibility of these shallow Jastrow-based ansätze for applications on near-term quantum hardware.