Qutrit-Native Spatial-Orbital Encoding for Resource-Efficient Quantum Chemistry Simulation

Abstract

Additional levels in a qudit can serve as more than extra computational capacity and can represent physically relevant correlations when the algorithmic design reflects the underlying physics of the problem. We demonstrate this principle for quantum chemistry simulation using a qutrit-native spatial-orbital encoding, where $|0\rangle$, $|1\rangle$, and $|2\rangle$ denote orbital occupation states. We establish a qutrit simulation framework that combines number-conserving pair-transfer and broken-pair generators with a projected-Hamiltonian energy estimator constructed from qutrit populations and coherences. Benchmarks for H$_2$, LiH, and H$_2$O show that the encoding reproduces the relevant potential-energy curves, while retaining a compact quantum resource structure. Direct comparison with the pair-only restriction confirms that the third level reduces errors by tens of mHa in LiH and by more than 100 mHa in H$_2$O. Despite a partial spin-coupling truncation in the compact H$_2$O encoding, the resulting energy curve deviates from FCI by only a few mHa over the tested range. Compared with a conventional qubit-based UCCSD approach, the qutrit scheme requires half as many quantum units and reduces the scaling of the parameterized ansatz generator count from $O(M^4)$ to $O(M^2)$, where $M$ is the number of spatial orbitals. This work elucidates how a physically motivated qutrit encoding can reduce quantum-resource requirements while retaining controlled electronic-structure accuracy, thereby providing a concrete starting point for broader qudit-native quantum algorithm design.