Towards Efficient Spatial Variational 2-RDM via Measurement Constraints

Abstract

Reduced density matrices (RDMs) offer a more scalable alternative to full wavefunctions when performing chemical calculations. The variational twoelectron RDM (v2RDM) method exploits the efficiency of RDMs, employingsemidefinite programming (SDP) to enable polynomial scaling of ground state simulations. Recent work by Avdic & Mazziotti seeks to improve the performance of the v2RDM by incorporating classical shadow constraints, simultaneously reducing the number of measurements required for tomography. Drawing from this work, we introduce a spatial orbital variant of the v2RDM with measurement constraints (m-v2RDM). The proposed method achieves comparable accuracy for small to medium-sized molecules such as H2, H4, and HF, while substantially reducing memory and runtime costs. Its comparatively simple implementation also allows for the approximation of larger systems like N2, which are otherwise intractable on modest computational resources using standard v2RDM. As a pedagogical resource, the spatial variant more closely resembles the underlying theory, making it an accessible introduction to RDMs. The spatial m-v2RDM further highlights the complementary nature of measurement constraints and N-representability conditions, framing the RDM as a potential tool for noise mitigation in quantum information processing.