Optimizing Quantum Chemistry Simulations with a Hybrid Quantization Scheme

Complex quantum simulation workflows are often hindered by incompatible wavefunction representations adopted across different algorithmic frameworks. In particular, the mismatch between the first- and second-quantization formalisms prevents algorithms specialized for their respective quantizations from being integrated within a single circuit, thereby forcing practitioners to rely on suboptimal methods simply to maintain a consistent representation. To address this challenge, we propose a hybrid quantization scheme that employs a conversion circuit to switch between the two, requiring $\mathcal{O}(N\log N\log M)$ gates for a system of N electrons and M orbitals. This capability is critical for constructing complex quantum simulation workflows, allowing us to use the most efficient quantization for each individual step. We discuss its applications to bring polynomial improvements in the characterization of ground-state, ab-initio molecular dynamics, and characterization of spectroscopic properties. Quantitative estimations of such applications found up to three orders of magnitude fewer ground-state preparations when measuring the 2-reduced density matrix of molecular systems.