Spin coupling is all you need: Encoding strong electron correlation in molecules on quantum computers
Daniel Marti-Dafcik, Hugh G. A. Burton, David P. Tew · Physical Review Research · 2025
The performance of quantum algorithms for eigenvalue problems, such as computing Hamiltonian spectra, depends strongly on the overlap of the initial wave function and the target eigenvector. In a basis of Slater determinants, the representation of energy eigenstates of systems with N strongly correlated electrons requires a number of determinants that scales exponentially with N . On classical processors, this restricts simulations to systems where N is small. Here, we show that quantum computers can efficiently simulate strongly correlated molecular systems by directly encoding the dominant entanglement structure in the form of spin-coupled initial states. This avoids resorting to expensive classical or quantum state preparation heuristics and instead exploits symmetries in the wave function. We provide quantum circuits for deterministic preparation of a family of spin eigenfunctions with ( N N / 2 ) Slater determinants with depth O ( N ) and O ( N 2 ) local gates. Their use as highly entangled initial states in quantum algorithms reduces the total runtime of quantum phase estimation and related fault-tolerant methods by orders of magnitude. Furthermore, we assess the application of spin-coupled wave functions as initial states for a range of heuristic quantum algorithms, namely, the variational quantum eigensolver, adiabatic state preparation, and different versions of quantum subspace diagonalization (QSD) including QSD based on real-time-evolved states. We also propose a QSD algorithm that exploits states obtained through adaptive quantum eigensolvers. For all algorithms, we demonstrate that using spin-coupled initial states drastically reduces the quantum resources required to simulate strongly correlated ground and excited states. Our work provides a crucial component for enabling scalable quantum simulation of classically challenging electronic systems.