Spin coupling is all you need: Encoding strong electron correlation in molecules on quantum computers

Abstract: The performance of quantum algorithms for eigenvalue problems, such as computing Hamiltonian spectra, depends strongly on the overlap of the initial wavefunction 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 wavefunction. We provide quantum circuits for deterministic preparation of a family of spin eigenfunctions with ${N \choose N/2}$ Slater determinants with depth $\mathcal{O}(N)$ and $\mathcal{O}(N^2)$ 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 wavefunctions as initial states for several 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 novel 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.