  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 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 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 paves the
way towards scalable quantum simulation of electronic structure for classically
challenging systems.
