  Electronic ground states are of central importance in chemical simulations,
but have remained beyond the reach of efficient classical algorithms except in
cases of weak electron correlation or one-dimensional spatial geometry. We
introduce a hybrid quantum-classical eigenvalue solver that constructs a
wavefunction ansatz from a linear combination of matrix product states in
rotated orbital bases, enabling the characterization of strongly correlated
ground states with arbitrary spatial geometry. The energy is converged via a
gradient-free generalized sweep algorithm based on quantum subspace
diagonalization, with a potentially exponential speedup in the off-diagonal
matrix element contractions upon translation into compact quantum circuits of
linear depth in the number of qubits. Chemical accuracy is attained in
numerical experiments for both a stretched water molecule and an octahedral
arrangement of hydrogen atoms, achieving substantially better correlation
energies compared to a unitary coupled-cluster benchmark, with orders of
magnitude reductions in quantum resource estimates and a surprisingly high
tolerance to shot noise. This proof-of-concept study suggests a promising new
avenue for scaling up simulations of strongly correlated chemical systems on
near-term quantum hardware.
