  Quantum computers are promising for simulations of chemical and physical
systems, but the limited capabilities of today's quantum processors permit only
small, and often approximate, simulations. Here we present a method, classical
entanglement forging, that harnesses classical resources to capture quantum
correlations and double the size of the system that can be simulated on quantum
hardware. Shifting some of the computation to classical post-processing allows
us to represent ten spin-orbitals on five qubits of an IBM Quantum processor to
compute the ground state energy of the water molecule in the most accurate
simulation to date. We discuss conditions for applicability of classical
entanglement forging and present a roadmap for scaling to larger problems.
