  Quantum computers promise to revolutionise electronic simulations by
overcoming the exponential scaling of many-electron problems. While electronic
wave functions can be represented using a product of fermionic unitary
operators, shallow quantum circuits for exact states have not yet been
achieved. We construct universal wave functions from gate-efficient,
symmetry-preserving fermionic operators by introducing an algorithm that
globally optimises the wave function in the discrete ansatz design and the
continuous parameter spaces. Our approach maximises the accuracy that can be
obtained with near-term quantum circuits. Highly accurate numerical simulations
on strongly correlated molecules, including water and molecular nitrogen, and
the condensed-matter Hubbard model, demonstrate that our algorithm reliably
advances the state-of-the-art, defining a new paradigm for quantum simulations
featuring strong electron correlation.
