  Quantum computational chemistry has emerged as an important application of
quantum computing. Hybrid quantum-classical computing methods, such as
variational quantum eigensolvers (VQE), have been designed as promising
solutions to quantum chemistry problems, yet challenges due to theoretical
complexity and experimental imperfections hinder progress in achieving reliable
and accurate results. Experimental works for solving electronic structures are
consequently still restricted to nonscalable (hardware efficient) or
classically simulable (Hartree-Fock) ansatz, or limited to a few qubits with
large errors. The experimental realisation of scalable and high-precision
quantum chemistry simulation remains elusive. Here, we address the critical
challenges {associated with} solving molecular electronic structures using
noisy quantum processors. Our protocol presents significant improvements in the
circuit depth and running time, key metrics for chemistry simulation. Through
systematic hardware enhancements and the integration of error mitigation
techniques, we push forward the limit of experimental quantum computational
chemistry and successfully scale up the implementation of VQE with an optimised
unitary coupled-cluster ansatz to 12 qubits. We produce high-precision results
of the ground-state energy for molecules with error suppression by around two
orders of magnitude. We achieve chemical accuracy for H$_2$ at all bond
distances and LiH at small bond distances in the experiment, even beyond the
two recent concurrent works. Our work demonstrates a feasible path towards a
scalable solution to electronic structure calculation, validating the key
technological features and identifying future challenges for this goal.
