  Quantum computers have the potential to perform accurate and efficient
electronic structure calculations, enabling the simulation of properties of
materials. However, today's noisy, intermediate-scale quantum (NISQ) devices
have a limited number of qubits and gate operations due to the presence of
errors. Here, we propose a systematically improvable end-to-end pipeline to
alleviate these limitations. Our proposed resource-efficient pipeline combines
problem decomposition techniques for compact molecular representations, circuit
optimization methods for compilation, solving the eigenvalue problem on
advanced quantum hardware, and error-mitigation techniques in post-processing
the results. Using the density matrix embedding theory for compact
representation, and an ion-trap quantum computer, we simulate a ring of 10
hydrogen atoms taking into account all electrons equally and explicitly in the
electronic structure calculation. In our experiment, we simulated the largest
molecular system on a quantum computer within chemical accuracy with respect to
total molecular energy calculated by the full CI method. Our methods reduce the
number of qubits required for high-accuracy quantum simulations by an order of
magnitude in the present work, enabling the simulation of larger, more
industrially relevant molecules using NISQ devices. They are further
systematically improvable as devices' computational capacity continues to grow.
