Quantum computing has the potential to provide an exponential speedup compared to classical computers, but the practical implementation is still in its infancy. Two central questions are: (1) in which field the current noisy intermediate-scale quantum (NISQ) hardware can provide benefits compared to classical computers and (2) which methods and algorithms enable this advantage? In this talk I will answer these questions by presenting how to enable accurate and efficient quantum chemistry calculations on NISQ devices for relevant chemical and physical problems. This is achieved by the use of an exact explicitly correlated method in the form of the transcorrelated (TC) method. TC methods provide an efficient way of partially transferring the description of electronic correlations from the ground state wavefunction directly into the underlying Hamiltonian. This reduces the necessary quantum resources two-fold: (1) The TC Hamiltonian possesses a more compact ground state wavefunction, which facilitates electronic structure calculations and thus requires shallower quantum circuits. (2) For ab initio quantum chemistry problems the TC method reduces the required number of qubits, by allowing to obtain highly accurate results with small basis sets. I will present results on the Hubbard model and small chemical test systems, like the hydrogen molecule and lithium hydride, where results within chemical accuracy to the complete basis set limit and experimental results are within reach with only 6 to 12 qubits.